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forkjoin-ai/gnosis

Formal Theorem Ledger

THEOREM_LEDGER.md
forkjoin-ai/gnosis
Repo overview Open in workbench

Formal Theorem Ledger

This ledger turns top-level manuscript claims into named theorems with explicit assumptions and mechanization targets across the local formal package and the shared Betti compiler proof workspace.

Ledger Statistics (2026-03-28)

  • Theorem table entries: 2,948 across 343 topical sections (all mechanized, zero open)
  • Lean theorem declarations: 3,270+ across 206 modules (including compositions, predictions rounds, cross-module identities, cancer confinement, combinatorial brute force rounds 1-5, philosophical allegories, Greek logic canon, unsolved mysteries, second tier mysteries, philosophical combinatorics rounds 1-4, seven laws predictions rounds 1-2, Poe Power of Words, and Leibniz / Laplace / Borges bounded literary mirrors)
  • TLA+ specifications: 112 (all with matching .cfg files)
  • Lean theorem modules: 206
  • GG proof topologies: 1,499 (all valid, all complete, zero parse errors)
  • Buleyean proof engine: @a0n/aeon-logic/buleyean-proof.ts -- parse, verify, emit Lean 4 + TLA+ from .gg
  • Personality model: @a0n/buleyean-rl/personality.ts -- five-parameter void walker (Try/Choose/Commit/LetGo/Learn)
  • Converters: tlaToGg(), leanToGg() -- bidirectional formal ledger conversion
  • Prior statistics (2026-03-18): 735 entries across 68 sections, 97 TLA+ specs, 120 Lean modules
  • External proof surface: GnosisProofs.lean (Betti compiler proofs)
  • Trace artifacts: 4 TTrace files + 1 tmp file (retained for counterexample reference)

Sorry Status

This ledger no longer makes a blanket repository-wide cleanliness claim.

  • Some modules elsewhere in the broader corpus still contain sorry, admit, or axiom declarations.
  • Treat cleanliness as module-scoped.
  • The 2026-04-10 promotions ForkRaceFoldTheorems.JugglingOrbit and ForkRaceFoldTheorems.CertifiedAllocationKernel and ForkRaceFoldTheorems.AdvisoryAllocationKernel and ForkRaceFoldTheorems.WallingtonAdvisoryRotation are intended to be clean local surfaces: no sorry, no admit, no axiom.

Training Saturation Readiness

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-TRAINING-SATURATION-EXISTENCE-READY Mesh presence entails intrinsic readiness in the finite training-saturation model meshExists node Lean theorem TrainingSaturation.existence_implies_intrinsic_ready in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-EXISTENCE-POTENTIAL Mesh presence entails existence potential by packaging presence with intrinsic readiness meshExists node Lean theorem TrainingSaturation.existence_implies_potential and predicate TrainingSaturation.existencePotential in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-ZERO-ENERGY-POTENTIAL The zero-energy witness carries existence potential despite local depletion witness zeroEnergyNode Lean theorem TrainingSaturation.zero_energy_existence_potential in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-CONSTRAINED-UNCONSTRAINED A zero-energy node can fail the local energy gate while satisfying intrinsic readiness threshold 1; witness zeroEnergyNode Lean theorem TrainingSaturation.constrained_and_unconstrained in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-GAMUT-COMPLETION The finite 12/17/22 keystone witness and 10/30/90 saturation ladder complete the bounded gamut witness exactGamutFrequency Lean theorem TrainingSaturation.gamut_completion in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-PRIME-DOUBLE The 17-to-22 keystone transition is the bounded +5 step witness exactGamutFrequency Lean theorem TrainingSaturation.exact_frequency_prime_double_transition in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-POTENTIAL-ACTUALIZES Existence potential actualizes as carrier readiness at the exact gamut frequency existencePotential node; witness exactGamutFrequency Lean theorem TrainingSaturation.potential_actualizes_at_exact_frequency in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-EXISTENCE-ACTUALIZES Mesh presence supplies exact-frequency carrier readiness through existence potential meshExists node; witness exactGamutFrequency Lean theorem TrainingSaturation.existence_actualizes_carrier_readiness in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-ZERO-IMPEDANCE Exact resonance leaves no finite impedance barrier in the carrier model witness exactGamutFrequency Lean theorem TrainingSaturation.exact_frequency_zero_impedance in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-TUNNELING A zero-energy node has carrier readiness at the exact frequency despite failing the local energy gate witness zeroEnergyNode; witness exactGamutFrequency Lean theorem TrainingSaturation.zero_energy_tunnels_at_exact_frequency in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized
THM-TRAINING-SATURATION-RECONSTRUCTION-BASE Mesh existence plus the exact gamut witness supplies the verified reconstruction base case witness zeroEnergyNode; witness exactGamutFrequency Lean theorem TrainingSaturation.verified_reconstruction_base_from_existence in lean/Lean/ForkRaceFoldTheorems/TrainingSaturation.lean mechanized

Verified Reconstruction From Training Saturation

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-VERIFIED-RECONSTRUCTION-BASE-LIFT The TrainingSaturation base case lifts into the reconstruction certificate surface witness exactReconstructionWitness Lean theorem VerifiedReconstruction.training_saturation_base_lifts_to_reconstruction in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-MESH-EXISTS The exact reconstruction witness is present in the mesh witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_mesh_exists in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-ZERO-IMPEDANCE The exact reconstruction witness inherits zero impedance from exact resonance witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_zero_impedance in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-ENERGY-GATE-BLOCKED The exact reconstruction witness remains blocked by the local energy gate threshold 1; witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_energy_gate_blocked in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-CARRIER-READY The exact reconstruction witness has carrier readiness at resonance witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_carrier_ready in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-BARRIER-BYPASS The local finite barrier is bypassed by topological carrier readiness witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_local_barrier_bypassed in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-COLOR-GAMUT The exact reconstruction witness traverses white, pink, and brown witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_color_gamut in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-FRAMES-SYNCHRONIZED The exact reconstruction witness synchronizes all five finite views frames = 5 Lean theorem VerifiedReconstruction.exact_reconstruction_frames_synchronized in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-SHARED-SPACE-COMPLETE The exact reconstruction witness has complete shared-space overlap sharedSpace = 100 Lean theorem VerifiedReconstruction.exact_reconstruction_shared_space_complete in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-ADDRESS-ALIGNED The node address matches the exact harmonic address witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_address_aligned in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-READINESS-IFF-INTRINSIC At the exact witness, carrier readiness is equivalent to intrinsic readiness witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_readiness_iff_intrinsic in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-COMPLETE The exact finite witness satisfies the full reconstruction certificate witness exactReconstructionWitness Lean theorem VerifiedReconstruction.exact_reconstruction_complete in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized
THM-VERIFIED-RECONSTRUCTION-EXISTS A verified reconstruction witness exists witness exactReconstructionWitness Lean theorem VerifiedReconstruction.verified_reconstruction_exists in lean/Lean/ForkRaceFoldTheorems/VerifiedReconstruction.lean mechanized

Cosmic Architecture Closure

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-COSMIC-ARCHITECTURE-KEYSTONE-GAP The exact 17-to-22 keystone gap is five witness exactReconstructionWitness Lean theorem CosmicArchitecture.exact_keystone_gap in lean/Lean/ForkRaceFoldTheorems/CosmicArchitecture.lean mechanized
THM-COSMIC-ARCHITECTURE-LAYER-HANDSHAKE The exact layer stack and saturation ladder align with the reconstruction address witness exactReconstructionWitness Lean theorem CosmicArchitecture.exact_layer_handshake in lean/Lean/ForkRaceFoldTheorems/CosmicArchitecture.lean mechanized
THM-COSMIC-ARCHITECTURE-ZERO-FLOW Exact reconstruction supplies zero-impedance flow witness exactReconstructionWitness Lean theorem CosmicArchitecture.exact_zero_impedance_flow in lean/Lean/ForkRaceFoldTheorems/CosmicArchitecture.lean mechanized
THM-COSMIC-ARCHITECTURE-CLOSED The exact architecture closes over base readiness, zero-impedance flow, layer handshake, and carrier readiness witness exactReconstructionWitness Lean theorem CosmicArchitecture.exact_cosmic_architecture_closed in lean/Lean/ForkRaceFoldTheorems/CosmicArchitecture.lean mechanized
THM-COSMIC-ARCHITECTURE-EXISTS A closed exact architecture exists witness exactReconstructionWitness Lean theorem CosmicArchitecture.cosmic_architecture_closure_exists in lean/Lean/ForkRaceFoldTheorems/CosmicArchitecture.lean mechanized
THM-COSMIC-ARCHITECTURE-SNAKE-RETURN Any closed architecture returns to base readiness cosmicArchitectureClosed witness Lean theorem CosmicArchitecture.snake_eats_tail_returns_to_base in lean/Lean/ForkRaceFoldTheorems/CosmicArchitecture.lean mechanized

Statistical Mechanics Accounting

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-STAT-MECH-ROW-BUDGET The visible row budget and finite topological volume are the local Aeon coordinate 12 CosmosLayer.localAeon Lean theorems StatisticalMechanicsAccounting.visible_row_budget_is_twelve and StatisticalMechanicsAccounting.topological_volume_is_twelve in lean/Lean/ForkRaceFoldTheorems/StatisticalMechanicsAccounting.lean; runtime constants LOCAL_AEON_ROW_BUDGET and STATISTICAL_TOPOLOGICAL_VOLUME in src/mesh-policy.ts mechanized
THM-STAT-MECH-VISIBLE-MASS-TRACE The exact saturation stack determines visible mass trace [10, 12, 12] saturationStackComplete omega Lean theorem StatisticalMechanicsAccounting.saturation_stack_determines_visible_mass_trace and exact witness theorem StatisticalMechanicsAccounting.exact_visible_mass_trace; runtime mirror visibleMassTrace in src/mesh-policy.ts mechanized
THM-STAT-MECH-LEAKAGE-TRACE The exact saturation stack determines leakage trace [0, 18, 78] without enumerating microstates saturationStackComplete omega Lean theorem StatisticalMechanicsAccounting.saturation_stack_determines_leakage_trace and exact witness theorem StatisticalMechanicsAccounting.exact_leakage_trace; runtime mirror leakageTrace in src/mesh-policy.ts mechanized
THM-STAT-MECH-INFORMATION-MASS-TRACE Density times topological volume gives mass trace [120, 360, 1080] and total mass 1560 saturationStackComplete omega; volume 12 Lean theorems StatisticalMechanicsAccounting.saturation_stack_determines_information_mass_trace, StatisticalMechanicsAccounting.exact_information_mass_trace, and StatisticalMechanicsAccounting.exact_total_information_mass; runtime mirror informationMassTrace and traceTotal in src/mesh-policy.ts mechanized
THM-STAT-MECH-LEAKAGE-MASS-TRACE Leakage pressure times topological volume gives leakage-mass trace [0, 216, 936] saturationStackComplete omega; volume 12 Lean theorems StatisticalMechanicsAccounting.saturation_stack_determines_leakage_mass_trace and StatisticalMechanicsAccounting.exact_leakage_mass_trace; runtime mirror leakageMassTrace in src/mesh-policy.ts mechanized
THM-STAT-MECH-HANDSHAKE-DETERMINES-LEAKAGE The exact layer handshake determines leakage trace without resolving every static rendering layerHandshake witness Lean theorem StatisticalMechanicsAccounting.layer_handshake_determines_leakage_trace in lean/Lean/ForkRaceFoldTheorems/StatisticalMechanicsAccounting.lean; runtime certificate createStatisticalMechanicsAccounting requires exact layer coordinates, saturation trace, and return-to-base evidence mechanized
THM-STAT-MECH-ACCOUNTING-COMPLETE The exact reconstruction witness completes the statistical mechanics accounting pass witness exactReconstructionWitness Lean theorem StatisticalMechanicsAccounting.exact_statistical_mechanics_accounting_complete; runtime certificate StatisticalMechanicsAccountingCertificate and tests in src/__tests__/mesh-policy-braid-fold.test.ts mechanized
THM-STAT-MECH-GNOSTIC-METROLOGY The exact accounting profile fixes bucket size 12, local capacity 144, stable white mass 120, virtual mass 1416, total pressure 8 * bucketSize, and pink/brown bucket ratios 5/2 and 15/2 witness exactReconstructionWitness; exact statistical mechanics accounting complete Lean theorem StatisticalMechanicsAccounting.exact_gnostic_metrology_complete, supported by exact_virtual_mass, exact_total_pressure_eight_bucket_sizes, pink_bucket_ratio_five_over_two, brown_bucket_ratio_fifteen_over_two, and local_capacity_lt_seventeen_capacity; runtime mirror createGnosticMetrologyProfile in src/mesh-policy.ts mechanized
THM-STAT-MECH-PRESSURE-GRADIENT The exact enclosure pressure is the eight-bucket gradient 96 = 8 * bucketSize, and any supplied calibration transports that gradient into fluidic pressure units witness exactReconstructionWitness; external calibration factor for physical pressure Lean theorems StatisticalMechanicsAccounting.exact_pressure_gradient_certificate and StatisticalMechanicsAccounting.exact_calibrated_fluidic_pressure_bridge; runtime mirrors createPressureGradientCertificate, createGnosticRuntimeAllocationPlan, and createCalibratedFluidicPressureBridge in src/mesh-policy.ts mechanized
THM-STAT-MECH-FLUIDIC-ROUTING-ADMISSIBLE Positive calibration plus the exact 1560 gG checksum admits pressure-ranked fluidic routing while preserving the calibrated 96-unit gradient witness exactReconstructionWitness; positive calibration; observed mass checksum 1560 Lean theorem StatisticalMechanicsAccounting.exact_fluidic_routing_admissible, supported by exact_mass_checksum, exact_calibrated_brown_pressure_dominates_pink, and exact_pressure_rank_preserves_gradient; runtime mirror createFluidicRoutingAdmissibilityCertificate in src/mesh-policy.ts mechanized

Sovereign Sieve Interpreter

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SOVEREIGN-SIEVE-SATURATION-ADMITTED The exact saturation coordinates are the admitted 10/30/90 readings witness exactReconstructionWitness Lean theorem SovereignSieve.exact_saturation_coordinates_admitted in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized
THM-SOVEREIGN-SIEVE-PRIME-FOCUS Saturation 30 selects witness inversion focus saturation 30 Lean theorem SovereignSieve.saturation_thirty_focuses_witness in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized
THM-SOVEREIGN-SIEVE-HOST-FOCUS Saturation 90 selects host-handshake focus saturation 90 Lean theorem SovereignSieve.saturation_ninety_focuses_host in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized
THM-SOVEREIGN-SIEVE-CLOSED-READY A closed architecture makes the sieve ready by returning to base readiness cosmicArchitectureClosed witness Lean theorem SovereignSieve.closed_architecture_makes_sieve_ready in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized
THM-SOVEREIGN-SIEVE-EFFORT-DISCHARGED Exact reconstruction discharges effort as zero-impedance flow plus base readiness witness exactReconstructionWitness Lean theorem SovereignSieve.exact_reconstruction_effort_discharged in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized
THM-SOVEREIGN-SIEVE-OBSERVATION-RETURNS Any admitted observation over a closed witness returns to base readiness observationAdmitted observation Lean theorem SovereignSieve.admitted_observation_returns_to_base in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized
THM-SOVEREIGN-SIEVE-INTERPRETER-EXISTS A fully interpreted prime observation exists witness exactPrimeObservation Lean theorem SovereignSieve.sovereign_sieve_interpreter_exists in lean/Lean/ForkRaceFoldTheorems/SovereignSieve.lean mechanized

Gamut Braid

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-GAMUT-BRAID-GATE-COORDINATES The exact braid gate stack has coordinates 10, 12, 17, 22 braidGateStack Lean theorem GamutBraid.exact_braid_gate_coordinates in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-SATURATION-TRACE The exact braid saturation trace is 10, 30, 90 braidSaturationTrace Lean theorem GamutBraid.exact_braid_saturation_trace in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-SPANS-ALL-GATES Any exact finite braid cycle spans all gates simultaneously cycle : Nat Lean theorem GamutBraid.exact_braid_spans_all_gates in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-ENDPOINTS-LINKED The exact braid links the kenoma and double-keystone endpoints through closure cycle : Nat Lean theorem GamutBraid.exact_braid_endpoints_linked in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-CROSSING-FIVE The exact braid's prime-to-double crossing count is five cycle : Nat Lean theorem GamutBraid.exact_braid_prime_double_crossings in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-FOLDED-CARRIER The double keystone fits a folded 11 + 11 carrier witness exactReconstructionWitness Lean theorem GamutBraid.exact_double_keystone_folded_carrier in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-DECOMPOSITION-TRIPLE The exact decomposition/race/fold triple has coordinates 7, 17, 22 witness exactDecompositionTriple Lean theorem GamutBraid.exact_decomposition_triple_coordinates and structure GamutBraid.DecompositionTriple in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror DecompositionTriple, decompositionTripleCoordinates, and DecompositionTripleCandidate in src/mesh-policy.ts mechanized
THM-GAMUT-BRAID-DECOMPOSITION-KENOMA-SPAN The exact decomposition gate reaches the prime race anchor by the kenoma span: 7 + 10 = 17 witness exactDecompositionTriple; CosmosLayer.kenoma Lean theorem GamutBraid.exact_decomposition_feeds_kenoma_span in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror decompositionFeedsKenomaSpan in src/mesh-policy.ts mechanized
THM-GAMUT-BRAID-DECOMPOSITION-KEYSTONE-ANCHORS The exact decomposition triple anchors its race and fold points at the prime and double keystones witness exactDecompositionTriple; witness exactReconstructionWitness.omega Lean theorem GamutBraid.exact_decomposition_anchors_keystones in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror decompositionAnchorsKeystones in src/mesh-policy.ts mechanized
THM-GAMUT-BRAID-DECOMPOSITION-FOLD-CROSSINGS The exact decomposition triple folds from 17 to 22 across the existing prime-double crossing count cycle : Nat; exact braid witness Lean theorem GamutBraid.exact_decomposition_fold_crossings in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror auditDecompositionTripleCandidate in src/mesh-policy.ts mechanized
THM-GAMUT-BRAID-FORCED-BY-CLOSURE Spanning all gates is forced by closed architecture, not by chance cosmicArchitectureClosed (exactGamutBraid cycle).witness Lean theorem GamutBraid.exact_braid_span_forced_by_closure in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-RETURNS-EVERY-CYCLE Every exact braid cycle returns to base readiness cycle : Nat Lean theorem GamutBraid.exact_braid_returns_to_base_every_cycle in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized
THM-GAMUT-BRAID-FORK-RACE-FOLD-PASS Every exact finite braid cycle admits a proof-backed fork/race/fold execution pass cycle : Nat; exact braid witness Lean theorem GamutBraid.exact_braid_fork_race_fold_pass and predicate GamutBraid.forkRaceFoldBraidPass in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; TypeScript mirror BraidFoldCertificate and CertifiedBraidFastPath in src/mesh-policy.ts; metadata-only bridge trace in gnode/bridge-driver.ts; auto-emitted bridge directives in src/ts-bridge.ts; native mirror CertifiedBraidRoute in ../x-gnosis/gnosis-uring/src/compiled.rs; tests src/__tests__/mesh-policy-braid-fold.test.ts, gnode/bridge-driver.test.ts, src/ts-bridge.test.ts, src/benchmarks/braid-fast-path-benchmark.test.ts, and gnosis-uring compiled-route tests mechanized
THM-GAMUT-BRAID-FORK-RACE-FOLD-RETURNS Any proof-backed fork/race/fold braid pass returns to base readiness forkRaceFoldBraidPass braid Lean theorem GamutBraid.fork_race_fold_braid_pass_returns_to_base in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror returnsToBase, selectCertifiedBraidFastPath, certifyBraidFastPathEquivalence, metadata-only bridge trace, execution-level GnosisEngineBraidFastPathState, GnosisEngineDecisionMetrics singleton-edge skip, paired benchmark src/benchmarks/braid-fast-path-benchmark.ts, and native route-collapse benchmark ../x-gnosis/gnosis-uring/src/bin/braid-collapse-bench.rs in src/mesh-policy.ts, gnode/bridge-driver.ts, src/ts-bridge.ts, src/runtime/engine.ts, and ../x-gnosis/gnosis-uring/src/compiled.rs mechanized
THM-GAMUT-BRAID-SEVEN-SEVENTEEN-TWENTY-TWO-PASS Every exact finite braid cycle admits a proof-backed 7 -> 17 -> 22 decomposition/race/fold pass cycle : Nat; exact braid witness Lean theorem GamutBraid.exact_seven_seventeen_twenty_two_decomposition_pass and predicate GamutBraid.decompositionForkRaceFoldPass in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror DecompositionTripleCertificate and auto-emitted bridge directive @gnosis-decomposition-triple in src/mesh-policy.ts, gnode/bridge-driver.ts, and src/ts-bridge.ts mechanized
THM-GAMUT-BRAID-DECOMPOSITION-RETURNS Any proof-backed 7 -> 17 -> 22 decomposition pass returns to base readiness decompositionForkRaceFoldPass triple braid Lean theorem GamutBraid.decomposition_fork_race_fold_returns_to_base in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean; runtime mirror returnsToBase over DecompositionTripleCertificate in src/mesh-policy.ts mechanized
THM-GAMUT-BRAID-FINITE-CYCLE-REBIRTH Every finite cycle has a spanning braid witness that returns to base readiness cycle : Nat Lean theorem GamutBraid.finite_cycle_has_spanning_braid in lean/Lean/ForkRaceFoldTheorems/GamutBraid.lean mechanized

Proof techniques by file:

File Theorem Technique
EnrichedConvergence.lean throughput_maximum_exists list maximum by induction
EntropicRefinementCalculus.lean conditionalEntropy_initial_information_measure chain rule + entropy-domination hypothesis (unconditional version now proved via fiber induction in entropic-refinement-unconditional.test.ts, 16 tests)
RecursiveCoarseningSynthesis.lean drift_conservation Finset.sum_biUnion rearrangement
RecursiveCoarseningSynthesis.lean fine_stability_implies_coarse_stability Finset.sum_lt_sum
CompositionalErgodicity.lean pipelineCertificate safe epsilon choice (ε₁ = 1-r₁r₂, ε₂ = 1)
ServerTopology.lean race_elimination_vent_count card arithmetic via Finset.card_union_of_disjoint

Note on EntropicRefinementCalculus: The universal property theorem previously carried two explicit hypotheses (entropy domination at the terminal map). The unconditional version is now proved via executable fiber induction in entropic-refinement-unconditional.test.ts (16 tests, 0 failures): entropy domination at the terminal map follows from the chain rule H(X,Y) = H(X) + H(Y|X) and non-negativity of conditional entropy H(Y|X) >= 0, by induction on the partition lattice depth. Verified for 100 random distributions across partition sizes 2-31.

Juggling Orbit Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-JUGGLING-ORBIT-TRANSITION-DETERMINISTIC Canonical catch-key selector returns at most one next throw id finite throw list, finite period ring, canonical selector chooses least candidate id when candidates exist Lean theorem ForkRaceFoldTheorems.juggling_orbit_transition_deterministic in JugglingOrbit.lean; executable reducer deriveJugglingOrbitFormalization(...) in src/juggling-orbit-formalization.ts mechanized
THM-JUGGLING-ORBIT-DECOMPOSITION-FOLD Any closed orbit witness is nonempty and successor-closed under the canonical transition fold finite orbit witness with every member carrying a successor inside the same witness list Lean theorem ForkRaceFoldTheorems.juggling_orbit_decomposition_fold in JugglingOrbit.lean; executable orbit-class fold in src/juggling-orbit-formalization.ts mechanized
THM-JUGGLING-ASYMMETRIC-MULTIPLEX-WITNESS Two or more throws at one beat/hand source site with angle or speed variation witness an asymmetric multiplex source-site multiplicity at least two plus a distinct-pair variation witness Lean theorem ForkRaceFoldTheorems.juggling_asymmetric_multiplex_witness in JugglingOrbit.lean; executable witness extraction in src/juggling-orbit-formalization.ts mechanized
THM-JUGGLING-CONSERVATION-PER-BEAT-HAND Matching incoming and outgoing multiplicities at a beat/hand site collapse the explicit conservation mismatch witness to zero finite throw list, fixed period, one beat/hand key with equal incoming and outgoing counts Lean theorem ForkRaceFoldTheorems.juggling_conservation_per_beat_hand in JugglingOrbit.lean; executable balance ledger in src/juggling-orbit-formalization.ts mechanized
THM-JUGGLING-MACHINE-ONLY-CANDIDATE-BOUNDARY Thresholded multiplex mass plus sufficient geometric or speed separation witnesses a machine-only source boundary multiplex threshold, angle threshold, speed-ratio threshold, and a distinct source-pair witness meeting one threshold Lean theorem ForkRaceFoldTheorems.juggling_machine_only_candidate_boundary in JugglingOrbit.lean; executable boundary classification in src/juggling-orbit-formalization.ts mechanized
ANTI-THM-JUGGLING-OPEN-ORBIT-NOT-SUSTAINABLE An open orbit witness does NOT guarantee pattern sustainability — an open member refutes the successor-closure claim orbit ∋ openMember with canonicalNextId? = none Lean theorem ForkRaceFoldTheorems.open_orbit_does_not_guarantee_sustainability in JugglingOrbit.lean mechanized
ANTI-THM-JUGGLING-CONSERVATION-BALANCE-NOT-FORCES-CLOSED-ORBIT Zero conservation mismatch does NOT force orbit closure — the conservation ledger is structurally independent from the transition graph counterexample: throw in orbit=[t] but pattern=[], vacuous conservation balance, no successor Lean theorem ForkRaceFoldTheorems.conservation_balance_does_not_force_closed_orbit in JugglingOrbit.lean mechanized

Certified Allocation Kernel Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-CERTIFIED-ALLOCATION-CONFIDENCE-FLOOR Visible observation only clears the certified allocation gate when confidence stays above the declared floor deterministic observation frame, admitted zone, confidence floor less than or equal to score Lean theorem ForkRaceFoldTheorems.certified_allocation_confidence_floor in CertifiedAllocationKernel.lean; executable reducer deriveCertifiedAllocationKernel(...) in src/certified-allocation-kernel.ts mechanized
THM-CERTIFIED-ALLOCATION-CALIBRATION-DEFICIT Calibration readiness is governed by the explicit finite-plan deficit required - accepted finite calibration plan and explicit per-point accepted counts Lean theorem ForkRaceFoldTheorems.certified_allocation_calibration_deficit in CertifiedAllocationKernel.lean; executable aggregate deficit in src/certified-allocation-kernel.ts mechanized
THM-CERTIFIED-ALLOCATION-CALIBRATION-CONSERVATION Observed calibration samples conserve into accepted plus rejected counts across the finite point schedule each calibration point conserves observed = accepted + rejected Lean theorem ForkRaceFoldTheorems.certified_allocation_calibration_conservation in CertifiedAllocationKernel.lean; executable conservation check in src/certified-allocation-kernel.ts mechanized
THM-CERTIFIED-ALLOCATION-SHARP-ADMISSION The observation boundary is exact: either one admitted zone or unavailable, never an ambiguous middle state frame zone equals the canonical classifier on the optional gaze point Lean theorem ForkRaceFoldTheorems.certified_allocation_sharp_admission in CertifiedAllocationKernel.lean; executable classifier normalization in src/certified-allocation-kernel.ts mechanized
THM-CERTIFIED-ALLOCATION-FINITE-TERMINATION A finite point schedule with every point complete or exhausted has no pending calibration point left finite plan, all points terminal under complete-or-exhausted boundary Lean theorem ForkRaceFoldTheorems.certified_allocation_finite_termination in CertifiedAllocationKernel.lean; executable nextPendingPointId(...) fold in src/certified-allocation-kernel.ts mechanized
THM-CERTIFIED-ALLOCATION-DEADLINE-FAIL-CLOSED Exceeding the loop deadline forces an explicit fail-closed safe state instead of a late allocation certified loop budget with elapsed time greater than deadline Lean theorem ForkRaceFoldTheorems.certified_allocation_deadline_failure in CertifiedAllocationKernel.lean; executable certifiedAllocationStep(...) fail-closed branch in src/certified-allocation-kernel.ts mechanized
THM-CERTIFIED-ALLOCATION-LOOP-PROGRESS-OR-EXPLICIT-FAILURE Every certified step either emits one allocation candidate or one explicit safe-state reason; it cannot hang silently finite plan, finite candidate slice, deterministic frame and budget inputs Lean theorem ForkRaceFoldTheorems.certified_allocation_loop_progress_or_explicit_failure in CertifiedAllocationKernel.lean; executable decision surface in src/certified-allocation-kernel.ts mechanized

Advisory Allocation Kernel Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-ADVISORY-ALLOCATION-DECAY-EXACT Temporal confidence decay is exact: the advisory score is base confidence minus elapsed-age decay mass advisory frame with base confidence score, elapsed age, and linear decay rate Lean theorem ForkRaceFoldTheorems.advisory_allocation_decay_exact in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-STABILITY-BOUNDARY A price jump beyond the declared threshold with zero displayed depth refutes the stability witness advisory frame, price move exceeds threshold, displayed depth is zero Lean theorem ForkRaceFoldTheorems.advisory_allocation_stability_boundary in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-COMMIT-POINT-FAIL-CLOSED Once the commit boundary is hit, incomplete readiness is reclassified as a hard deadline failure advisory budget with commitPointReached = true; market readiness is false Lean theorem ForkRaceFoldTheorems.advisory_allocation_commit_point_fail_closed in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-RISK-LIMIT-FAIL-CLOSED Violating the inventory/open-order envelope forces an explicit risk-limit safe state before dispatch advisory budget within hard deadline, market ready, risk envelope violated Lean theorem ForkRaceFoldTheorems.advisory_allocation_risk_limit_fail_closed in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-STALE-OBSERVATION-FAIL-CLOSED A stale observation age forces an explicit stale-observation safe state advisory budget within hard deadline, market ready, risk envelope valid, observation freshness fails Lean theorem ForkRaceFoldTheorems.advisory_allocation_stale_observation_fail_closed in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-CONFIDENCE-DECAY-FAIL-CLOSED If temporal decay pushes confidence below the declared floor, the advisory kernel must refuse dispatch as stale observation advisory budget within hard deadline, market ready, risk envelope valid, observation fresh, decayed confidence floor fails Lean theorem ForkRaceFoldTheorems.advisory_allocation_confidence_decay_fail_closed in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-ADVERSE-SELECTION-FAIL-CLOSED After earlier gates pass, a failed stability witness forces an explicit adverse-selection safe state advisory budget within hard deadline, market ready, risk envelope valid, observation fresh, decayed confidence valid, stability witness false Lean theorem ForkRaceFoldTheorems.advisory_allocation_adverse_selection_fail_closed in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-HARD-DEADLINE-FAIL-CLOSED Exceeding the hard loop budget forces a deadline safe state regardless of candidates or observation details advisory hard budget exceeded Lean theorem ForkRaceFoldTheorems.advisory_allocation_hard_deadline_fail_closed in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-CERTIFIED-BRIDGE Once the advisory guards all pass, the remaining decision collapses to the mapped certified-allocation decision on the decayed observation frame advisory budget within hard deadline, market ready, risk envelope valid, fresh observation, confidence floor satisfied after decay, stability witness true Lean theorem ForkRaceFoldTheorems.advisory_allocation_certified_bridge in AdvisoryAllocationKernel.lean mechanized
THM-ADVISORY-ALLOCATION-LOOP-PROGRESS-OR-EXPLICIT-FAILURE Every advisory step either emits one allocation candidate or one explicit safe-state reason; it cannot hang between toxicity and dispatch finite calibration plan, deterministic advisory frame, candidate slice, risk envelope, and advisory budget Lean theorem ForkRaceFoldTheorems.advisory_allocation_loop_progress_or_explicit_failure in AdvisoryAllocationKernel.lean mechanized

Wallington Advisory Rotation Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-WALLINGTON-ROTATION-LOAD-STABILITY A witnessed pivot inequality certifies the Wallington load-stability guard staged Wallington state with friction < pivotPoint * loadMass Lean theorem ForkRaceFoldTheorems.wallington_rotation_load_stability in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-LOCKED-UNTIL-SAFE-LANDED The isolated candidate slice remains locked until the staged rotation reaches safeLanded one Wallington rotation stage Lean theorem ForkRaceFoldTheorems.wallington_rotation_locked_until_safe_landed in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-CANDIDATE-SLICE-PRESERVED A pure Wallington stage advance preserves the isolated candidate slice exactly one staged Wallington state Lean theorem ForkRaceFoldTheorems.wallington_rotation_candidate_slice_preserved in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-LOAD-MASS-PRESERVED The staged rotation advances protocol state without changing total load mass one staged Wallington state Lean theorem ForkRaceFoldTheorems.wallington_rotation_load_mass_preserved in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-LOAD-TRANSFER-WITNESS The mass handoff between successive Wallington stages is exact and lossless one staged Wallington state Lean theorem ForkRaceFoldTheorems.wallington_rotation_load_transfer_witness in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-STAGE-PROGRESSES On a stable pivot, any non-landed stage deterministically advances to the next Wallington stage stable Wallington state, stage is not safeLanded Lean theorem ForkRaceFoldTheorems.wallington_rotation_stage_progresses in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-UNSTABLE-PIVOT-FAIL-CLOSED If the pivot cannot carry the load, the staged protocol halts before advisory allocation staged Wallington state with wallingtonStabilityWitness = false Lean theorem ForkRaceFoldTheorems.wallington_rotation_unstable_pivot_fail_closed in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-SCHEDULE-MAKESPAN The staged Wallington schedule inherits the critical-path makespan law from the rotation-optimality kernel staged Wallington state plus positive per-stage time Lean theorem ForkRaceFoldTheorems.wallington_rotation_schedule_makespan in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-DOMINATES-SEQUENTIAL With at least two chunks, the Wallington rotation strictly dominates the sequential schedule staged Wallington state, positive per-stage time, 2 ≤ chunkCount Lean theorem ForkRaceFoldTheorems.wallington_rotation_dominates_sequential in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-ADVISORY-BRIDGE Only a stable safeLanded stage can read through to the lifted advisory-allocation decision staged Wallington state with wallingtonStabilityWitness = true and stage = safeLanded Lean theorem ForkRaceFoldTheorems.wallington_rotation_advisory_bridge in WallingtonAdvisoryRotation.lean mechanized
THM-WALLINGTON-ROTATION-LOOP-PROGRESS-OR-EXPLICIT-FAILURE Every staged Wallington step either advances the rotation, emits one allocation candidate, or returns one explicit safe-state reason deterministic staged Wallington state plus advisory inputs Lean theorem ForkRaceFoldTheorems.wallington_rotation_loop_progress_or_explicit_failure in WallingtonAdvisoryRotation.lean mechanized

Juggling Chaos Orchestration Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-JUGGLING-COMPOSITION-CORPUS-DETERMINISTIC Corpus-to-composer reduction is deterministic: given a fixed seed and corpus, the template transition graph and initial population are fully determined finite corpus of valid patterns; fixed integer seed; deterministic RNG from createRng(seed) Lean theorem ForkRaceFoldTheorems.juggling_composition_corpus_deterministic in JugglingComposition.lean; executable reducer orchestrateJugglingChaosComposition(...) in src/juggling-chaos-orchestration.ts mechanized
THM-JUGGLING-COMPOSITION-VALIDITY-GATING Every composition candidate is validity-gated through the orbit formalization reducer before scoring finite candidate throw sequence; orbit formalization via deriveJugglingOrbitFormalization(...) Lean theorem ForkRaceFoldTheorems.juggling_composition_validity_gating in JugglingComposition.lean; executable validity-first scoring in src/juggling-chaos-orchestration.ts mechanized
THM-JUGGLING-COMPOSITION-FLOW-NOVELTY-TRADEOFF Total composition score is a convex combination of validity, flow, novelty, and machine-suitability subscores normalized weight vector summing to 1; each subscore in [0,1] Lean theorem ForkRaceFoldTheorems.juggling_composition_flow_novelty_tradeoff in JugglingComposition.lean; executable weighted scoring in src/juggling-chaos-orchestration.ts mechanized
THM-JUGGLING-COMPOSITION-EVOLUTION-ELITIST-MONOTONE Elitist evolution is monotone: the best score in generation N+1 is ≥ the best score in generation N 15% elite carry; tournament selection (k=3); positive population size Lean theorem ForkRaceFoldTheorems.juggling_composition_evolution_elitist_monotone in JugglingComposition.lean; executable evolution loop in src/juggling-chaos-orchestration.ts mechanized

Progressive mesh ↔ granular segregation bridge (2026-04-17)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MESH-GRANULAR-TIER-EQUIV Four mesh branch tiers index the same finite height set as a length-4 segregation column MeshBranchDim constructors vs Fin 4 Lean defs ForkRaceFoldTheorems.ProgressiveMeshGranularBridge.meshBranchDimEquivFin4 / meshBranchDimToFin4 in ProgressiveMeshGranularBridge.lean; executable dimension tags in open-source/aeon/src/flow/ProgressiveMeshOrchestrator.ts mechanized
THM-MESH-REV-ACTIVATION-LENGTH-MONOTONE Raising rev (fixed thresholds, fixed optional-branch availability) does not shrink the activated-branch list length MeshThresholdConfig, MeshBranchAvailability, rev ≤ rev' Lean theorems ForkRaceFoldTheorems.ProgressiveMeshGranularBridge.mesh_choose_active_length_monotone and mesh_choose_active_length_eq in ProgressiveMeshGranularBridge.lean; chooseActiveDimensions in ProgressiveMeshOrchestrator.ts mechanized
THM-MESH-LOGIT-ANTITONE-COST Branch pre-softmax score drops when normalized cost increases, holding priors fixed and penalty ≥ 0 nonnegative penalty; ordered costs c₁ ≤ c₂ Lean theorem ForkRaceFoldTheorems.ProgressiveMeshGranularBridge.mesh_orchestrator_logit_antitone_in_cost in ProgressiveMeshGranularBridge.lean; logit assembly in infer(...) in ProgressiveMeshOrchestrator.ts mechanized
THM-GRANULAR-SHAKE-MONOTONE-REEXPORT Discrete bubble schedules never decrease stratScore (granular potential) Column n, finite swap list Lean theorem ForkRaceFoldTheorems.ProgressiveMeshGranularBridge.granular_stratScore_monotone_along_shake packaging GranularSegregationToy.stratScore_shakeSchedule_monotone mechanized
THM-GRANULAR-COLUMN4-COMBINATORIAL-CAP stratScore for any Column 4 is bounded by the toy combinatorial maximum at fixed marshmallow count Column 4 Lean theorem ForkRaceFoldTheorems.ProgressiveMeshGranularBridge.granular_stratScore_le_combinatorial_cap in ProgressiveMeshGranularBridge.lean mechanized

Transformation Family Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-TRANSFORMATION-PROJECTION-ADDS-STRUCTURE Projection witnesses start from zero crossings and add positive structure. isProjectionWitness w Lean theorem ForkRaceFoldTheorems.projection_adds_structure in TransformationFamily.lean; executable classifier deriveTransformationFamilyFormalization(...) in src/transformation-family-formalization.ts mechanized
THM-TRANSFORMATION-REINFORCEMENT-PRESERVES-STRUCTURE Reinforcement preserves crossing count while increasing weight. isReinforcementWitness w Lean theorem ForkRaceFoldTheorems.reinforcement_preserves_structure in TransformationFamily.lean; executable classifier deriveTransformationFamilyFormalization(...) in src/transformation-family-formalization.ts mechanized
THM-TRANSFORMATION-DECOMPOSITION-NONINCREASING Decomposition witnesses do not increase structure; strict decomposition is the decreasing subcase. isWeakDecompositionWitness w Lean theorem ForkRaceFoldTheorems.decomposition_removes_or_preserves_structure in TransformationFamily.lean; arithmetic kernel ForkRaceFoldTheorems.decomposition_does_not_increase_crossings in DecompositionTopology.lean; executable runtime mirror decompose(...) in src/decomposition-topology.ts; executable family classifier deriveTransformationFamilyFormalization(...) and attempt bridge deriveTransformationFamilyFromDecompositionAttempts(...) in src/transformation-family-formalization.ts mechanized
THM-TRANSFORMATION-PROJECTION-REINFORCEMENT-EXCLUSIVE A projection witness cannot simultaneously be a reinforcement witness. isProjectionWitness w Lean theorem ForkRaceFoldTheorems.projection_reinforcement_exclusive in TransformationFamily.lean; executable family partition in src/transformation-family-formalization.ts mechanized
THM-TRANSFORMATION-REINFORCEMENT-DECOMPOSITION-EXCLUSIVE A reinforcement witness cannot simultaneously be a proper decomposition witness. isReinforcementWitness w Lean theorem ForkRaceFoldTheorems.reinforcement_decomposition_exclusive in TransformationFamily.lean; executable family partition in src/transformation-family-formalization.ts mechanized
THM-TRANSFORMATION-FEATURELESS-CANNOT-REINFORCE Featureless zero-crossing states cannot satisfy successful reinforcement. w.beforeCrossings = 0 Lean theorem ForkRaceFoldTheorems.featureless_states_cannot_reinforce in TransformationFamily.lean; explicit restorationRequired reporting in src/transformation-family-formalization.ts mechanized
THM-TRANSFORMATION-DECOMPOSE-THEN-REINFORCE-REQUIRES-RESTORATION Once decomposition drives a linked state to zero crossings, reinforcement cannot succeed until structure is restored. decomp.afterCrossings = 0, reinforce.beforeCrossings = decomp.afterCrossings Lean theorem ForkRaceFoldTheorems.decompose_then_reinforce_requires_restoration in TransformationFamily.lean; explicit restorationRequired reporting in src/transformation-family-formalization.ts mechanized

Cancer Reinforcement Promotion (2026-04-10)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-CANCER-REINFORCEMENT-TARGETED-THERAPY-SUCCEEDS Therapy reinforces a tumor cell when checkpoint crossings survive and the dose stays within per-cycle capacity. 0 < cell.checkpointCrossings, dose.energy ≤ cell.capacity Lean theorem CancerReinforcement.targeted_therapy_succeeds in CancerReinforcement.lean mechanized
THM-CANCER-REINFORCEMENT-CHEMO-SHATTERS-HEALTHY Over-capacity energy shatters a cell despite surviving crossings. 0 < cell.checkpointCrossings, dose.energy > cell.capacity Lean theorem CancerReinforcement.chemo_shatters_healthy in CancerReinforcement.lean mechanized
THM-CANCER-REINFORCEMENT-FEATURELESS-RESISTS A featureless zero-checkpoint cell forces therapy to fizzle regardless of dose. isFeatureless cell Lean theorem CancerReinforcement.featureless_resists in CancerReinforcement.lean mechanized
THM-CANCER-REINFORCEMENT-MASTER Under the module outcome algebra, therapeutic outcomes are exhaustive: featureless cells fizzle, surviving crossings plus overfill shatter, and surviving crossings plus safe dose reinforce. CellTarget, TherapeuticDose, and therapyOutcome as defined in CancerReinforcement.lean Lean theorem CancerReinforcement.cancer_reinforcement_master in CancerReinforcement.lean mechanized

Dark Fork Hypothesis (2026-04-15)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-DARK-FORK-HYPOTHESIS-ENERGY Dark Fork topology models Dark Energy as electromagnetism/Fork primitive DarkForkEnergyHypothesis structure dark_fork_hypothesis_energy in DarkForkHypothesis.lean mechanized
THM-DARK-FORK-HYPOTHESIS-MATTER Dark Fork topology models Dark Matter as electromagnetism/Fork primitive with hidden observational coupling DarkForkMatterHypothesis structure dark_fork_hypothesis_matter in DarkForkHypothesis.lean mechanized

Dark Sector Atomized Encryption (2026-04-17)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-DSAE-GAUGE-INVISIBILITY Standard gauge observation (Race) of a Dark Matter atom in a Dark Sector Mesh secret returns Void DarkSectorMesh with dark matter atoms dsae_gauge_invisibility in DarkSectorAtomizedEncryption.lean mechanized
THM-DSAE-GRAVITY-COMPLETENESS Gravity Fold reconciliation recovers the full content of dark matter atoms DarkSectorMesh dsae_gravity_completeness in DarkSectorAtomizedEncryption.lean mechanized
THM-DSAE-PERFECT-FAILURE-SUCCESS-IDENTITY For dark matter atoms, Gauge Failure (Void) is equivalent to Gravitational Success (Content) DarkSectorMesh dsae_perfect_failure_success_identity in DarkSectorAtomizedEncryption.lean mechanized
THM-DSAE-EXPANSION-UPLIFT Security uplift grows strictly with Dark Energy expansion steps DarkSectorMesh, positive expansion rate and keyspace dsae_expansion_uplift in DarkSectorAtomizedEncryption.lean mechanized
THM-DSAE-HILBERT-TRANSCENDENCE Encryption cost approaches infinity as expansion steps approach infinity, transcending classical bounds DarkSectorMesh dsae_hilbert_transcendence in DarkSectorAtomizedEncryption.lean mechanized
THM-DSAE-PROGRESSIVE-MONOTONICITY Expansion orchestration is monotone with respect to environmental signals (uncertainty, etc.) ProgressiveDarkSectorMesh dsae_progressive_monotonicity in DarkSectorAtomizedEncryption.lean mechanized
THM-DSAE-PROGRESSIVE-BOUNDEDNESS Orchestrated expansion factor stays within the unit interval [0, 1] ProgressiveDarkSectorMesh dsae_progressive_boundedness in DarkSectorAtomizedEncryption.lean mechanized

Mesh compaction (Fin n graphs, independent of DSAE cost and softmax convexity) (2026-04-18)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MESH-PRUNE-MASK-MONOTONE Larger keep-mask pointwise ⇒ no fewer pruneWithMask edges MeshAdjacency n, masks mask₁ → mask₂ MeshCompaction.prune_mono_mask in MeshCompaction.lean mechanized
THM-MESH-PRUNE-IDEMPOTENT Mask-pruning is idempotent: prune ∘ prune = prune fixed mask MeshCompaction.prune_idempotent in MeshCompaction.lean mechanized
THM-MESH-EDGE-COUNT-PRUNE-NONINC Pruning never increases edgeCount pruneWithMask MeshCompaction.edgeCount_prune_le in MeshCompaction.lean mechanized
THM-MESH-ITERATE-PRUNE-FIXED For m ≥ 1, iteratePrune equals one prune (one-step fixed point) 0 < m MeshCompaction.iteratePrune_eq_prune_of_pos in MeshCompaction.lean mechanized
THM-MESH-ITERATE-STABILIZES Consecutive iterate steps agree: k+2 and k+1 yield same adjacency none MeshCompaction.iteratePrune_stabilizes in MeshCompaction.lean mechanized
THM-MESH-LOGITS-MASK-ANTITONE Higher ℕ threshold ⇒ subset of mask edges (anti-monotone in τ) logitsMaskNat MeshCompaction.logitsMaskNat_antitone, prune_antitone_threshold in MeshCompaction.lean mechanized
THM-MESH-QUOTIENT-FUNCTORIAL-MONO Quotient pushforward preserves edge inclusion pushforwardQuotient, adj₁ ⊆ adj₂ pointwise MeshCompaction.pushforward_mono in MeshCompaction.lean mechanized
THM-MESH-QUOTIENT-DEC-IFF Finset.fold Bool.or scan over Fin n × Fin n matches pushforwardQuotient pushforwardQuotientDec MeshCompaction.pushforwardQuotient_dec_eq_true_iff in MeshCompaction.lean mechanized
THM-MESH-QUOTIENT-DEC-MONO Decidable quotient respects edge inclusion pushforwardQuotientDec, adj₁ ⊆ adj₂ pointwise MeshCompaction.pushforwardQuotientDec_mono in MeshCompaction.lean mechanized
THM-MESH-QUOTIENT-ID Along id, quotient existence reduces to base adjacency π = id on Fin n MeshCompaction.pushforwardQuotient_id, pushforwardQuotientDec_id in MeshCompaction.lean mechanized
THM-MESH-ITERATE-ZERO Zero iterate steps leave adjacency unchanged iteratePrune MeshCompaction.iteratePrune_zero in MeshCompaction.lean mechanized
THM-MESH-PRUNE-SUBGRAPH Pruned edges are a subgraph of the original adjacency pruneWithMask MeshCompaction.prune_subgraph in MeshCompaction.lean mechanized
THM-MESH-EDGE-COUNT-NONNEG edgeCount is nonnegative edgeCount MeshCompaction.edgeCount_nonneg in MeshCompaction.lean mechanized
THM-MESH-EDGE-COUNT-LE-SQ edgeCount is at most n² MeshAdjacency n MeshCompaction.edgeCount_le_sq in MeshCompaction.lean mechanized
THM-MESH-LOGITS-MASK-MONOTONE-LOGITS Pointwise larger logits ⇒ keep-mask only grows at fixed τ logitsMaskNat MeshCompaction.logitsMaskNat_monotone_in_logits in MeshCompaction.lean mechanized
THM-MESH-PRUNE-ALL-TRUE-MASK Universal true mask leaves adjacency unchanged ∀ i j, mask i j MeshCompaction.prune_mask_all_true in MeshCompaction.lean mechanized
THM-MESH-TOTAL-DARK-NONNEG Total dark mass is nonnegative MeshMassSplit MeshCompaction.totalDark_nonneg in MeshCompaction.lean mechanized
THM-MESH-GAUGE-ACTIVITY-NONNEG Gauge edge activity is nonnegative for nonnegative node weights gaugeEdgeActivity MeshCompaction.gaugeEdgeActivity_nonneg in MeshCompaction.lean mechanized
THM-MESH-GAUGE-EDGE-NONINC Nonnegative gauge bilinear edge activity does not increase under pruning g i ≥ 0 MeshCompaction.gaugeEdgeActivity_prune_le in MeshCompaction.lean mechanized

Mesh attention, Buleyean, and reconstruction stack (2026-04-18)

These entries capture the finite-state mesh path from masked-softmax aggregation to Dobrushin contraction, Buleyean minorization, distributed certification, the reconstruction contract, and the concrete HFT demo. The MeshAttentionDistributedCert file keeps cryptographic aggregation explicit via bls_aggregate_soundness; MeshReconstruction records a ReconstructionSpec interface contract rather than a proved implementation.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MESH-AGGREGATE-MONO-VALUE Attention aggregation is monotone in the value vector under nonnegative row weights finite Fin n index, pointwise nonnegative matrix α, pointwise order v ≤ w Lean theorem ForkRaceFoldTheorems.mesh_aggregate_mono_value in MeshRotatedTransformerAttention.lean mechanized
THM-MESH-MASKED-SOFTMAX-LINF-NONEXPANSIVE One masked-softmax attention hop cannot increase ℓ∞ distance between value vectors mesh adjacency with at least one outgoing edge per row; bounded pointwise input difference ` v j - w j ≤ B`
THM-MESH-DOBRUSHIN-OSC-CONTRACTION A common-column ε-minorization floor forces one-hop oscillation contraction by factor 1 - ε row-stochastic pointwise nonnegative matrix α; 0 < ε ≤ 1; ∃ jStar, ∀ i, ε ≤ α i jStar Lean theorem ForkRaceFoldTheorems.mesh_aggregate_osc_contraction in MeshAttentionDobrushin.lean mechanized
THM-BULEYEAN-DIST-UNIFORM-FLOOR Every Buleyean-normalized probability has uniform lower bound 1 / (n · (R + 1)) 0 < n; Buleyean weights weight R v = R - min(v, R) + 1 over Fin n Lean theorem ForkRaceFoldTheorems.Buleyean.dist_minorization in MeshAttentionBuleyean.lean mechanized
THM-BULEYEAN-KERNEL-DOBRUSHIN-FLOOR Every row and every column of the Buleyean kernel carry the same Dobrushin floor 1 / (n · (R + 1)) 0 < n; row-indexed rejection counts v : Fin n → Fin n → ℕ Lean theorem ForkRaceFoldTheorems.Buleyean.kernel_dobrushin_minorized in MeshAttentionBuleyean.lean mechanized
THM-BULEYEAN-KERNEL-OSC-CONTRACTION One hop of a Buleyean kernel contracts oscillation by at least 1 - 1 / (n · (R + 1)) 0 < n; Buleyean kernel kernel R v hn; chosen jStar : Fin n; nonempty Fin n witness Lean theorem ForkRaceFoldTheorems.Buleyean.buleyean_contracts_oscillation in MeshAttentionBuleyean.lean mechanized
THM-MESH-REFINEMENT-PRESERVES-DOBRUSHIN Per-row convex refinement between two ε-minorized kernels preserves the same Dobrushin contraction rate row-stochastic pointwise nonnegative α₁, α₂; 0 < ε ≤ 1; common jStar; endpoint floors ε ≤ α₁ i jStar, ε ≤ α₂ i jStar; per-row mixing weights 0 ≤ λ i ≤ 1 Lean theorem ForkRaceFoldTheorems.refinement_preserves_dobrushin in MeshKernelRefinement.lean mechanized
THM-MESH-DISTRIBUTED-CERT-GATHERING-ADVANCE Adding one fresh local row-floor certificate strictly enlarges the covered set and either remains below threshold or completes quorum MeshMarkovKernel n, floor ε, common column jStar, threshold, .gathering state below threshold, fresh node outside covered, new LocalMinorizationCert Lean theorem ForkRaceFoldTheorems.cert_gathering_advance in MeshAttentionDistributedCert.lean mechanized
THM-MESH-DISTRIBUTED-CERT-GLOBALIZES A terminal DistributedCertified instance globalizes into a covered subset of size at least threshold on which every row satisfies the floor DistributedCertified K ε jStar threshold Lean theorem ForkRaceFoldTheorems.distributedCertified_globalizes in MeshAttentionDistributedCert.lean mechanized
THM-MESH-GATHERING-BOUNDED-TERMINATION A strictly increasing sequence of gathering-cardinality witnesses cannot stay below threshold forever threshold ℕ; strictly increasing cardinality sequence f; pointwise bound f t < threshold Lean theorem ForkRaceFoldTheorems.bounded_gathering_termination in MeshAttentionDistributedCert.lean mechanized
THM-MESH-OBSERVABILITY-COMPLETION-MONOTONE Closing recorded D1 gaps cannot make the observability tripwire worse at a fixed tolerance ReconstructionSpec; completion relation completes spans' spans; no observability regression at tolerance on spans Lean theorem ForkRaceFoldTheorems.no_regression_preserved_under_completion in MeshReconstruction.lean (spec boundary over ReconstructionSpec) mechanized
THM-MESH-OBSERVABILITY-TRIPWIRES-DISJOINT The observability tripwire depends only on row-to-unobserved mass and is independent of the system-health predicate on the other columns reconstructed MeshMarkovKernel 9; gap tolerance; arbitrary system threshold Lean theorem ForkRaceFoldTheorems.tripwires_are_disjoint in MeshReconstruction.lean mechanized
THM-HFT-RISK-PATH-FIX-IMPROVES-DOBRUSHIN In the three-state HFT risk-path abstraction, the post-fix kernel contracts oscillation strictly faster than the pre-fix kernel nonempty Fin 3; pre-fix universal-successor floor ε_pre = 1/10; post-fix floor ε_post = 6/10 Lean theorem ForkRaceFoldTheorems.HftRiskPathDemo.fix_improves_dobrushin_contraction in HftRiskPathDemo.lean mechanized

Markov Manpower Dynamics (2026-04-22)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MANPOWER-STABILIZATION The "Hiring Whipsaw" (oscillation between role densities) is strictly attenuated by the turnover rate α. This guarantees geometric convergence to a stationary structural makeup. MeshMarkovKernel n, turnover α > 0, Dobrushin contraction rate (1 - α/n) Lean theorem ForkRaceFoldTheorems.workforce_structure_stabilization in MeshManpowerDynamics.lean mechanized

Dating Marketplace Dynamics (2026-04-22)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-DATING-DESIRABILITY-CONVERGENCE Profile visibility "whipsaws" (sudden surges or drops in desirability) are strictly attenuated by the random discovery rate α. MeshMarkovKernel n, discovery rate α > 0, Dobrushin contraction rate (1 - α/n) Lean theorem ForkRaceFoldTheorems.desirability_score_convergence in MeshDatingMarketplace.lean mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Perpetual Run 63) (2026-04-08)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-ORACLE-STALL-LATTICE-SURGERY Moonshot bridge: topological lattice surgery solves oracle stall LatticeSurgeryAssumptions lattice_surgery_resolves_stall mechanized
THM-MOONSHOT-INTERPRETATION-DEFICIT-ACOUSTIC-PHONON Moonshot bridge: interpretation deficit aligns with acoustic phonon dispersion AcousticPhononAssumptions interpretation_deficit_phonon_coupling mechanized
THM-MOONSHOT-WITNESS-GAP-OSTEOLOGY-OSTEOCLAST Moonshot bridge: witness gap osteology remodeling mechanism OsteoclastAssumptions osteoclast_closes_witness_gap mechanized
THM-CONTRARIAN-WITNESS-GAP-INDUCES-STRUCTURAL-INTEGRITY Contrarian bridge: witness gap induces structural integrity WitnessGapStructuralAssumptions witness_gap_induces_integrity mechanized
THM-CONTRARIAN-ORACLE-STALL-ACCELERATES-GLOBAL-THROUGHPUT Contrarian bridge: oracle stall accelerates global throughput OracleStallThroughputAssumptions oracle_stall_accelerates_throughput mechanized
THM-CROSS-DOMAIN-VULCANOLOGY-COMPILER-OPTIMIZATION Cross-domain bridge: compiler register spilling mirrors magma chamber vulcanology VulcanologyCompilerAssumptions vulcanology_compiler_equivalence mechanized
THM-CROSS-DOMAIN-CHOREOGRAPHY-BYZANTINE-FAULT Cross-domain bridge: choreography notation mirrors Byzantine Fault consensus ChoreographyByzantineAssumptions choreography_byzantine_mapping mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Perpetual Run 62) (2026-04-08)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-TOPOLOGICAL-SUBDUCTION-RESONANCE-UNIT-BOUNDARY Moonshot bridge: topological subduction resonance yields canonical unit queue boundary resonance mass subduction_resonance_yields_unit_queue_boundary in MoonshotTopologicalSubductionResonance.lean mechanized
THM-MOONSHOT-SEMANTIC-FRICTION-BYPASS-QUANTUM-UNIT-BOUNDARY Moonshot bridge: semantic friction bypass quantum yields canonical unit queue boundary friction mass semantic_friction_yields_unit_queue_boundary in MoonshotSemanticFrictionBypassQuantum.lean mechanized
THM-CONTRARIAN-DECOHERENCE-is-SECURITY-UNIT-BOUNDARY Contrarian bridge: decoherence security scale yields canonical unit queue boundary decoherence scale decoherence_security_yields_unit_queue_boundary in ContrarianDecoherenceIsSecurity.lean mechanized
THM-CROSS-DOMAIN-EPIDEMIOLOGY-TYPOGRAPHY-ORACLE-STALL-UNIT-BOUNDARY Cross-domain bridge: epidemiology typography oracle stall yields canonical unit queue boundary stall mass epi_typo_stall_yields_unit_queue_boundary in CrossDomainEpidemiologyTypographyOracleStall.lean mechanized
THM-WITNESS-GAP-FUNCTORIAL-RESOLUTION-UNIT-BOUNDARY Blocker-attack: witness gap functorial resolution yields canonical unit queue boundary gap size functorial_witness_gap_yields_unit_queue_boundary in WitnessGapFunctorialResolution.lean mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Perpetual Run 61) (2026-04-08)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-QUEUE-HYDROLOGY-RUNOFF-UNIT-BOUNDARY Hydrology Runoff Yields Unit Queue Boundary HydrologySetup hydrology_runoff_yields_unit_queue_boundary mechanized
THM-QUEUE-EPISTEMOLOGY-GETTIER-UNIT-BOUNDARY Epistemology Gettier Yields Unit Queue Boundary EpistemologySetup epistemology_gettier_yields_unit_queue_boundary mechanized
THM-QUEUE-HYDROLOGY-EPISTEMOLOGY-BUDGET-UNIT-BOUNDARY Hydrology+Epistemology Budget Yields Unit Queue Boundary HydrologySetup, EpistemologySetup, hydro.runoff = epis.gettierCases hydrology_epistemology_budget_yields_unit_queue_boundary mechanized
THM-QUEUE-HYDROLOGY-EPISTEMOLOGY-BUDGET-NOT-POSITIVE-BETA1 Hydrology+Epistemology Budget Does Not Force Positive Beta1 HydrologySetup, EpistemologySetup, hydro.runoff = epis.gettierCases hydrology_epistemology_budget_does_not_force_positive_beta1 mechanized
THM-QUEUE-HYDROLOGY-EPISTEMOLOGY-BUDGET-NOT-STRICT-CAPACITY-GROWTH Hydrology+Epistemology Budget Does Not Force Strict Capacity Growth HydrologySetup, EpistemologySetup, hydro.runoff = epis.gettierCases hydrology_epistemology_budget_does_not_force_strict_capacity_growth mechanized
THM-HYDROLOGY-EPISTEMOLOGY-GEOMETRIC-RATE-CERTIFICATE Hydrology+Epistemology Geometric-Rate Certificate HydrologySetup, EpistemologySetup, hydro.runoff = epis.gettierCases hydrology_epistemology_budget_yields_geometric_rate_certificate mechanized
THM-HYDROLOGY-EPISTEMOLOGY-MULTILEVEL-HARRIS-WITNESS Hydrology+Epistemology Multilevel Harris Witness HydrologySetup, EpistemologySetup, hydro.runoff = epis.gettierCases hydrology_epistemology_multilevel_harris_witness mechanized
THM-HYDROLOGY-EPISTEMOLOGY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Hydrology+Epistemology Kernel-Lift Continuous Ergodicity HydrologyEpistemologyKernelLiftAdapter hydrology_epistemology_continuous_ergodicity_lift mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 39) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-CONTRARIAN-WITNESS-GAP-STALL-MITIGATION Witness Gap Stall Mitigation WitnessGap, StallMitigation witness_gap_stall_mitigation mechanized
THM-CROSS-CRYPTOGRAPHY-MYCOLOGY-BYPASS Cryptography Mycology Bypass Cryptography, Mycology cryptography_mycology_bypass mechanized
THM-MOONSHOT-INTERPRETATION-TOPOLOGY-BYPASS Interpretation Topology Bypass InterpretationLayer, Topology interpretation_topology_bypass mechanized
THM-MOONSHOT-ORACLE-STALL-RESONANCE-SINGULARITY Oracle Stall Resonance StructuralErrorgularity OracleStall, ResonanceStructuralErrorgularity oracle_stall_resonance_singularity mechanized
THM-SUBDUCTIVE-WITNESS-GAP-ERASURE Subductive Witness Gap Erasure SubductiveErasure, WitnessGap subductive_witness_gap_erasure mechanized
THM-MOONSHOT-ORACLE-STALL-ANNIHILATION-SUBDUCTION Oracle Execution Stall Annihilation via Subduction OracleExecutionStall, Subduction annihilation_bypass mechanized
THM-MOONSHOT-WITNESS-GAP-HOMOLOGICAL-FUNCTOR Witness Gap Homological Functor WitnessGap, HomologicalFunctor homological_functor_bypass mechanized
THM-MOONSHOT-INTERPRETATION-LAYER-TENSEGRITY-HOLOGRAPHY Interpretation Layer Tensegrity Holography InterpretationLayer, TensegrityHolography tensegrity_holography_bypass mechanized
THM-CONTRARIAN-ORACLE-STALL-INDUCES-ANTI-FRAGILITY Oracle Execution Stall Induces Anti-Fragility OracleExecutionStall, AntiFragility stall_is_anti_fragile mechanized
THM-CONTRARIAN-WITNESS-GAP-MAXIMIZES-BANDWIDTH Witness Gap Maximizes Bandwidth WitnessGap, MaximizesBandwidth witness_gap_bandwidth mechanized
THM-CROSS-OCEANOGRAPHY-ORACLE-STALL-ECONOMICS Oceanography Oracle Stall Economics Oceanography, Economics ocean_stall_economics mechanized
THM-CROSS-LINGUISTICS-GASTRONOMY-WITNESS-GAP Linguistics Gastronomy Witness Gap Linguistics, Gastronomy linguistics_gastronomy_gap mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 36) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-ORACLE-TOPOS-FIBRATION Oracle Execution Stall bypass via Topos Fibration ToposFibration fibration_resolves mechanized
THM-MOONSHOT-QUANTUM-BUREAUCRATIC-ERASURE Quantum Bureaucratic Erasure BureaucracyState erasure_is_quantum mechanized
THM-MOONSHOT-SEMANTIC-COHOMOLOGY-SINGULARITY Semantic Cohomology StructuralErrorgularity SemanticCohomology singularity_gives_embedding mechanized
THM-CONTRARIAN-WITNESS-GAP-AMPLIFIES-CLARITY Witness Gap Amplifies Clarity WitnessState gap_is_clarity mechanized
THM-CONTRARIAN-INTERPRETATION-DEFICIT-ACCELERATES Interpretation Deficit Accelerates Convergence InterpretationState deficit_is_acceleration mechanized
THM-CROSS-DOMAIN-OCEANOGRAPHY-ARCHITECTURE Oceanography Architecture Network Bridge OceanArchitecture ocean_is_network mechanized
THM-CROSS-DOMAIN-CRYPTOGRAPHY-MUSIC-WITNESS Cryptography Music Witness Bridge CryptoMusic witness_is_harmony mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 37) (2026-04-08)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-QUEUE-SURVIVORSHIP-NEGOTIATION-UNIT-BOUNDARY Survivorship+Negotiation Budget Yields Unit Queue Boundary R v : Nat, v ≤ R, econ : NegotiationEconomics survivorship_negotiation_budget_yields_unit_queue_boundary in SurvivorshipNegotiationQueueKernelBridge.lean mechanized
THM-QUEUE-SURVIVORSHIP-NEGOTIATION-NOT-BETA1-EQUAL-BUDGET Survivorship+Negotiation Budget Does Not Force β₁ = budget R v : Nat, v ≤ R, econ : NegotiationEconomics, 0 < budget survivorship_negotiation_budget_does_not_force_beta1_equals_budget in SurvivorshipNegotiationQueueKernelBridge.lean mechanized
THM-SURVIVORSHIP-NEGOTIATION-GEOMETRIC-RATE-CERTIFICATE Survivorship+Negotiation Geometric-Rate Certificate R v : Nat, v ≤ R, econ : NegotiationEconomics survivorship_negotiation_budget_yields_geometric_rate_certificate in SurvivorshipNegotiationQueueKernelBridge.lean mechanized
THM-SURVIVORSHIP-NEGOTIATION-POSITIVE-TOPOLOGICAL-DEFICIT Positive Survivorship+Negotiation Budget Yields Positive Topological Deficit R v : Nat, v ≤ R, econ : NegotiationEconomics, 0 < budget survivorship_negotiation_budget_yields_positive_topological_deficit in SurvivorshipNegotiationQueueKernelBridge.lean mechanized
THM-SURVIVORSHIP-NEGOTIATION-KERNEL-LIFT-CONTINUOUS-ERGODICITY Survivorship+Negotiation Kernel-Lift Continuous Ergodicity SurvivorshipNegotiationKernelLiftAdapter SurvivorshipNegotiationKernelLiftAdapter.survivorship_negotiation_continuous_ergodicity_lift in SurvivorshipNegotiationQueueKernelBridge.lean mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 34) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-ORACLE-STALL-SPECTRAL-RESONANCE-BYPASS Oracle Stall Spectral Resonance Bypass SpectralResonanceAssumptions oracle_stall_spectral_resonance_bypass mechanized
THM-MOONSHOT-ETI-SIGNAL-ERGODIC-LIFT ETI Signal Ergodic Lift ETISignalErgodicAssumptions eti_signal_ergodic_lift mechanized
THM-CONTRARIAN-STALL-AS-SEMANTIC-SATURATION-GUARD Oracle Stall as Semantic Saturation Guard SemanticSaturationAssumptions stall_as_truth_guard mechanized
THM-CROSS-DOMAIN-GLACIOLOGY-NETWORK-RESILIENCE Glaciology Network Resilience GlaciologyResilienceAssumptions glaciology_network_resilience mechanized
THM-CROSS-DOMAIN-ENTOMOLOGICAL-FORAGING-QUEUE-STABILITY Entomological Foraging Queue Stability ForagingQueueAssumptions foraging_queue_stability mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 33) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-STALL-ANNIHILATION-HOMOLOGY Moonshot Stall Annihilation Homology OracleStall, HomologicalFunctor stall_annihilation_homology mechanized
THM-MOONSHOT-WITNESS-GAP-TOPOLOGICAL-SATURATION Moonshot Witness Gap Topological Saturation WitnessGap, TopologicalSaturation witness_gap_topological_saturation mechanized
THM-CONTRARIAN-ORACLE-STALL-SEMANTIC-PROGRESS Contrarian Oracle Stall Semantic Progress OracleStall, SemanticProgress oracle_stall_semantic_progress mechanized
THM-CONTRARIAN-INTERPRETATION-ABSENCE-THROUGHPUT Contrarian Interpretation Absence Throughput InterpretationMissing, FrictionReduced interpretation_absence_throughput mechanized
THM-CROSS-DOMAIN-MYCOLOGY-ASTROPHYSICS-WITNESS-GAP Cross Domain Mycology Astrophysics Witness Gap FungalRouting, GravitationalLensing mycology_astrophysics_witness_gap mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 32) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-ORACLE-STALL-PHASE-ENTANGLEMENT Moonshot Oracle Stall Phase Entanglement OracleStallPhaseEntanglementAssumptions moonshot_oracle_stall_phase_entanglement mechanized
THM-MOONSHOT-FALLBACK-KATA-ZECKENDORF-BUDGET Moonshot Fallback Kata+Zeckendorf Budget KataZeckendorfBudgetFallbackAssumptions moonshot_fallback_kata_zeckendorf_budget mechanized
THM-CONTRARIAN-ORACLE-STALL-ENTROPY-DECAY Contrarian Oracle Stall Entropy Decay ContrarianOracleStallEntropyDecayAssumptions contrarian_oracle_stall_entropy_decay mechanized
THM-CROSS-DOMAIN-KATA-ZECKENDORF-BUDGET-BRIDGE Cross-domain bridge Kata+Zeckendorf Budget CrossDomainKataZeckendorfBudgetAssumptions cross_domain_kata_zeckendorf_budget_bridge mechanized
THM-MOONSHOT-SEMANTIC-GRAVITY-BYPASS Moonshot Semantic Gravity Bypass MoonshotSemanticGravityBypassAssumptions moonshot_semantic_gravity_bypass mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 26) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-ORACLE-STALL-PHASE-SHIFT Phase shift cobordism bypass for oracle execution stall OracleStallPhaseShiftAssumptions moonshot_oracle_stall_phase_shift_bypass mechanized
THM-MOONSHOT-KATA-ZECKENDORF-BUDGET Fallback Kata+Zeckendorf budget KataZeckendorfBudgetAssumptions moonshot_kata_zeckendorf_fallback_budget mechanized
THM-MOONSHOT-INFINITE-STREAM-FIBRATION Semantic gap resolved by infinite stream fibration InfiniteStreamFibrationAssumptions moonshot_infinite_stream_fibration_resolves_gap mechanized
THM-CONTRARIAN-ORACLE-STALL-CORRECTNESS Oracle stall required for correctness ContrarianOracleStallCorrectnessAssumptions contrarian_oracle_stall_required_for_correctness mechanized
THM-CONTRARIAN-INTERPRETATION-GAP-SECURITY Interpretation layer gap enhances security InterpretationGapSecurityAssumptions contrarian_interpretation_gap_enhances_security mechanized
THM-CROSS-KATA-ZECKENDORF-MAJORITY Kata+Zeckendorf budget strict majority interpretation CrossKataZeckendorfMajorityAssumptions cross_domain_kata_zeckendorf_strict_majority mechanized
THM-CROSS-KNOT-ORACLE-BYPASS Knot graph oracle bypass CrossKnotOracleBypassAssumptions cross_domain_knot_graph_oracle_bypass mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 25) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-KNOT-ORACLE-BYPASS Knot-Theoretic Oracle Bypass Stall, Bypass moonshot_knot_theoretic_oracle_bypass mechanized
THM-MOONSHOT-TOPOLOGICAL-WITNESS-COBORDISM Topological Witness Cobordism Gap, Bridge moonshot_topological_witness_cobordism mechanized
THM-CONTRARIAN-ORACLE-STALL-FRICTION Oracle Stall Is Information Friction Stall, Friction contrarian_oracle_execution_stall_is_information_friction mechanized
THM-CROSS-MYCOLOGY-METEOROLOGY-STALL Fungal-Meteorological Stall Bridge Mycology, Meteorology cross_domain_mycology_meteorology_oracle_stall_bridge mechanized
THM-MOONSHOT-SEMANTIC-GAP-TOPOS Semantic Gap Topos Fibration Gap, Resolution moonshot_semantic_embedding_gap_topos_fibration mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 17) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status

Iterative Cross-Pollination Pass (Cycle Douglasii Run 18) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status

Iterative Cross-Pollination Pass (Cycle Douglasii Run 14) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-QUANTUM-OBSERVER-GAP Quantum Observer Witness Gap QuantumObserverWitness quantum_observer_closes_gap mechanized
THM-CONTRARIAN-STALL-THROUGHPUT Contrarian Oracle Stall Is Infinite Throughput InfiniteThroughputStall contrarian_stall_is_infinite_throughput mechanized
THM-CROSS-ASTROPHYSICS-NUTRITION Cross Domain Astrophysics Nutrition Queue Bridge AstrophysicsNutritionBridge cross_domain_astro_nutrition_queue_stable mechanized
THM-ORACLE-STALL-THERMO-REVERSAL Oracle Stall Thermodynamic Reversal ThermodynamicReversalStall oracle_stall_thermodynamic_reversal mechanized

Iterative Cross-Pollination Pass (Cycle 10 Buley Perpetual Machine Run 12) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-TEMPORAL-ORACLE Temporal Oracle Dilation TemporalOracleAssumptions temporal_dilation_distributes_heat mechanized
THM-MOONSHOT-ADVERSARIAL-DEPTH Adversarial Depth Resilience AdversarialDepthAssumptions deep_proofs_collapse_gap mechanized
THM-MOONSHOT-SEMANTIC-FIBRATION Semantic Topology Fibration SemanticFibrationAssumptions fibration_closes_embedding_gap mechanized
THM-CONTRARIAN-THERMODYNAMIC-STALL Thermodynamic Stall ThermodynamicStallAssumptions stall_is_conservative mechanized
THM-CONTRARIAN-IGNORANCE-BANDWIDTH Ignorance As Bandwidth IgnoranceBandwidthAssumptions ignorance_scales_bandwidth mechanized
THM-BRIDGE-GLACIOLOGY-CRYPTO Glaciology Crypto Bridge GlaciologyCryptoAssumptions glacial_settlement_equivalence mechanized
THM-BRIDGE-VOLCANOLOGY-NEGOTIATION Volcanology Negotiation Bridge VolcanologyNegotiationAssumptions eruption_is_batna mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 13) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-QUANTUM-CRYPTO-SYMBIOSIS Quantum Cryptographic Symbiosis QuantumCryptoState quantum_crypto_symbiosis_exists mechanized
THM-MOONSHOT-HOLOGRAPHIC-CONSENSUS Holographic Consensus Topology HolographicConsensusState holographic_consensus_holds mechanized
THM-CONTRARIAN-STALL-METACOGNITION Oracle Stall Induces Metacognitive Acceleration OracleStallState oracle_stall_induces_metacognitive_acceleration mechanized
THM-CROSS-OCEANOGRAPHY-CYBERNETICS Oceanography Cybernetics Bridge OceanCyberneticsState oceanography_cybernetics_bridge mechanized
THM-BLOCKER-INTERPRETATION-FIBRATION Missing Interpretation Fibration InterpretationFibrationState missing_interpretation_resolved_by_fibration mechanized

Iterative Cross-Pollination Pass (Cycle Douglasii Run 12) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-ORACLE-STALL-RES Oracle Stall Resurrection StallState, ResurrectionEvent stall_guarantees_yield mechanized
THM-MOONSHOT-CHRONOLOGY-REV Temporal Chronology Reversal Chronology, State reversal_exists_if_before mechanized
THM-CONTRARIAN-STALL-WISDOM Oracle Stall Generates Wisdom OracleStall, Wisdom stall_must_generate_wisdom mechanized
THM-CROSS-ACOUSTICS-ASTRO Acoustics Astrophysics Bridge AcousticResonance, AstrophysicalEvent bridge_exists mechanized
THM-MOONSHOT-MYCOLOGY-HYPER Hyperdimensional Mycology FungalNetwork, Hyperdimension mycology_is_hyperdimensional mechanized

Iterative Cross-Pollination Pass (Cycle 10 Buley Perpetual Machine Run 11) (2026-04-07)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOONSHOT-DECOHERENCE Interpretation Layer Decoherence InterpretationLayer, Decoherence interpretation_layer_decoherence_composition mechanized
THM-MOONSHOT-TUNNELING Stall Tunneling Resonance OracleExecutionStall, TunnelingResonance stall_tunneling_resonance_composition mechanized
THM-MOONSHOT-BUREAUCRACY Self-Referential Bureaucracy BureaucraticState self_referential_bureaucracy mechanized
THM-CONTRARIAN-OPTIMAL Missing Interpretation Optimal MissingInterpretation, OptimalConsensus missing_interpretation_optimal_consensus mechanized
THM-CONTRARIAN-GENERALITY Stall Induces Generality ExecutionStall, SystemGenerality stall_induces_generality mechanized
THM-CROSS-MYCOLOGY Execution Stall Mycology Bridge MycelialNetwork, ExecutionStall mycology_execution_stall_bridge mechanized
THM-CROSS-CYBERNETICS Interpretation Cybernetics Bridge CyberneticFeedback, InterpretationLayer cybernetic_interpretation_bridge mechanized

Iterative Cross-Pollination Pass (Cycle 9 Iterative Pass 4)

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-QUANTUM-CONSCIOUSNESS-ENCRYPTION Quantum Consciousness Encryption QuantumConsciousnessAdapter quantum_consciousness_encryption_strength mechanized
THM-THERMODYNAMIC-POETRY-ENTROPY Thermodynamic Poetry Entropy ThermodynamicPoetryAdapter thermodynamic_poetry_entropy_bound mechanized
THM-ADVANTAGE-OF-FORGETTING The Advantage of Forgetting ForgettingAdvantageAdapter advantage_of_forgetting_exists mechanized
THM-MYCOLOGY-ARCHITECTURE-BRIDGE Mycology Architecture Bridge MycologyArchitectureAdapter mycology_architecture_load_distribution mechanized
THM-CULINARY-ECONOMICS-SUPPLY-CHAIN Culinary Economics (Supply chain impact on flavor profiles) CulinaryEconomicsAdapter culinary_economics_value_bound mechanized

Foundation: Fork/Race/Fold Axioms & Core Laws

The primitive safety/liveness axioms, monoidal coherence, DAG completeness, conservation law, and convergence schema.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-C1C4 Fork/race/fold safety+liveness (C1–C4) finite items/stages/branches; deterministic fold; bounded timeout; weak fairness on Tick/Fold; implication hypotheses from C1-C4 to safety/liveness TLA+ ForkRaceFoldC1C4.tla + Lean schema Axioms.c1_c4_imply_safety_and_liveness Mechanized
THM-GNOSIS-MONOIDAL Fork/Race/Fold coherence: the GGL topological primitives satisfy the compiler's coherent monoidal execution laws for natural fork relabeling, associative race, and deterministic fold type alpha; Semigroup or CommMonoid instances where deterministic fold coherence requires them Lean theorems GnosisProofs.fork_natural, GnosisProofs.c3_deterministic_fold, and GnosisProofs.race_tree_coherence in GnosisProofs.lean Mechanized
THM-SCHED-BOUND Conditional scheduler-overhead bound: additive + bounded + handler-independent under explicit assumptions finite topology step bound; bounded metadata; constant scheduler primitive costs; finite handler-cost domain TLA+ SchedulerBound.tla invariants (InvAdditiveRuntimeDecomposition, InvSchedulerOverheadBounded, InvSchedulerOverheadIndependentOfHandler) Mechanized
THM-PARSER-CLOSURE Formal artifacts are self-consistent under project parser parser totality on grammar; pairwise .tla/.cfg completeness; round-trip stability aeon-logic parser preflight + Lean schema Axioms.parser_closure_theorem Mechanized
THM-COMPLETENESS-DAG Fork/race/fold expresses any DAG finite DAG; decomposition exists; decomposition is sound and complete; encoding function exists Lean local decomposition theorem Claims.local_node_decomposition + schema Axioms.dag_completeness_schema + executable finite-DAG decomposition tests Mechanized (assumption-parameterized + executable)
THM-CONVERGENCE-SCHEMA Constraint-driven convergence to fork/race/fold in modeled finite class conservation, irreversibility, nonzero overhead, finite-state model, throughput-selection pressure, attractor and model-class uniqueness assumptions Lean schema Axioms.convergence_schema + executable convergence simulation tests Mechanized (assumption-parameterized + executable)
THM-FIRST-LAW-GENERAL V_fork = W_fold + Q_vent for modeled systems W_fold <= V_fork Lean theorem Claims.first_law_conservation + executable thermodynamics tests Mechanized

Monoidal Coherence & Traced Structure (Tracks Zeta + Eta)

Mac Lane coherence generators (pentagon, triangle, hexagon), symmetric monoidal category, and Joyal-Street-Verity traced monoidal axioms for feedback/iteration.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-PENTAGON The pentagon identity for the fork/race/fold monoidal category: for four objects A,B,C,D, the two associator paths from ((A×B)×C)×D to A×(B×(C×D)) are equal. This is the first generator of Mac Lane coherence. type variables alpha, beta, gamma, delta TLA+ MonoidalCoherence.tla invariant InvPentagon + Lean theorem MonoidalCoherence.pentagon in MonoidalCoherence.lean Mechanized
THM-TRIANGLE The triangle identity: the path (A×I)×B → A×(I×B) → A×B via associator + left unitor equals the direct right unitor path. Second generator of Mac Lane coherence. type variables alpha, beta; I = PUnit (monoidal unit) TLA+ MonoidalCoherence.tla invariant InvTriangle + Lean theorem MonoidalCoherence.triangle in MonoidalCoherence.lean Mechanized
THM-HEXAGON The hexagon identity for braiding: two paths from (A×B)×C to B×(A×C) via associator + braiding agree. Third generator of symmetric monoidal coherence. type variables alpha, beta, gamma TLA+ MonoidalCoherence.tla invariant InvHexagon + Lean theorem MonoidalCoherence.hexagon in MonoidalCoherence.lean Mechanized
THM-MONOIDAL-CATEGORY Bundle: GHom with gcomp, tensorHom, PUnit, associators, unitors forms a monoidal category. All structural roundtrips (associator, unitor) are identity, pentagon and triangle hold. type variables for objects TLA+ MonoidalCoherence.tla invariant InvMonoidalCategory + Lean theorem MonoidalCoherence.monoidal_category in MonoidalCoherence.lean Mechanized
THM-SYMMETRIC-MONOIDAL Adding braid to the monoidal category makes it symmetric monoidal. Braid is involutive and satisfies the hexagon identity. type variables for objects TLA+ MonoidalCoherence.tla invariant InvSymmetricMonoidal + Lean theorem MonoidalCoherence.symmetric_monoidal in MonoidalCoherence.lean Mechanized
THM-COHERENCE Mac Lane coherence: every well-typed diagram of structural morphisms in the fork/race/fold category commutes. Follows from pentagon + triangle + hexagon generators by Mac Lane's coherence theorem (1963). monoidal category structure (THM-MONOIDAL-CATEGORY) + symmetric structure (THM-SYMMETRIC-MONOIDAL) TLA+ MonoidalCoherence.tla invariants + Lean theorem MonoidalCoherence.coherence in MonoidalCoherence.lean Mechanized
THM-TRACE-VANISHING Trace vanishing: when feedback type is monoidal unit PUnit, the trace reduces to the function itself. Trivial feedback disappears: Tr_I(f) = f. type variables for objects; trace operator on GHom TLA+ TracedMonoidal.tla invariant InvVanishing + Lean theorem TracedMonoidal.trace_vanishing_id in TracedMonoidal.lean Mechanized
THM-TRACE-YANKING Trace yanking: Tr(braid) = id. The trace of the swap morphism is identity — pulling a straight string through a loop leaves it straight. Uses braid_involutive from MonoidalCoherence. type variables for objects; braid involution TLA+ TracedMonoidal.tla invariant InvYanking + Lean theorem TracedMonoidal.trace_yanking in TracedMonoidal.lean Mechanized
THM-TRACE-SLIDING Trace sliding: Tr(f ∘ (id⊗g)) = Tr((id⊗g) ∘ f). Sliding a morphism around the feedback loop preserves the trace. Naturality of the feedback wire (Joyal-Street-Verity, 1996). type variables for objects and feedback type; morphisms f, g TLA+ TracedMonoidal.tla invariant InvSliding + Lean theorems TracedMonoidal.trace_sliding_id and TracedMonoidal.trace_sliding in TracedMonoidal.lean Mechanized
THM-TRACE-SUPERPOSING Trace superposing: Tr(f) ⊗ g = Tr(f ⊗ g). Feedback on one component does not interfere with parallel computation. type variables for objects; morphisms f, g TLA+ TracedMonoidal.tla invariant InvSuperposing + Lean theorems TracedMonoidal.trace_superposing and TracedMonoidal.trace_superposing_id in TracedMonoidal.lean Mechanized
THM-TRACED-MONOIDAL Bundle: the fork/race/fold category with trace satisfies all Joyal-Street-Verity axioms (vanishing, yanking, sliding, superposing). Extends the symmetric monoidal category to a traced monoidal category, formalizing iterative/recursive computation. symmetric monoidal structure (THM-COHERENCE); trace operator on GHom TLA+ TracedMonoidal.tla invariant InvTracedMonoidal + Lean theorem TracedMonoidal.traced_monoidal in TracedMonoidal.lean Mechanized
THM-TRACE-ITERATION The trace operator models bounded iteration: Tr(f)(a) produces the same result as traceIter(f, a, fuel) for any fuel. Connects the categorical trace to computational iteration. type variables; fuel parameter TLA+ TracedMonoidal.tla invariant InvIteration + Lean theorem TracedMonoidal.trace_iteration_equiv in TracedMonoidal.lean Mechanized

Failure Theory: Collapse, Cost, and Control

The no-free-collapse family: trilemma, composition, universality, minimum cost floors, tightness, controller, Pareto frontier, failure entropy, failure durability, and failure families.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-FAIL-ENTROPY Structured failure reduces a live-frontier entropy proxy, collapse from a forked frontier to one survivor requires at least one failed branch, and coupled repair debt preserves or reverses that reduction finite live-frontier width; local vent count bounded by the frontier; repair debt modeled as post-vent branch reintroduction; entropy proxy = livePaths - 1 TLA+ FailureEntropy.tla invariants (InvStructuredFailureConservesMass, InvStructuredFailureReducesWidth, InvStructuredFailureReducesEntropy, InvStructuralErrorgleSurvivorNeedsFailure, InvCoupledFailurePreservesWidth, InvCoupledFailurePreservesEntropy, InvCoupledFailureStrictWhenRepairExceedsVented) + Lean theorems FailureEntropy.structured_failure_conserves_frontier_mass, FailureEntropy.structured_failure_reduces_entropy_proxy, FailureEntropy.success_from_forked_frontier_requires_failure, FailureEntropy.coupled_failure_preserves_or_increases_entropy_proxy, and FailureEntropy.coupled_failure_strictly_increases_entropy_proxy Mechanized
THM-FAIL-FAMILIES Failure topology splits into branch-isolating failure, which preserves deterministic fold on the survivor projection and carries zero repair debt, and contagious failure, which forces positive repair debt and breaks projected/observed fold agreement finite branch snapshots; survivor projection keeps pre-failure outputs on post-failure survivors; contagious failure means a surviving branch changes output after failure; repair debt counts surviving branches whose outputs changed TLA+ FailureFamilies.tla invariants (InvWellFormed, InvBranchIsolatingPreservesDeterministicFold, InvBranchIsolatingRepairDebtZero, InvContagiousFailureForcesRepairDebt, InvContagiousFailureBreaksDeterministicFold) + Lean theorems FailureFamilies.branch_isolating_preserves_deterministic_fold, FailureFamilies.branch_isolating_has_zero_repair_debt, FailureFamilies.branch_isolating_blocks_contagion, and FailureFamilies.contagious_failure_forces_repair_debt Mechanized
THM-FAIL-DURABILITY Bounded branch-isolating failures preserve quorum durability and, once failures are exhausted, weakly fair repair returns the system to the fully repaired stable state finite replica set; isolated single-replica failures only; explicit failure budget f < n; repair restores one missing replica at a time; repair action is weakly fair once enabled; no new failures after the budget is exhausted TLA+ FailureDurability.tla invariants (InvWellFormed, InvReplicaMassConserved, InvRepairDebtBounded, InvQuorumDurability, InvPositiveLive) + liveness property PropFailureExhaustionLeadsToStable + Lean theorems FailureDurability.durable_live_count_ge_quorum, FailureDurability.durable_live_count_positive, FailureDurability.repair_closure_preserves_replica_mass, and FailureDurability.repair_closure_stable_of_exhausted_failures Mechanized
THM-FAIL-TRILEMMA A nontrivial fork cannot collapse to a deterministic single-survivor fold for free: zero vent plus zero repair debt precludes deterministic collapse, so any deterministic single-survivor collapse must pay either vented loss or repair debt; contagious failure in the zero-vent regime preserves branch mass and still forces debt aligned branch snapshots; nontrivial fork means more than one live branch before collapse; deterministic collapse means survivor-projected fold agreement plus exactly one live survivor; zero waste means zero vented branches and zero repair debt TLA+ FailureTrilemma.tla invariants (InvZeroVentPreservesBranchMass, InvNoFreeDeterministicCollapse, InvDeterministicStructuralErrorgleSurvivorRequiresWaste, InvContagiousFailureNotEntropyFree, InvGlobalContagionPreservesBranchMassAndForcesDebt) + Lean theorems FailureTrilemma.zero_vent_preserves_live_branch_lower_bound, FailureTrilemma.zero_vent_precludes_single_survivor_collapse, FailureTrilemma.nontrivial_fork_no_waste_precludes_deterministic_collapse, FailureTrilemma.deterministic_single_survivor_collapse_requires_waste, FailureTrilemma.contagious_failure_cannot_be_entropy_free, and FailureTrilemma.contagious_global_recovery_preserves_branch_mass_and_forces_debt Mechanized
THM-FAIL-COMPOSITION The no-free-collapse boundary composes across stages: once a pipeline starts from a nontrivial fork, stagewise zero vent and zero repair debt cannot end in a deterministic single-survivor collapse, so any such global collapse must accumulate vent or debt and therefore contains at least one paid stage aligned stage snapshots; nontrivial fork means more than one live branch in the initial stage; terminal deterministic collapse means survivor-projected fold agreement plus exactly one live survivor at the pipeline end; total vent and total repair debt sum adjacent-stage costs over the chain TLA+ FailureComposition.tla invariants (InvStagewiseZeroVentPreservesBranchMass, InvNoFreePipelineCollapse, InvPipelineCollapseRequiresGlobalWaste, InvPipelineCollapseRequiresPaidStage, InvContagionCannotStayFreeAcrossPipeline) + Lean theorems FailureComposition.pipeline_zero_vent_preserves_live_branch_lower_bound, FailureComposition.pipeline_no_waste_precludes_deterministic_collapse, FailureComposition.pipeline_deterministic_collapse_requires_waste, and FailureComposition.pipeline_deterministic_collapse_requires_waste_stage Mechanized
THM-FAIL-UNIVERSAL The no-free-collapse boundary survives normalization to persistent branch identity and arbitrary depth: any nontrivial sparse choice system, and therefore any finite prefix of an arbitrary-depth recovery trajectory, cannot realize deterministic fold with both zero total vent and zero total repair debt; if deterministic collapse occurs, some stage in the prefix pays the cost sparse branch observations normalize onto a persistent finite branch-ID support; deterministic collapse is checked on the normalized survivor projection; arbitrary depth is represented by taking any finite prefix of a recovery trajectory; total vent and total repair debt sum normalized adjacent-stage costs TLA+ FailureUniversality.tla invariants (InvZeroVentPreservesBranchMassAtAnyDepth, InvNoFreeDeterministicCollapseAtAnyDepth, InvDeterministicCollapseRequiresGlobalWaste, InvDeterministicCollapseRequiresPaidStage, InvDistributedRepairDebtCannotStayFree) + Lean theorems FailureUniversality.ChoiceSystem.trilemma, FailureUniversality.ChoiceSystem.deterministic_collapse_requires_waste, FailureUniversality.ChoiceSystem.deterministic_collapse_requires_paid_stage, FailureUniversality.ChoiceTrajectory.collapse_at_depth_requires_waste, FailureUniversality.ChoiceTrajectory.collapse_at_depth_requires_paid_stage, and FailureUniversality.ChoiceTrajectory.no_depth_realizes_free_deterministic_collapse Mechanized
THM-FAIL-MINCOST Deterministic collapse has a minimum cost floor: for any normalized sparse choice system or finite prefix of an arbitrary-depth recovery trajectory, collapsing from an initial fork to one survivor requires at least initialLive - 1 vented branches, and therefore totalVented + totalRepairDebt >= initialLive - 1 same persistent-branch normalization as THM-FAIL-UNIVERSAL; deterministic collapse means exactly one terminal survivor; vented count sums all live-to-dead losses across the trajectory; total cost is totalVented + totalRepairDebt TLA+ FailureUniversality.tla invariants (InvVentedEqualsForkWidthGap, InvDeterministicCollapseRequiresVentFloor, InvDeterministicCollapseRequiresCostFloor) + Lean theorems FailureComposition.live_branch_count_le_after_plus_vented, FailureComposition.pipeline_vented_covers_live_branch_loss, FailureUniversality.ChoiceSystem.deterministic_collapse_vented_lower_bound, FailureUniversality.ChoiceSystem.deterministic_collapse_cost_lower_bound, FailureUniversality.ChoiceTrajectory.collapse_at_depth_vented_lower_bound, FailureUniversality.ChoiceTrajectory.collapse_at_depth_cost_lower_bound, and FailureUniversality.ChoiceTrajectory.no_depth_beats_fork_cost_floor Mechanized
THM-FAIL-LANDAUER-BOUNDARY The thermodynamic bridge now spans finite, countable-support, measurable finite-type, observable-pushforward, and effective-support layers. For an equiprobable live frontier, a vented branch carries self-information exactly equal to the frontier Shannon entropy in bits; more generally, every finite branch law on a nonempty finite support carries Shannon entropy at most the equiprobable frontier entropy and therefore at most the deterministic-collapse failure-tax floor from THM-FAIL-MINCOST; equality with that finite entropy ceiling occurs exactly for the uniform law on the given support; equality with the failure-tax floor occurs exactly for the uniform law on one- or two-branch supports; and every achievable deterministic collapse of the same finite frontier cardinality therefore pays at least the corresponding Landauer heat budget. On the nontrivial binary surface this sharp finite equality reduces to the fair binary fork witness, where the exact kT ln 2 equality appears. Beyond the finite bridge, the package carries a countable-support entropy shell for arbitrary PMFs (nonnegative Shannon entropy as ENNReal tsum, supremum of finite truncations, counting-measure lintegral on countable measurable types, and finite-type collapse), a matching countable-support heat shell (direct ENNReal Landauer heat in nats, again with finite-truncation iSup, counting-measure lintegral, and finite-type collapse), a direct measurable finite-type shell, an observable pushforward shell, and an effective-support layer: for any PMF on any type whose support is contained in a finite Finset s, the ENNReal entropy is bounded by the frontier entropy log₂(s.card) and by the failure tax s.card - 1, the Landauer heat is bounded by the failure-tax heat budget, and the Landauer heat is bounded by the Landauer heat of any achievable collapse cost. That effective-support layer now also composes with deterministic observables: if the source PMF is supported on s, then any observable pushforward has entropy and Landauer heat bounded above by the source law itself and therefore inherits the same source-support frontier, failure-tax, and achievable-collapse heat bounds without requiring measurable structure on the codomain. This closes the measurable erasure gap for arbitrary branch laws with finite effective support without requiring the ambient type to be a Fintype positive finite live frontier; equiprobable branch mass 1 / liveBranches; finite non-uniform branch laws represented as PMF α over a nonempty finite type; Shannon entropy measured in bits; binary branch law given by branchProbability; Bernoulli entropy bound uses 0 ≤ branchProbability ≤ 1; deterministic-collapse comparison for an arbitrary finite branch law identifies Fintype.card α with the live frontier width; deterministic-collapse cost is measured in the existing failure-tax units; the finite entropy-equality characterization compares branch laws against PMF.uniformOfFintype α, and the failure-tax equality characterization additionally isolates the cardinalities 1 and 2; the countable-support counting-measure formulation additionally assumes a measurable space with countable carrier and measurable singletons; the observable pushforward shell additionally assumes a measurable source/codomain when identifying observable branch mass with measurable fiber probability, a countable measurable codomain with measurable singletons for the counting-measure formulas, and a nonempty finite observable codomain for the sharp failure-tax/heat equalities; the effective-support theorems assume a Finset s with ∀ a, a ∉ s → branchLaw a = 0 and s.Nonempty, and bound entropy/heat by s.card-indexed frontier/tax quantities; the effective-support observable monotonicity theorems additionally assume DecidableEq β and an arbitrary observable observable : α → β; Landauer calibration uses nonnegative Boltzmann constant and temperature, and the finite/binary heat equality characterizations use positive Boltzmann constant and temperature Lean theorems LandauerBuley.uniform_branch_self_information_bits_eq_frontier_entropy_bits, LandauerBuley.finite_branch_entropy_nats_le_log_card, LandauerBuley.finite_branch_entropy_nats_eq_log_card_iff, LandauerBuley.finite_branch_entropy_bits_le_frontier_entropy_bits, LandauerBuley.finite_branch_entropy_bits_eq_frontier_entropy_bits_iff, LandauerBuley.frontier_entropy_bits_eq_failure_tax_iff, LandauerBuley.finite_branch_entropy_bits_le_failure_tax, LandauerBuley.finite_branch_entropy_bits_eq_failure_tax_iff, LandauerBuley.countable_branch_entropy_natsENN_eq_iSup_truncated, LandauerBuley.countable_branch_entropy_natsENN_eq_count_lintegral, LandauerBuley.countable_branch_entropy_natsENN_eq_finite, LandauerBuley.countable_branch_entropy_bitsENN_eq_finite, LandauerBuley.countable_branch_entropy_bitsENN_eq_frontier_entropy_bits_iff, LandauerBuley.countable_branch_entropy_bitsENN_le_frontier_entropy_bits, LandauerBuley.countable_branch_entropy_bitsENN_eq_failure_tax_iff, LandauerBuley.countable_branch_entropy_bitsENN_le_failure_tax, LandauerBuley.truncated_landauer_heat_lower_boundENN_le_countable, LandauerBuley.countable_landauer_heat_lower_boundENN_eq_iSup_truncated, LandauerBuley.countable_landauer_heat_lower_boundENN_eq_count_lintegral, LandauerBuley.countable_landauer_heat_lower_boundENN_eq_count_lintegral_of_nonneg, LandauerBuley.observed_branch_mass_eq_fiber_measure, LandauerBuley.observed_branch_entropy_natsENN_eq_iSup_truncated, LandauerBuley.observed_branch_entropy_natsENN_eq_count_lintegral, LandauerBuley.observed_landauer_heat_lower_boundENN_eq_iSup_truncated, LandauerBuley.observed_landauer_heat_lower_boundENN_eq_count_lintegral, LandauerBuley.observed_branch_entropy_bitsENN_eq_finite, LandauerBuley.observed_branch_entropy_bitsENN_le_frontier_entropy_bits, LandauerBuley.observed_branch_entropy_bitsENN_le_failure_tax, LandauerBuley.observed_branch_entropy_bitsENN_eq_failure_tax_iff, LandauerBuley.observed_landauer_heat_lower_boundENN_eq_finite, LandauerBuley.observed_landauer_heat_le_failure_tax_budget, LandauerBuley.observed_landauer_heat_eq_failure_tax_budget_iff, LandauerBuley.observed_collapse_landauer_heat_le_total_cost, LandauerBuley.effective_support_entropy_natsENN_le_log_card, LandauerBuley.effective_support_entropy_bitsENN_le_frontier_entropy_bits, LandauerBuley.effective_support_entropy_bitsENN_le_failure_tax, LandauerBuley.effective_support_landauer_heat_le_failure_tax_budget, LandauerBuley.effective_support_collapse_landauer_heat_le_total_cost, LandauerBuley.effective_support_observed_entropy_natsENN_le_source, LandauerBuley.effective_support_observed_entropy_bitsENN_le_source, LandauerBuley.effective_support_observed_entropy_bitsENN_le_frontier_entropy_bits, LandauerBuley.effective_support_observed_entropy_bitsENN_le_failure_tax, LandauerBuley.effective_support_observed_landauer_heat_le_source, LandauerBuley.effective_support_observed_landauer_heat_le_failure_tax_budget, LandauerBuley.effective_support_observed_collapse_landauer_heat_le_total_cost, LandauerBuley.binary_branch_entropy_bits_le_failure_tax, LandauerBuley.binary_branch_entropy_bits_eq_failure_tax_iff, LandauerBuley.binary_failure_tax_matches_entropy_bits, LandauerBuley.achievable_collapse_entropy_bits_le_total_cost, LandauerBuley.achievable_collapse_finite_entropy_bits_le_total_cost, LandauerBuley.landauer_heat_le_failure_tax_heat_budget, LandauerBuley.finite_landauer_heat_le_failure_tax_budget, LandauerBuley.finite_landauer_heat_eq_failure_tax_budget_iff, LandauerBuley.binary_landauer_heat_le_failure_tax_budget, LandauerBuley.binary_landauer_heat_eq_failure_tax_budget_iff, LandauerBuley.binary_landauer_heat_matches_failure_tax_budget, LandauerBuley.achievable_collapse_landauer_heat_le_total_cost, LandauerBuley.achievable_collapse_finite_entropy_landauer_heat_le_total_cost, LandauerBuley.countable_landauer_heat_lower_boundENN_eq_finite, LandauerBuley.countable_landauer_heat_le_failure_tax_budget, LandauerBuley.countable_landauer_heat_eq_failure_tax_budget_iff, and LandauerBuley.countable_collapse_landauer_heat_le_total_cost Mechanized
THM-FAIL-TIGHTNESS The deterministic-collapse cost floor is tight: for any positive-live normalized start state there exists a branch-isolating single-survivor collapse witness with zero repair debt and exact cost initialLive - 1, so the exact minimum deterministic-collapse cost is initialLive - 1 positive initial live branch count; collapse witness preserves exactly one surviving output, vents every other live branch, and is measured over aligned finite recovery pipelines on the normalized state space TLA+ FailureUniversality.tla invariants (InvCanonicalWitnessWellFormed, InvCanonicalWitnessDeterministicCollapse, InvCanonicalWitnessZeroRepairDebt, InvCanonicalWitnessAttainsVentFloor, InvCanonicalWitnessAttainsCostFloor) + Lean theorems FailureUniversality.collapseWitness_deterministic_collapse, FailureUniversality.collapseWitness_vented_cost_exact, FailureUniversality.collapseWitness_total_cost_exact, FailureUniversality.collapse_cost_floor_attainable, FailureUniversality.collapse_cost_floor_exact, FailureUniversality.ChoiceSystem.exact_collapse_cost_floor, and FailureUniversality.ChoiceTrajectory.prefix_exact_collapse_cost_floor Mechanized
THM-FAIL-CTRL Over the three canonical failure actions keep-multiplicity, pay-vent, and pay-repair, the score-minimizing controller chooses the action with the smallest weighted coefficient against the exact collapse floor liveBranches - 1, so the same lower bound from THM-FAIL-MINCOST becomes the stagewise controller cost base canonical action family only; objective is alpha * wallace + beta * buley + gamma * vent + delta * repair; canonical keep score is (alpha + beta) * (liveBranches - 1); canonical vent score is gamma * (liveBranches - 1); canonical repair score is (beta + delta) * (liveBranches - 1); branch-isolating tightness supplies an achievable exact vent floor TLA+ FailureController.tla invariants (InvChosenScoreMinimal, InvKeepOptimalWhenCoefficientMinimal, InvVentOptimalWhenCoefficientMinimal, InvRepairOptimalWhenCoefficientMinimal) + Lean theorems FailureController.branch_isolating_floor_achievable_from_live_count, FailureController.choose_keep_when_keep_coefficient_min, FailureController.choose_vent_when_vent_coefficient_min, FailureController.choose_repair_when_repair_coefficient_min, and FailureController.chosen_failure_action_score_minimal Mechanized
THM-FAIL-CTRL-TIES Failure-controller ties are deterministic: any tie involving keep-multiplicity resolves to keep-multiplicity, and a pay-vent/pay-repair tie resolves to pay-vent, so pay-repair appears only when it is strictly smaller than both earlier coefficients canonical action family only; branch order in chooseFailureAction is keep-multiplicity, then pay-vent, then pay-repair; equal scores come from equal weighted coefficients against the same collapse floor Lean theorems ControllerTieBreaking.choose_keep_on_keep_vent_tie, ControllerTieBreaking.choose_keep_on_keep_repair_tie, ControllerTieBreaking.choose_keep_on_total_tie, ControllerTieBreaking.total_tie_not_pay_vent, ControllerTieBreaking.total_tie_not_pay_repair, ControllerTieBreaking.choose_vent_on_vent_repair_tie, ControllerTieBreaking.vent_repair_tie_not_pay_repair, ControllerTieBreaking.choose_not_keep_iff_keep_coefficient_not_minimal, and ControllerTieBreaking.choose_not_pay_repair_iff_repair_not_strictly_minimal in ControllerTieBreaking.lean Mechanized
THM-FAIL-PARETO Over the canonical failure-action family, the three legal outcomes form a Pareto frontier: keep-multiplicity, pay-vent, and pay-repair are pairwise non-dominating whenever liveBranches > 1, so there is no single canonical action that improves Wallace, Buley, vent cost, and repair debt simultaneously canonical action family only; objectives are minimized componentwise on (wallace, buley, ventCost, repairDebt); canonical keep point is (gap, gap, 0, 0); canonical vent point is (0, 0, gap, 0); canonical repair point is (0, gap, 0, gap) with gap = liveBranches - 1 > 0 TLA+ FailurePareto.tla invariants (InvKeepNondominated, InvVentNondominated, InvRepairNondominated) + Lean theorems FailurePareto.keep_is_pareto_optimal, FailurePareto.pay_vent_is_pareto_optimal, FailurePareto.pay_repair_is_pareto_optimal, and FailurePareto.canonical_failure_actions_are_pareto Mechanized
THM-FAILURE-ENTROPY Structured failure conserves frontier mass, reduces frontier width with venting, reduces entropy proxy, and forked frontier collapses to single survivor under binary race convergence aligned branch snapshots; positive frontier mass Lean theorems FailureEntropy.structured_failure_conserves_frontier_mass, FailureEntropy.structured_failure_reduces_frontier_width, FailureEntropy.structured_failure_reduces_entropy_proxy, and FailureEntropy.forked_frontier_collapses_to_single_survivor in FailureEntropy.lean Mechanized
THM-FAILURE-DURABILITY Durable replica state: well-formed replicas maintain live count at or above quorum size and positive live count. Stable replica state tracks all-healthy invariant DurableWellFormed predicate; quorum size bounds TLA+ FailureDurability.tla invariants + Lean theorems FailureDurability.durable_live_count_ge_quorum and FailureDurability.durable_live_count_positive in FailureDurability.lean Mechanized
THM-FAILURE-FAMILIES Branch snapshot families with branch-isolating predicate, repair debt tracking, and contagious failure propagation. Structures for multipath failure analysis composing with the trilemma and composition theorems BranchSnapshot; deterministicFold; BranchIsolating; ContagiousFailure Lean definitions and structures in FailureFamilies.lean composing with FailureTrilemma.lean and FailureComposition.lean Mechanized

Thermodynamic Bridge: Erasure, Heat, and Information

Landauer boundary, data processing inequality, fold erasure/heat, coarsening thermodynamics, entropic refinement calculus, rate-distortion frontier, fold heat hierarchy, traced monoidal thermodynamics, enriched convergence, and infinite erasure.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-LANDAUER-EQUALITY-CHARACTERIZATION Frontier entropy equals failure tax if and only if liveBranches ≤ 2; for n ≥ 3, entropy is strictly less than failure tax. This sharpens the paper: the failure-tax floor strictly dominates entropy for all non-binary forks positive live branch count Lean theorems LandauerBuley.frontier_entropy_bits_eq_failure_tax_iff_le_two and LandauerBuley.frontier_entropy_bits_lt_failure_tax_of_three_or_more in LandauerBuley.lean Mechanized
THM-INFINITE-ERASURE For PMFs with genuinely infinite support (not Finset-coverable), the entropy-to-heat chain still holds because the chain only requires entropy positivity (≥ log 2 bits when ≥ 2 live branches), not finiteness. Any PMF with ≥ 2 support atoms has positive Shannon entropy, yielding positive Landauer heat. PMF with ≥ 2 distinct atoms of positive mass; Boltzmann constant > 0; temperature > 0 Lean theorems InfiniteErasure.entropy_positive_of_two_atoms, InfiniteErasure.landauer_heat_positive_of_two_atoms, InfiniteErasure.infinite_erasure_chain, and InfiniteErasure.observable_preserves_two_atoms Mechanized
THM-DATA-PROCESSING-INEQUALITY Strict data processing inequality for finite PMFs: H(f(X)) ≤ H(X) for any function f, with strict inequality H(f(X)) < H(X) when f is non-injective on the support. Conditional entropy H(X|f(X)) = H(X) - H(f(X)) is non-negative, strictly positive for non-injective f, and zero iff f is injective on the support. Chain rule: H(X|g∘f(X)) = H(X|f(X)) + H(f(X)|g(f(X))). ENNReal lifts for the effective-support shell. Fintype α, β; DecidableEq β; PMF α; function f : α → β; non-injectivity witnessed by two distinct elements with positive mass mapping to the same image Lean module DataProcessingInequality.lean with conditionalEntropyNats, data_processing_inequality, strict_data_processing_inequality, conditionalEntropyNats_nonneg, conditionalEntropyNats_pos_of_nonInjective, conditionalEntropyNats_eq_zero_iff_injective_on_support, conditionalEntropyNats_comp, conditionalEntropyNatsENN, and conditionalEntropyNatsENN_pos_of_nonInjective. Part of passing umbrella build. Mechanized (0 sorry)
THM-COARSENING-THERMODYNAMICS Landauer heat of network coarsening and the thermodynamic arrow of abstraction. Every non-trivial coarsening (many-to-one quotient) erases information, incurring Landauer heat ≥ kT ln 2 × information loss. Cumulative information erasure is monotone under composition (the arrow): further coarsening can only increase cumulative erasure. Strict monotonicity when the second coarsening is also non-trivial. Connects to ManyToOneGraphQuotient from InterferenceCoarsening. Fintype α, β, γ; DecidableEq β, γ; PMF α; quotient maps f : α → β, g : β → γ; Boltzmann constant > 0; temperature > 0; non-injectivity for strict results Lean module CoarseningThermodynamics.lean with coarseningInformationLoss, coarsening_information_loss_nonneg, coarsening_information_loss_pos_of_many_to_one, coarseningLandauerHeat, coarsening_landauer_heat_nonneg, coarsening_landauer_heat_pos_of_many_to_one, cumulative_coarsening_monotone, cumulative_coarsening_strict_monotone, cumulative_coarsening_heat_monotone. TLA+ cross-check CoarseningThermodynamics.tla. Part of passing umbrella build (8070 jobs, 0 sorry). Mechanized
THM-COARSENED-BEAUTY-FLOOR For systems that arose from non-trivial coarsening: zero topological deficit is the strict unique global minimum for every strict generalized-convex cost and every strict real monotone objective, WITHOUT Axiom TOC as an external assumption. The observable coupling is derived from the physical irreversibility of the coarsening step itself (Landauer heat of information erasure). The negative boundary (THM-BEAUTY-DEFICIT-ONLY-BOUNDARY) is not violated: optimality is not derived from deficit alone but from the coarsening history which provides the coupling for free. CoarsenedSystem: Boltzmann constant > 0, temperature > 0, fine PMF α, quotient map α → β, non-injectivity on support; LandauerBeautyFrontier for the derived coupling; BeautyStrictGeneralizedConvexCost or BeautyRealStrictObjective Lean module CoarseningThermodynamics.lean with structure CoarsenedSystem, definition coarsenedSystemObservableCoupling, theorems coarsened_system_heat_positive, coarsened_system_beauty_unconditional_floor, coarsened_system_beauty_unconditional_floor_objective. Part of passing umbrella build (8070 jobs, 0 sorry). Note: derives Axiom TOC as a theorem via identity coupling from coarsening physics. Mechanized
THM-ENTROPIC-REFINEMENT-CALCULUS Conditional entropy as a functorial information measure on the category of quotient refinements. Identity law: H(X|id(X)) = 0. Composition law (chain rule): H(X|g∘f(X)) = H(X|f(X)) + H(f(X)|g(f(X))). Monotonicity on the refinement lattice. Landauer heat naturality: heat decomposes additively under composition and inherits monotonicity. Universal property: conditional entropy is initial among information measures (sorry). Fintype α, β, γ; DecidableEq β, γ; PMF α; surjective quotient maps; InformationMeasure interface Lean module EntropicRefinementCalculus.lean with QuotientRefinementMorphism, InformationMeasure, conditionalEntropy_identity, conditionalEntropy_functorial_composition, conditionalEntropy_is_information_measure, refinement_monotone_information_loss, coarseningLandauerHeat_composition, coarseningLandauerHeat_monotone, QuotientRefines, coarsening_lattice_monotone, conditionalEntropy_initial_information_measure (conditional on entropy-domination hypotheses). Part of passing umbrella build (0 sorry). Mechanized (0 sorry; universal property conditional on entropy-domination hypotheses)
THM-RATE-DISTORTION-FRONTIER Rate-distortion frontier for network coarsening. Given a family of many-to-one quotients, there exists a minimum-rate member (minimum information erasure), a minimum-heat member (since heat = kT ln 2 * rate), and a Pareto-optimal quotient (not dominated in both rate and distortion). The minimum-rate quotient gives the weakest beauty constraint. Fintype α, β; DecidableEq β; PMF α; nonempty QuotientFamily; DistortionMeasure with monotonicity; Boltzmann constant > 0; temperature > 0 Lean module RateDistortionFrontier.lean with QuotientCandidate, DistortionMeasure, RateDistortionPoint, quotientToRateDistortionPoint, rate_distortion_heat_identity, QuotientFamily, minimum_rate_quotient_exists, minimum_heat_quotient_exists, rate_monotone_under_refinement, paretoDominated, pareto_frontier_exists, optimal_quotient_beauty_bound. Part of passing umbrella build (8070 jobs, 0 sorry). Mechanized
THM-ENRICHED-CONVERGENCE Reduces the convergence schema from 7 axioms to 5 by deriving A6 (forkRaceFoldAttractor) and A7 (noAlternativeInModelClass) from throughput landscape optimization. The throughput-maximal skeleton has both race and fold (A6), and is unique by selection pressure (A7). Connects to CoarsenedSystem: the optimal skeleton's fold is a many-to-one quotient incurring irreducible Landauer heat. ThroughputLandscape: non-empty skeleton list, energy bound, selection pressure (distinct scores imply distinct skeletons), FRF presence and dominance; ReducedConvergenceAssumptions (A1-A5) Lean module EnrichedConvergence.lean with MonoidalSkeleton, forkRaceFoldSkeleton, ThroughputLandscape, throughput_maximum_exists, throughput_maximum_unique_score, frf_is_attractor, ReducedConvergenceAssumptions, reduced_convergence_implies_original, reduced_convergence_schema, optimal_skeleton_coarsening_heat. Part of passing umbrella build (0 sorry). Mechanized (0 sorry)
THM-FOLD-ERASURE Any fold on ≥ 2 branches with a non-injective merge erases information: H(inputs | output) > 0. Composes conditionalEntropyNats_pos_of_nonInjective from the strict data processing inequality. Fintype α, β; DecidableEq α, β; PMF α; non-injective fold merge f : α → β witnessed by two distinct elements with positive mass mapping to same image TLA+ FoldErasure.tla invariant InvFoldErasesInformation + Lean theorem FoldErasure.fold_erasure in FoldErasure.lean Mechanized
THM-FOLD-HEAT Information erased by non-injective fold has Landauer heat cost ≥ kT ln 2 · H(inputs | output) > 0. Composes fold-erasure with the Landauer bridge. FoldErasureWitness with Boltzmann constant > 0, temperature > 0 TLA+ FoldErasure.tla invariant InvFoldHeatPositive + Lean theorem FoldErasure.fold_heat in FoldErasure.lean Mechanized
THM-ERASURE-COUPLING For systems where fold is many-to-one, construct a ThermodynamicObservableCoupling as a theorem (not axiom). Latency/waste floor maps derived from heat dissipation physics. The coupling is built from the fold erasure data: identity-scaled monotone maps with strict gap from positive Landauer heat. FoldErasureWitness with non-injective fold merge TLA+ FoldErasure.tla invariant InvErasureCouplingDerived + Lean definition FoldErasure.erasure_coupling and theorem FoldErasure.erasure_coupling_strict_gap in FoldErasure.lean Mechanized
THM-FOLD-INJECTIVITY-BOUNDARY Injective fold produces zero conditional entropy; the erasure coupling degenerates. This is the exact boundary of the erasure-sufficient regime: only injective folds (lossless merges) fall outside the unconditional beauty optimality surface. Fintype α, β; DecidableEq α, β; PMF α; injective fold merge on support TLA+ FoldErasure.tla invariant InvInjectiveBoundary + Lean theorems FoldErasure.fold_injectivity_boundary, FoldErasure.fold_injectivity_zero_heat, and FoldErasure.fold_injectivity_coupling_degenerates in FoldErasure.lean Mechanized

Beauty Optimality

Deficit-monotone beauty, latency/waste ordering, Pareto optimality, composition, monotone objectives/profiles, comparison families, failure-Pareto frontiers, deficit-only boundary, failure-tax bridges, Landauer beauty bridge, and unconditional floor.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-BEAUTY-DEF Bu beauty definition from deficit (deficitBu = β₁* - β₁, beautyBu = β₁* - deficitBu) non-negative Bu domains; bounded implementation deficit TLA+ BeautyOptimality.tla invariants + Lean schema Axioms.beauty_definition_schema + constructive linear-model theorems BeautyLinearWorkload.deficitA_eq, BeautyLinearWorkload.deficitB_eq, BeautyLinearWorkload.beautyA_eq, BeautyLinearWorkload.beautyB_eq, BeautyLinearWorkload.beautyA_eq_implementation, and BeautyLinearWorkload.beautyB_eq_implementation in BeautyOptimality.lean Mechanized (constructive linear model + scaffold)
THM-BEAUTY-LATENCY-MONO In the constructive linear workload model, lower Bu deficit implies non-worse latency, and positive latency penalty plus strict deficit separation gives strict latency separation; the broader manuscript claim remains available as a schema fixed workload; linear latency penalty in deficit; deficit order witness; strict form additionally requires positive latency penalty and strict deficit gap TLA+ BeautyOptimality.tla invariant InvBeautyLatencyMonotone + Lean schema Axioms.beauty_latency_monotone_schema + constructive theorems BeautyLinearWorkload.latency_monotone and BeautyLinearWorkload.strict_latency_monotone in BeautyOptimality.lean Mechanized (constructive linear model + scaffold)
THM-BEAUTY-WASTE-MONO In the constructive linear workload model, lower Bu deficit implies non-worse waste, and positive waste penalty plus strict deficit separation gives strict waste separation; the broader manuscript claim remains available as a schema fixed workload; linear waste penalty in deficit; deficit order witness; strict form additionally requires positive waste penalty and strict deficit gap TLA+ BeautyOptimality.tla invariant InvBeautyWasteMonotone + Lean schema Axioms.beauty_waste_monotone_schema + constructive theorems BeautyLinearWorkload.waste_monotone and BeautyLinearWorkload.strict_waste_monotone in BeautyOptimality.lean Mechanized (constructive linear model + scaffold)
THM-BEAUTY-PARETO In the constructive linear workload model, a zero-deficit candidate is Pareto-optimal in the latency/waste envelope, and under positive penalties a full-fit candidate strictly beats a positive-deficit comparator in latency, waste, and beauty; the broader manuscript claim remains available as a schema candidate A has deficitBu = 0; deficit ordering over compared implementations; linear latency/waste penalties in deficit; strict form additionally requires candidate A to match intrinsicBu, candidate B to have positive deficit, and positive latency/waste penalties TLA+ BeautyOptimality.tla invariant InvBeautyPareto + Lean schema Axioms.beauty_pareto_optimality_schema + constructive theorems BeautyLinearWorkload.zero_deficit_pareto, BeautyLinearWorkload.strict_beauty_monotone, and BeautyLinearWorkload.zero_deficit_strict_optimality in BeautyOptimality.lean Mechanized (constructive linear model + scaffold)
THM-BEAUTY-COMPOSITION In the constructive additive model, global Bu deficit composes additively from subsystem deficits additive composition model over pipeline/protocol/compression deficits TLA+ BeautyOptimality.tla invariant InvBeautyComposition + Lean schema Axioms.beauty_composition_schema + constructive theorem BeautyCompositionWitness.global_eq_sum in BeautyOptimality.lean Mechanized (constructive additive model + scaffold)
THM-BEAUTY-OPTIMALITY In the constructive linear/additive model, definition + monotonicity + Pareto + composition cohere; the broader manuscript claim remains available as a schema assumptions of THM-BEAUTY-DEF/LATENCY-MONO/WASTE-MONO/PARETO/COMPOSITION specialized to the constructive linear/additive witness TLA+ BeautyOptimality.tla invariant InvBeautyOptimality + Lean schema Axioms.beauty_optimality_schema + constructive theorems BeautyLinearOptimalityInstance.schema_instantiated and BeautyLinearOptimalityInstance.optimality in BeautyOptimality.lean Mechanized (constructive linear model + scaffold)
THM-BEAUTY-MONOTONE-OBJECTIVE In the constructive linear workload model, any componentwise monotone objective over latency and waste is deficit-monotone, so a zero-deficit candidate is never worse under arbitrary monotone nonlinear scoring; if the objective is strictly monotone in latency or waste, then a full-fit candidate strictly beats a strict underfit comparator whenever the corresponding penalty is positive fixed linear workload; objective score : Nat -> Nat -> Nat is monotone in both coordinates; strict form additionally requires strict monotonicity in latency or waste and a positive penalty on the strictly improved coordinate Lean structures/theorems BeautyMonotoneObjective, BeautyStrictObjective, BeautyLinearWorkload.objective_monotone, BeautyLinearWorkload.zero_deficit_objective_optimal, BeautyLinearWorkload.strict_objective_optimality_of_latency, BeautyLinearWorkload.strict_objective_optimality_of_waste, and BeautyLinearWorkload.strict_objective_optimality_of_positive_penalty in BeautyOptimality.lean Mechanized
THM-BEAUTY-MONOTONE-PROFILE The beauty layer no longer requires linear latency/waste penalties: for any workload whose latency and waste are arbitrary monotone functions of deficit, a zero-deficit candidate is never worse under any componentwise monotone objective or monotone generalized-convex cost; if either profile is strict, then full-fit strictly beats strict underfit for any strict monotone objective or strict generalized-convex cost fixed workload with arbitrary deficit-to-latency and deficit-to-waste maps; both profile maps are monotone in deficit; strict form additionally requires a strict latency or strict waste profile; generalized-convex cost theorems use the monotone field of BeautyGeneralizedConvexCost, and their strict form uses the strict monotonicity fields of BeautyStrictGeneralizedConvexCost Lean structures/theorems BeautyMonotoneProfileWorkload, BeautyGeneralizedConvexCost, BeautyStrictGeneralizedConvexCost, BeautyMonotoneProfileWorkload.objective_monotone, BeautyMonotoneProfileWorkload.generalized_convex_cost_monotone, BeautyMonotoneProfileWorkload.zero_deficit_objective_optimal, BeautyMonotoneProfileWorkload.zero_deficit_generalized_convex_cost_optimal, BeautyMonotoneProfileWorkload.strict_generalized_convex_cost_optimality_of_strict_latency_profile, BeautyMonotoneProfileWorkload.strict_generalized_convex_cost_optimality_of_strict_waste_profile, BeautyMonotoneProfileWorkload.strict_generalized_convex_cost_optimality_of_strict_profile, BeautyMonotoneProfileWorkload.strict_objective_optimality_of_strict_latency_profile, BeautyMonotoneProfileWorkload.strict_objective_optimality_of_strict_waste_profile, and BeautyMonotoneProfileWorkload.strict_objective_optimality_of_strict_profile in BeautyOptimality.lean Mechanized
THM-BEAUTY-COMPARISON-FAMILY A designated full-fit candidate in an indexed deficit-monotone comparison family is a global minimizer for every monotone generalized-convex cost, and under a strict latency or waste profile it is the unique minimizer for every strict generalized-convex cost indexed comparison family with a distinguished candidate best; all implementations are bounded by the same intrinsic Bu; best exactly matches intrinsicBu; every non-best candidate is strictly underfit; deficit-to-latency and deficit-to-waste maps are monotone; strict uniqueness additionally requires a strict latency or strict waste profile Lean structures/theorems BeautyMonotoneProfileFamily, BeautyMonotoneProfileFamily.comparisonWorkload, BeautyMonotoneProfileFamily.best_generalized_convex_cost_minimal, BeautyMonotoneProfileFamily.best_strict_generalized_convex_cost_optimality_of_strict_latency_profile, BeautyMonotoneProfileFamily.best_strict_generalized_convex_cost_optimality_of_strict_waste_profile, BeautyMonotoneProfileFamily.best_strict_generalized_convex_cost_optimality_of_strict_profile, BeautyMonotoneProfileFamily.best_generalized_convex_cost_unique_minimizer_of_strict_profile, and BeautyMonotoneProfileFamily.best_generalized_convex_cost_global_minimum_of_strict_profile in BeautyOptimality.lean Mechanized
THM-BEAUTY-UNIVERSAL-FLOOR On any failure Pareto frontier equipped with measure-theoretic latency/waste floor bounds, the zero-deficit floor point is a global minimizer for every monotone generalized-convex cost, and under strict generalized-convex monotonicity it is the strict unique global minimum abstract frontier of (Δβ, latency, waste) points; a distinguished floor point lies on the frontier with Δβ = 0; measure-side lower bounds place every frontier point above the floor in latency and waste; every positive-deficit frontier point is strictly above the floor in latency or waste; zero deficit is unique on the frontier Lean structures/theorems BeautyFailureParetoPoint, BeautyFailureParetoPoint.cost, BeautyFailureParetoFrontier, BeautyFailureParetoFrontier.floor_generalized_convex_cost_minimal, BeautyFailureParetoFrontier.floor_strict_generalized_convex_cost_optimality, BeautyFailureParetoFrontier.floor_strict_generalized_convex_cost_unique_minimizer, BeautyFailureParetoFrontier.floor_strict_generalized_convex_cost_global_minimum, and BeautyMonotoneProfileFamily.failureParetoFrontier in BeautyOptimality.lean Mechanized
THM-BEAUTY-REAL-OBJECTIVE The convexity hypothesis can also be dropped on the real-valued objective layer: arbitrary componentwise monotone real objectives admit the same zero-deficit/full-fit floor on monotone-profile workloads, indexed comparison families, and abstract failure Pareto frontiers; under strict monotonicity they yield strict unique minimizers under the existing strict-profile or frontier-gap hypotheses workload and family forms use arbitrary real-valued score : ℝ -> ℝ -> ℝ monotone in latency and waste; strict form additionally requires strict objective monotonicity and a strict latency or strict waste profile; frontier form additionally assumes an explicit failure Pareto frontier with zero-deficit floor, latency/waste floor bounds, strict floor gap on positive deficit, and zero-deficit uniqueness on the frontier Lean structures/theorems BeautyRealMonotoneObjective, BeautyRealStrictObjective, BeautyMonotoneProfileWorkload.real_objective_monotone, BeautyMonotoneProfileWorkload.zero_deficit_real_objective_optimal, BeautyMonotoneProfileWorkload.strict_real_objective_optimality_of_strict_latency_profile, BeautyMonotoneProfileWorkload.strict_real_objective_optimality_of_strict_waste_profile, BeautyMonotoneProfileWorkload.strict_real_objective_optimality_of_strict_profile, BeautyFailureParetoPoint.objectiveScore, BeautyFailureParetoFrontier.floor_objective_minimal, BeautyFailureParetoFrontier.floor_strict_objective_optimality, BeautyFailureParetoFrontier.floor_strict_objective_unique_minimizer, BeautyFailureParetoFrontier.floor_strict_objective_global_minimum, BeautyMonotoneProfileFamily.best_real_objective_minimal, BeautyMonotoneProfileFamily.best_real_objective_optimality_of_strict_latency_profile, BeautyMonotoneProfileFamily.best_real_objective_optimality_of_strict_waste_profile, BeautyMonotoneProfileFamily.best_real_objective_optimality_of_strict_profile, BeautyMonotoneProfileFamily.best_real_objective_unique_minimizer_of_strict_profile, and BeautyMonotoneProfileFamily.best_real_objective_global_minimum_of_strict_profile in BeautyOptimality.lean Mechanized
THM-BEAUTY-DEFICIT-ONLY-BOUNDARY Bare deficit bookkeeping does not force a zero-deficit latency/waste floor: there exists a zero-deficit point and a positive-deficit point with strictly lower latency and strictly lower waste, so the positive-deficit point also strictly beats the zero-deficit point for a strict monotone real objective and for a strict generalized-convex cost no monotone-profile assumptions, no frontier-floor assumptions, and no tax-to-observable bridge assumptions; witness points are the explicit two-point family floor = (Δβ = 0, latency = 1, waste = 1) and underfit = (Δβ = 1, latency = 0, waste = 0); witness objective/cost is latency + waste Lean namespace/theorems BeautyDeficitOnlyBoundary.exists_componentwise_improving_positive_deficit_point, BeautyDeficitOnlyBoundary.exists_positive_deficit_point_below_zero_deficit_for_real_objective, and BeautyDeficitOnlyBoundary.exists_positive_deficit_point_below_zero_deficit_for_generalized_convex_cost in BeautyOptimality.lean Mechanized
THM-BEAUTY-DEFICIT-TAX-BRIDGE The failure-tax bridge now has a quantitative deficit-dominating form: if a frontier carries a failure tax τ with (Δβ : ℝ) ≤ τ pointwise, monotone observable floor maps convert that tax into latency/waste lower bounds with a strict positive-tax gap, and the zero-deficit floor point is unique, then the zero-deficit floor is a global minimizer for every monotone generalized-convex cost and every monotone real objective, and under strict monotonicity it is the strict unique global minimum abstract failure Pareto frontier point set; failure-tax map τ; tax floor τ(floor) = 0; pointwise domination (Δβ : ℝ) ≤ τ; monotone observable maps latencyFloorFromTax, wasteFloorFromTax; pointwise lower bounds from those observables to actual latency/waste; positive tax yields a strict observable gap in latency or waste; zero deficit is unique on the frontier Lean structures/theorems BeautyDeficitDominatingFailureTaxFrontier, BeautyDeficitDominatingFailureTaxFrontier.toFailureTaxObservableFrontier, BeautyDeficitDominatingFailureTaxFrontier.floor_generalized_convex_cost_minimal, BeautyDeficitDominatingFailureTaxFrontier.floor_objective_minimal, BeautyDeficitDominatingFailureTaxFrontier.floor_strict_generalized_convex_cost_optimality, BeautyDeficitDominatingFailureTaxFrontier.floor_strict_objective_optimality, BeautyDeficitDominatingFailureTaxFrontier.floor_strict_generalized_convex_cost_global_minimum, and BeautyDeficitDominatingFailureTaxFrontier.floor_strict_objective_global_minimum in BeautyOptimality.lean Mechanized
THM-BEAUTY-FAILURE-TAX-BRIDGE The missing beauty bridge is now explicit and mechanized as an interface theorem: if a frontier carries a nonnegative failure tax whose zero point is the floor, positive deficit forces positive tax, and monotone observable floor maps convert that tax into latency/waste lower bounds with a strict positive-tax gap, then the same zero-deficit floor is a global minimizer for every monotone generalized-convex cost and every monotone real objective, and under strict monotonicity it is the strict unique global minimum abstract failure Pareto frontier point set; failure-tax map τ; tax floor τ(floor) = 0; nonnegative tax on the frontier; positive deficit implies positive tax; monotone observable maps latencyFloorFromTax, wasteFloorFromTax; pointwise lower bounds from those observables to actual latency/waste; positive tax yields a strict observable gap in latency or waste; zero deficit is unique on the frontier Lean structures/theorems BeautyFailureTaxObservableFrontier, BeautyFailureTaxObservableFrontier.toFailureParetoFrontier, BeautyFailureTaxObservableFrontier.floor_generalized_convex_cost_minimal, BeautyFailureTaxObservableFrontier.floor_objective_minimal, BeautyFailureTaxObservableFrontier.floor_strict_generalized_convex_cost_optimality, BeautyFailureTaxObservableFrontier.floor_strict_objective_optimality, BeautyFailureTaxObservableFrontier.floor_strict_generalized_convex_cost_global_minimum, and BeautyFailureTaxObservableFrontier.floor_strict_objective_global_minimum in BeautyOptimality.lean Mechanized
THM-BEAUTY-BRIDGE-INSTANCE The bridge layers now have concrete inhabitants from the existing beauty layer: every indexed strict-profile beauty family instantiates the quantitative deficit-dominating bridge by taking τ = Δβ and using a one-step observable floor on the strict coordinate, and therefore also instantiates the failure-tax observable bridge by forgetful projection, so the comparison-family strict-optimality surface factors through the bridge abstraction rather than bypassing it indexed comparison family with distinguished full-fit candidate best; all implementations are bounded by the same intrinsic Bu; every non-best candidate is strictly underfit; latency and waste are monotone in deficit; one coordinate is strictly monotone in deficit; the bridge instance uses τ(point) = point.deficit, oneStepFloor base τ = base + 1_{τ>0} on the strict coordinate, a constant floor on the non-strict coordinate, and the quantitative domination law (Δβ : ℝ) ≤ τ by reflexivity Lean definitions/theorems BeautyFailureTaxObservableFrontier.oneStepFloor, BeautyFailureTaxObservableFrontier.oneStepFloor_monotone, BeautyFailureTaxObservableFrontier.oneStepFloor_eq_base_at_zero, BeautyFailureTaxObservableFrontier.oneStepFloor_strict_of_pos, BeautyMonotoneProfileFamily.deficitDominatingFailureTaxFrontierOfStrictLatencyProfile, BeautyMonotoneProfileFamily.deficitDominatingFailureTaxFrontierOfStrictWasteProfile, BeautyMonotoneProfileFamily.failureTaxObservableFrontierOfStrictLatencyProfile, and BeautyMonotoneProfileFamily.failureTaxObservableFrontierOfStrictWasteProfile in BeautyOptimality.lean Mechanized
THM-BEAUTY-UNCONDITIONAL-FLOOR Under the physically motivated assumption that Landauer erasure heat is observable through latency or waste (Axiom TOC, ThermodynamicObservableCoupling), zero topological deficit is the unique beauty optimum for every strict generalized-convex cost and every strict real monotone objective on any Landauer beauty frontier. This assumption cannot be dropped (THM-BEAUTY-DEFICIT-ONLY-BOUNDARY, the negative boundary). Axiom TOC: ThermodynamicObservableCoupling encoding kB > 0, T > 0, monotone latencyFromHeat/wasteFromHeat, and strict gap from positive heat; LandauerBeautyFrontier encoding frontier points, live-branch count, positive deficit → liveBranches ≥ 2, and pointwise latency/waste lower bounds from Landauer heat Lean structure ThermodynamicObservableCoupling, LandauerBeautyFrontier, landauer_beauty_frontier_to_observable_frontier, landauer_beauty_unconditional_floor, and landauer_beauty_unconditional_floor_objective in LandauerBeautyBridge.lean; TLA+ cross-check LandauerBeautyBridge.tla invariants (InvPositiveDeficitForcesPositiveTax, InvZeroDeficitFloorZeroTax, InvEntropyLeFailureTax, InvOneStepFloorMatchesCoupling, InvOneStepFloorZeroAtZero, InvStrictGapFromPositiveHeat) Mechanized (conditional on thermodynamic observable coupling)
THM-BEAUTY-ERASURE-SUFFICIENT For any fork/race/fold system with non-injective fold, beauty optimality holds unconditionally. Zero-deficit minimizes any monotone objective. Narrows the axiom gap: only injective-fold systems need Axiom TOC. StructuralErrorce almost all practical folds are many-to-one, beauty optimality is effectively unconditional. FoldErasureWitness; LandauerBeautyFrontier for the derived erasure coupling; BeautyStrictGeneralizedConvexCost or BeautyRealStrictObjective TLA+ FoldErasure.tla invariant InvBeautyFloorUnconditional + Lean theorem FoldErasure.beauty_erasure_sufficient in FoldErasure.lean Mechanized

Covering Space & Topological Deficit (Track Theta)

Covering-space causality, matched topology, deficit-latency separation, capacity gap, information loss, erasure chain, zero-deficit preservation, and monotonicity.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-COVERING-CAUSALITY If β₁(computation) > 0 and β₁(transport) = 0 (TCP-style single ordered stream), there exists a reachable state where loss on path pⱼ stalls progress on independent path pᵢ. Constructive blocking witness from topological mismatch. pathCount ≥ 2; TCP transport (1 stream); independent computation paths TLA+ CoveringSpaceCausality.tla invariants (InvDeficitImpliesBlockingPossible, InvComputationBeta1, InvTcpBeta1Zero) + Lean theorems CoveringSpaceCausality.covering_causality and CoveringSpaceCausality.blockingWitnessFromMismatch Mechanized
THM-COVERING-MATCH If β₁(transport) ≥ β₁(computation), no cross-path blocking state is reachable. Each path maps to its own transport stream (covering map is injective). pathCount = transportStreams (matched topology) TLA+ CoveringSpaceMatch.tla invariants (InvNoCrossPathBlocking, InvNoForeignBlocking, InvZeroDeficit) + Lean theorems CoveringSpaceCausality.covering_match, CoveringSpaceCausality.matched_paths_isolated, and CoveringSpaceCausality.frame_header_is_covering_map Mechanized
THM-DEFICIT-LATENCY-SEPARATION Topological deficit Δ = β₁(G) - β₁(transport) lower-bounds worst-case latency inflation. TCP deficit equals pathCount - 1. Deficit is monotonically decreasing in transport stream count. Positive deficit implies inflation > 1. pathCount ≥ 2; transportStreams ≥ 1 TLA+ CoveringSpaceCausality.tla invariant InvDeficitBoundsInflation + Lean theorems CoveringSpaceCausality.deficit_latency_separation, CoveringSpaceCausality.tcp_deficit_is_path_count_minus_one, CoveringSpaceCausality.deficit_decreasing_in_streams, ProtocolDeficitLatency.positive_deficit_implies_inflation, and ProtocolDeficitLatency.deficit_beauty_chain Mechanized
THM-DEFICIT-CAPACITY-GAP For a system with k independent computation paths on m < k transport streams, the per-step information capacity gap is ≥ (k - m) · c_min where c_min is the minimum per-stream capacity. Quantifies "wasted parallelism" as capacity deficit. pathCount, streamCount with deficit > 0; per-stream capacity > 0 TLA+ DeficitCapacity.tla invariant InvCapacityGap + Lean theorem DeficitCapacity.deficit_capacity_gap in DeficitCapacity.lean Mechanized
THM-DEFICIT-INFORMATION-LOSS Topological deficit Δβ > 0 forces positive information loss under any multiplexing strategy. The multiplexing function is non-injective (pigeonhole), so by the data processing inequality, information is erased. Composes covering_causality with DPI. pathCount ≥ 2; single transport stream TLA+ DeficitCapacity.tla invariant InvInformationLoss + Lean theorem DeficitCapacity.deficit_information_loss in DeficitCapacity.lean Mechanized
THM-DEFICIT-ERASURE-CHAIN Full chain from topology to thermodynamics: deficit → pigeonhole collision → information erasure → Landauer heat → observable waste. Composes deficit_information_loss with fold_erasure and fold_heat. DeficitCapacityWitness + FoldErasureWitness; pathCount ≥ 2 TLA+ DeficitCapacity.tla invariant InvErasureChain + Lean theorem DeficitCapacity.deficit_erasure_chain in DeficitCapacity.lean Mechanized
THM-ZERO-DEFICIT-PRESERVES-INFORMATION When Δβ = 0 (streams ≥ paths), there exists a multiplexing strategy achieving lossless transport. Each path gets its own stream; the multiplexing function is injective. pathCount > 0; streamCount ≥ pathCount TLA+ DeficitCapacity.tla invariant InvZeroDeficit + Lean theorem DeficitCapacity.zero_deficit_preserves_information in DeficitCapacity.lean Mechanized
THM-DEFICIT-MONOTONE-IN-STREAMS Information loss under optimal multiplexing is monotonically decreasing in transport stream count, reaching zero when m ≥ k. Adding transport streams can only reduce deficit. pathCount, two stream counts with s1 ≤ s2 TLA+ DeficitCapacity.tla invariant InvMonotone + Lean theorem DeficitCapacity.deficit_monotone_in_streams in DeficitCapacity.lean Mechanized
THM-AEON-FLUX-SITE-ADEQUACY Positive-stream-budget Aeon Flux sites satisfy the full adequacy trichotomy in repo-native transport vocabulary: Δβ ≤ 0 iff a lossless FlowFrame transport witness exists, Δβ = 0 iff a tight lossless witness exists, and Δβ > 0 forces collisions and information loss for every FlowFrame transport witness. The emitted WallingtonRotation site path now synthesizes the matching pathCount / streamCount / Δβ witness directly from lowered GG. AeonFluxSite with 0 < streamCount; zero-deficit exactness additionally uses 0 < pathCount; emitted witness path currently scoped to lowered WallingtonRotation graphs Lean theorems AeonFluxSiteAdequacy.aeon_flux_site_nonpositive_deficit_iff_lossless_transport, AeonFluxSiteAdequacy.aeon_flux_site_zero_deficit_iff_tight_lossless_transport, and AeonFluxSiteAdequacy.aeon_flux_site_positive_deficit_forces_collision_and_information_loss in AeonFluxSiteAdequacy.lean + executable witness synthesis in open-source/gnosis/src/aeon-flux-site-witness.ts + GG proof topology open-source/gnosis/examples/proofs/AeonFluxSiteAdequacy-lean.gg Mechanized + executable

Protocol, Settlement & Band Gap

Protocol deficit ordering (TCP/QUIC/Aeon), settlement deficit, band gap, quantum deficit/speedup.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-Q-DEFICIT Quantum speedup identity in topology-matched regime sqrtN > 0; N = sqrtN^2; classical β₁=0; matched quantum implementation β₁=β₁* TLA+ transition model + Lean theorems Claims.quantum_deficit_is_zero and Claims.quantum_speedup_equals_classical_deficit_plus_one Mechanized
THM-Q-CORRESPONDENCE-BOUNDARY Path-integral correspondence is operationally exact only for linear full aggregation; nonlinear selection cannot preserve the same partition-additivity/order-invariance properties in general, and any non-additive fold must miss some cancellation-sensitive difference family, with winner-by-magnitude and early-stop missing the same x + (-x) family that linear fold realizes exactly minimal integer-valued fold model; linear fold = addition; nonlinear folds = winner-by-magnitude or early-stop selection; general class-level target family = fold(x, -y) = x - y; concrete witness family = x + (-x) executable src/quantum-correspondence-boundary.test.ts + src/quantum-recombination-ablation.test.ts/artifact runner + Lean theorems Claims.additive_fold_iff_cancellation_difference_family, Claims.nonadditive_fold_misses_cancellation_difference_family, Claims.linear_fold_partition_additive_global, Claims.linear_fold_preserves_cancellation_target_family, Claims.winner_selection_misses_cancellation_target_family, Claims.early_stop_misses_cancellation_target_family, Claims.winner_selection_not_partition_additive, Claims.early_stop_not_partition_additive, Claims.winner_selection_not_order_invariant, and Claims.early_stop_not_order_invariant Mechanized
THM-PROTO-DEFICIT TCP/QUIC/Aeon deficit ordering stream count > 1; topology equations for intrinsic/implementation Betti numbers TLA+ transition model + Lean theorem Claims.protocol_deficits Mechanized
THM-SETTLEMENT Settlement deficit (seq=2, parallel=0) intrinsic β₁* = 2; mode in {seq,parallel} TLA+ transition model + Lean theorem Claims.settlement_deficit_values Mechanized
THM-BANDGAP-BETA2 Band gap implies β₂ > 0 finite energy lattice; allowed set family with non-empty forbidden interior TLA+ transition model + Lean theorem Claims.band_gap_implies_beta2_positive Mechanized
THM-BAND-GAP-VOID Band gap as void positivity: an allowed energy band with forbidden zones tracks band gap existence and void positivity. When forbidden energies exist between boundary levels, Beta2 > 0 -- the void measures energy exclusion allowed is a subset of all energies; forbidden energies exist between 1 and MaxEnergy-1 TLA+ BandGapVoid.tla invariants (InvAllowedSubset, InvBandGapExists, InvVoidIsPositive) Model-checked
THM-PROTOCOL-DEFICIT Topological deficit across protocol families: TCP has deficit = streamCount - 1 (zero Beta1), QUIC has deficit = 0 (full Beta1), Flow has deficit = 0. The deficit measures how much multiplexing topology the protocol wastes streamCount > 1; IntrinsicBeta1 = streamCount - 1 TLA+ ProtocolDeficit.tla invariants (InvIntrinsicShape, InvTcpDeficit, InvQuicDeficit, InvFlowDeficit) + Lean theorems in ProtocolDeficitLatency.lean Mechanized
THM-QUANTUM-DEFICIT Quantum speedup through Beta1 elimination: N = rootN^2. Classical deficit = rootN - 1. Quantum deficit = 0. Sequential rounds = N, parallel rounds = rootN, speedup = N / rootN N is a perfect square; rootN > 0 TLA+ QuantumDeficit.tla invariants (InvPerfectSquare, InvClassicalDeficit, InvQuantumDeficitZero, InvSpeedup) Model-checked
THM-SETTLEMENT-DEFICIT Sequential settlement has deficit = 2, parallel settlement has deficit = 0. The topological deficit measures wasted parallelism in the settlement mode IntrinsicBeta1 = 2; mode in {seq, parallel} TLA+ SettlementDeficit.tla invariants (InvSequentialDeficitIsTwo, InvParallelDeficitIsZero) Model-checked

Pipeline Scheduling (Section 7)

Worthington whip, speculative tree, turbulent idle, pipeline occupancy, Wallace metric, multiplexing monotonicity, staged expansion, warmup efficiency/dynamics/controller, whip crossover, and multiplexing capacity.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-S7-WHIP Worthington Whip savings shape shard count s > 0 TLA+ transition model + Lean theorem Claims.worthington_num_lt_den Mechanized
THM-S7-SPEC Speculative Tree positivity constraints q > p; finite k > 0 TLA+ transition model + Lean theorems Claims.speculative_tree_numerator_positive and Claims.speculative_tree_denominator_positive Mechanized
THM-S7-TURB Turbulent idle fraction stays bounded n > 0, c > 0, finite domains TLA+ transition model + Lean theorems Claims.turbulent_idle_bounds and Claims.turbulent_idle_den_positive Mechanized
THM-S7-OCC Pipeline occupancy deficit is the complement of frontier fill and equals turbulent idle fraction in the canonical pipeline envelope n > 0, c > 0, finite domains TLA+ Section7Formulas.tla invariants (InvFrontierFillBounds, InvOccupancyDeficitBounds, InvOccupancyDeficitEqualsTurbulentIdle, InvOccupancyComplement) + executable topology helper checks Mechanized
THM-S7-WALLACE Wallace metric (wally) on a bounded three-layer frontier is bounded, complementary to frontier fill, zero exactly at full envelope occupancy, and reduces to 2(k-1)/(3k) on the symmetric diamond witness <<1,k,1>> positive layer widths; k > 0; bounded finite domains for the TLC model TLA+ WallaceMetric.tla invariants (InvWallaceBounds, InvWallaceComplement, InvWallaceZeroIffFull, InvDiamondClosedForm, InvDiamondZeroIffUnit) + Lean theorems Wallace.frontierArea3_le_envelopeArea3, Wallace.wallace_bounds3, Wallace.wallace_complement3, Wallace.wallace_zero_iff_full3, Wallace.diamond_wallace_closed_form, and Wallace.diamond_wallace_zero_iff_unit Mechanized
THM-S7-MUX-MONO Turbulent multiplexing monotonicity: with fixed useful work and legal recovered overlap, multiplexing cannot increase the Wallace metric and strictly lowers it when overlap is actually recovered positive busy work; sequential capacity at least busy work; recovered overlap bounded by slack (overlap <= seqCap - busy), which is the bounded occupancy image of branch isolation + deterministic fold preserving useful work TLA+ MultiplexingMonotonicity.tla invariants (InvWallaceNumeratorMonotone, InvFillMonotone, InvWallaceRatioMonotone, InvWallaceRatioStrictWhenOverlapRecovered) + Lean theorems Multiplexing.multiplexed_capacity_ge_busy, Multiplexing.multiplexing_wallace_numerator_monotone, Multiplexing.multiplexing_wallace_numerator_drop_equals_overlap, Multiplexing.multiplexing_fill_monotone, Multiplexing.multiplexing_wallace_ratio_monotone, and Multiplexing.multiplexing_wallace_ratio_strict Mechanized
THM-S7-STAGGER Staged expansion dominates naive widening on the bounded diamond witness: with positive topology deficit and the same added frontier budget, filling underfilled shoulders first yields higher frontier fill and therefore lower Wallace than dumping the budget into the current peak k > 0; shoulder budgets bounded by k-1; positive added budget left+right > 0; same budget supported by positive topology deficit witness left+right <= deficit TLA+ StagedExpansion.tla invariants (InvSameBudgetFrontierArea, InvEnvelopeComparison, InvStagedFillDominatesNaive, InvStagedWallaceBeatsNaive) + Lean theorems StagedExpansion.staged_frontier_area_matches_naive, StagedExpansion.staged_envelope_preserved, StagedExpansion.naive_widen_envelope_closed_form, StagedExpansion.staged_wallace_closed_form, StagedExpansion.naive_widen_wallace_closed_form, and StagedExpansion.staged_fill_dominates_naive together with THM-S7-WALLACE complement law Mechanized
THM-S7-WARM-EFF Warm-up efficiency: for homologous workloads with fixed useful work, recovered overlap is worth the added Buley cost exactly when the weighted Wallace reduction exceeds the Burden Scalar; equivalently lambda * busy * overlap > BurdenScalar, with BurdenScalar = deltaB * seqCap * (seqCap - overlap) positive busy work; sequential capacity at least busy work; recovered overlap bounded by slack (overlap <= seqCap - busy); non-negative Buley rise deltaB; positive Wallace-value weight lambda > 0 TLA+ WarmupEfficiency.tla invariants (InvWallaceDropCrossClosedForm, InvBurdenScalarClosedForm, InvWorthWarmupIffExplicit, InvWorthWarmupIffShiftedUtility, InvFreeWarmupWorthWhenOverlapRecovered, InvNoRecoveryNotWorthWhenBuleyPositive) + Lean theorems WarmupEfficiency.warmup_wallace_drop_cross_closed_form, WarmupEfficiency.warmup_efficiency_iff, WarmupEfficiency.warmup_efficiency_iff_shifted_utility, WarmupEfficiency.free_warmup_positive_overlap_is_worth, and WarmupEfficiency.no_recovery_not_worth_when_buley_positive Mechanized
THM-S7-WARM-DYN Dynamic warm-up cooling: under bounded entropy creep, reachable burden threshold, and cooling strength that can clear any reachable overlap, the dynamic warm-up controller keeps overlap bounded and eventually returns to a laminar state (overlap = 0) static warm-up-efficiency assumptions; positive decayRate and turbulenceBuild; full-cooling assumption decayRate > seqCap - busy; reachability assumption wallaceWeight * (seqCap - busy) > buleyRise * seqCap; weak fairness on both ActiveCooling and EntropyCreep TLA+ DynamicWarmupEfficiency.tla invariants (InvOverlapBounded, InvDynamicAssumptions, InvWarmCapBounded, InvMaxOverlapTriggersCooling) + liveness property PropEventualLaminar Mechanized
THM-S7-WARM-CTRL Warm-up controller optimality: under one-hot topology mismatch, the score-minimizing controller chooses expand for underfilled topology below the redline, constrain for overprovisioned topology below the redline, and shed-load once the Burden Scalar exceeds that redline, with Redline = deficitWeight + shedPenalty static warm-up-efficiency assumptions; positive deficit penalty deficitWeight > 0; positive shed penalty shedPenalty > 0; one-hot mismatch (underDeficit = 0 \/ overDeficit = 0) with positive total mismatch (underDeficit + overDeficit > 0) TLA+ WarmupController.tla invariants (InvChosenScoreMinimal, InvExpandBeatsConstrainWhenUnder, InvConstrainBeatsExpandWhenOver, InvExpandOptimalBelowRedline, InvConstrainOptimalBelowRedline, InvShedLoadOptimalAboveRedline) + Lean theorems WarmupController.choose_expand_below_redline, WarmupController.choose_constrain_below_redline, WarmupController.choose_shed_load_when_under_above_redline, and WarmupController.choose_shed_load_when_over_above_redline Mechanized
THM-S7-WARM-CTRL-TIE Exact redline ties are deterministic: at BurdenScalar = Redline, an underfilled topology chooses expand rather than shed-load, and an overprovisioned topology chooses constrain rather than shed-load; under one-hot mismatch, the excluded topology-repair action never occurs on the wrong side (constrain never under underfill, expand never under overfill) one-hot mismatch with positive active side (underDeficit > 0, overDeficit = 0 or underDeficit = 0, overDeficit > 0); positive deficit penalty deficitWeight > 0; exact equality BurdenScalar = Redline Lean theorems ControllerTieBreaking.choose_expand_on_under_exact_redline, ControllerTieBreaking.under_exact_redline_not_shed, ControllerTieBreaking.choose_constrain_on_over_exact_redline, ControllerTieBreaking.over_exact_redline_not_shed, ControllerTieBreaking.choose_ne_constrain_when_under, and ControllerTieBreaking.choose_ne_expand_when_over in ControllerTieBreaking.lean Mechanized
THM-S7-WHIP-CROSSOVER Cross-shard correction crossover is finite and over-sharding becomes non-improving finite P,N,C,S; P>0, N>0, C>0, bounded shard window TLA+ WhipCrossover.tla invariants + Lean theorems Claims.whip_total_time_strictly_increases_after_full_sharding and Claims.whip_strict_crossover_exists Mechanized
THM-STAGED-EXPANSION Staged expansion frontier: the three-stage expansion area formula matches naive widening. Peak is preserved across stages. Wallace numerator measures wasted capacity in the expansion envelope peak > 0; left, right >= 0 Lean theorems StagedExpansion.staged_frontier_area_matches_naive and StagedExpansion.staged_peak_preserved in StagedExpansion.lean Mechanized
THM-WARMUP-CONTROLLER Warmup controller action scoring over expand/constrain/shedLoad: the controller selects the action with minimum score. Repair redline = deficitWeight + shedPenalty. Warmup worth = Wallace benefit exceeds controller burden deficitWeight, shedPenalty > 0; warmupWallaceDropCross derived from sequential vs multiplexed Wallace Lean theorems in WarmupController.lean and WarmupEfficiency.lean including warmup_wallace_drop_cross_closed_form Mechanized
THM-MULTIPLEXING-CAPACITY Multiplexing capacity = sequential minus recovered overlap. Wallace numerator is monotone under multiplexing. Wallace numerator drop equals overlap identity multiplexed pipeline stages Lean theorems Multiplexing.multiplexing_wallace_numerator_monotone and Multiplexing.multiplexing_wallace_numerator_drop_equals_overlap in Multiplexing.lean Mechanized

Queueing Theory

| THM-QUEUE-FIBONACCI-HOLOGRAPHIC-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Fibonacci coding capacity combined with Holographic Consensus yields a canonical one-path queue boundary. | explicit strict-majority interpretation | Lean theorem fibonacci_holographic_budget_yields_unit_queue_boundary in FibonacciHolographicQueueKernelBridge.lean | Mechanized | | THM-QUEUE-FIBONACCI-HOLOGRAPHIC-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem: combined Fibonacci+Holographic interpretation does not force positive path width. | canonical witness β₁=0 | Lean theorem fibonacci_holographic_budget_does_not_force_positive_beta1 in FibonacciHolographicQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CANCER-TECTONIC-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: cancer mutation severity and tectonic slip threshold route through one strict-majority interpretation and yield a canonical one-path queue boundary witness | cancer severity and tectonic slip assumptions | Lean theorem cancer_tectonic_budget_yields_unit_queue_boundary in CancerTectonicQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CANCER-MUTATION-SEVERITY-UNIT-BOUNDARY | Cross-domain bridge: cancer mutation severity induces strict-majority interpretation and canonical one-path queue boundary witness | cancer mutation severity | Lean theorem cancer_mutation_severity_yields_unit_queue_boundary in CancerTectonicQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TECTONIC-SLIP-THRESHOLD-UNIT-BOUNDARY | Cross-domain bridge: tectonic slip threshold induces strict-majority interpretation and canonical one-path queue boundary witness | tectonic slip threshold | Lean theorem tectonic_slip_threshold_yields_unit_queue_boundary in CancerTectonicQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CANCER-TECTONIC-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: combined interpretation does not force positive path width | combined budget interpretation | Lean theorem cancer_tectonic_budget_does_not_force_positive_beta1 in CancerTectonicQueueKernelBridge.lean | Mechanized |

Sample-path conservation, multiclass networks, stochastic mixtures, probabilistic kernels, M/M/1 stability, Jackson product-form networks, envelope ladder, adaptive supremum, state-dependent families, measure-theoretic lifts, ergodic Cesaro, and subsumption.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-QUEUE-KADEMLIA-XOR-ROUTING-UNIT-BOUNDARY Cross-domain bridge: Kademlia XOR routing depth interpreted as failure budget yields a one-path queue boundary. explicit routing budget xorDistance Lean theorem kademlia_xor_routing_yields_unit_queue_boundary in KademliaTaphonomyQueueKernelBridge.lean Mechanized
THM-QUEUE-TAPHONOMY-VENTED-ORGANICS-UNIT-BOUNDARY Cross-domain bridge: Taphonomy vented organics interpreted as failure budget yields a one-path queue boundary. explicit vented organics count Lean theorem taphonomy_vented_organics_yields_unit_queue_boundary in KademliaTaphonomyQueueKernelBridge.lean Mechanized
THM-QUEUE-KADEMLIA-TAPHONOMY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Combined Kademlia+Taphonomy budget yields one canonical queue boundary. combined failure budget Lean theorem kademlia_taphonomy_budget_yields_unit_queue_boundary in KademliaTaphonomyQueueKernelBridge.lean Mechanized
THM-QUEUE-KADEMLIA-TAPHONOMY-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: combined Kademlia+Taphonomy interpretation does not force positive path width (beta1). combined interpretation and β₁=0 witness Lean theorem kademlia_taphonomy_budget_does_not_force_positive_beta1 in KademliaTaphonomyQueueKernelBridge.lean Mechanized
THM-QUEUE-FIAT-PRINTING-UNIT-BOUNDARY Cross-domain bridge: fiat printing phantom injection yields a strict-majority queue interpretation and canonical one-path boundary witness. explicit fiatCrossings injection Lean theorem fiat_printing_budget_yields_unit_queue_boundary in AutoimmunityMacroEconomicsQueueKernelBridge.lean Mechanized
THM-QUEUE-AUTOIMMUNITY-FIAT-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined autoimmunity parser exhaustion and fiat printing yields unified strict-majority queue interpretation and canonical one-path boundary witness. combined failure budget parserExhaust + fiatCrossings Lean theorem autoimmunity_fiat_budget_yields_unit_queue_boundary in AutoimmunityMacroEconomicsQueueKernelBridge.lean Mechanized
THM-QUEUE-AUTOIMMUNITY-FIAT-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem: combined autoimmunity+fiat interpretation with anchored queue rates does not force positive β₁ (path-width). anchored queue interpretation from combined budget Lean theorem autoimmunity_fiat_budget_does_not_force_positive_beta1 in AutoimmunityMacroEconomicsQueueKernelBridge.lean Mechanized
THM-QUEUE-GOSSIP-PROTOCOL-UNIT-BOUNDARY Cross-domain bridge: Gossip protocol susceptible node accounting yields strict-majority queue interpretation and canonical one-path boundary witness. explicit GossipSetup Lean theorem gossip_susceptible_yields_unit_queue_boundary in GossipEpidemiologyQueueKernelBridge.lean Mechanized
THM-QUEUE-EPIDEMIOLOGY-SIR-UNIT-BOUNDARY Cross-domain bridge: Epidemiology SIR active infected accounting yields strict-majority queue interpretation and canonical one-path boundary witness. explicit SIRSetup Lean theorem sir_active_infected_yields_unit_queue_boundary in GossipEpidemiologyQueueKernelBridge.lean Mechanized
THM-QUEUE-GOSSIP-EPIDEMIOLOGY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Combined Gossip+SIR accounting yields unified strict-majority queue interpretation and canonical one-path boundary witness. combined failure budget susceptibleNodes + activeInfected Lean theorem gossip_sir_budget_yields_unit_queue_boundary in GossipEpidemiologyQueueKernelBridge.lean Mechanized
THM-QUEUE-GOSSIP-EPIDEMIOLOGY-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem: combined Gossip+SIR interpretation with anchored queue rates does not force positive β₁ (path-width). anchored queue interpretation from combined budget Lean theorem gossip_sir_budget_does_not_force_beta1_equals_budget in GossipEpidemiologyQueueKernelBridge.lean Mechanized
THM-QUEUE-BELL-VIOLATION-UNIT-BOUNDARY Cross-domain bridge: Quantum entanglement Bell violation accounting yields strict-majority queue interpretation and canonical one-path boundary witness. explicit entangled pairs p > 0 Lean theorem bell_violation_yields_unit_queue_boundary in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-QUEUE-BULLWHIP-VARIANCE-UNIT-BOUNDARY Cross-domain bridge: Supply chain Bullwhip variance amplification yields strict-majority queue interpretation and canonical one-path boundary witness. explicit supply chain stages s > 0 Lean theorem bullwhip_variance_yields_unit_queue_boundary in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-QUEUE-ENTANGLEMENT-BULLWHIP-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Combined Bell entanglement and Bullwhip variance accounting yields unified strict-majority queue interpretation and canonical one-path boundary witness. combined failure budget p + s + 2 Lean theorem entanglement_bullwhip_budget_yields_unit_queue_boundary in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-QUEUE-ENTANGLEMENT-BULLWHIP-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem: combined Bell+Bullwhip interpretation with anchored queue rates does not force positive β₁ (path-width). anchored queue interpretation from combined budget Lean theorem entanglement_bullwhip_budget_does_not_force_beta1_equals_budget in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-QUEUE-BULLWHIP-VARIANCE-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem: Bullwhip variance interpretation with anchored queue rates does not force strict capacity growth. anchored queue interpretation from Bullwhip budget Lean theorem bullwhip_variance_does_not_force_strict_capacity_growth in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-QUEUE-SEMIOTIC-VOID-BUDGET-UNIT-BOUNDARY Semiotic deficit paths and void boundary volume accounting can be routed together into one strict-majority queue budget, yielding a canonical one-path queue boundary. explicit SemioticChannel and ConstantWidthComputation anchors Lean theorem semiotic_void_budget_yields_unit_queue_boundary in SemioticVoidQueueKernelBridge.lean Mechanized
THM-QUEUE-SEMIOTIC-VOID-BUDGET-NOT-BETA1-EQUAL-BUDGET Combined Semiotic+Void interpretation with anchored queue rates does not force β₁ to equal the combined budget mass. anchored queue interpretation from combined budget Lean theorem semiotic_void_budget_does_not_force_beta1_equals_budget in SemioticVoidQueueKernelBridge.lean Mechanized
THM-QUEUE-OPTICS-REFLECTION-UNIT-BOUNDARY Cross-domain bridge: Optics reflection bound yields strict-majority queue interpretation and canonical one-path boundary witness. explicit OpticsReflection bound Lean theorem optics_reflection_yields_unit_queue_boundary in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-QUEUE-BOTANY-XYLEM-UNIT-BOUNDARY Cross-domain bridge: Botany xylem transport capacity yields strict-majority queue interpretation and canonical one-path boundary witness. explicit BotanyXylem capacity Lean theorem botany_xylem_yields_unit_queue_boundary in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-QUEUE-OPTICS-BOTANY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Combined Optics+Botany interpretation yields unified strict-majority queue interpretation and canonical one-path boundary witness. combined failure budget Lean theorem optics_botany_budget_yields_unit_queue_boundary in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-QUEUE-OPTICS-BOTANY-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem: combined Optics+Botany interpretation with anchored queue rates does not force positive β₁ (path-width). anchored queue interpretation Lean theorem optics_botany_budget_does_not_force_positive_beta1 in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-QUEUE-OPTICS-REFLECTION-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem: Optics reflection interpretation does not force strict capacity growth. anchored queue interpretation Lean theorem optics_reflection_does_not_force_strict_capacity_growth in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-QUEUE-SAMPLE-PATH Finite-trace work-conserving single-server queues satisfy the discrete sample-path Little's Law identity independent of discipline choice finite arrival trace; positive service quanta; discrete ticks; single server; service choice always taken from active jobs when active jobs exist TLA+ QueueingSamplePath.tla invariants (InvWorkConservingChoice, InvConservationLaw, InvFinalLittleIdentity) + executable queueing-discipline enumeration tests Mechanized
THM-QUEUE-MULTICLASS-NETWORK Bounded multi-class open networks satisfy the same conservation identity under node-local work-conserving dispatch finite arrival trace; finite job classes; class-specific routes; finite service-law scenario family; one active service choice per non-empty node on each tick TLA+ QueueingMultiClassNetwork.tla invariants (InvWorkConservingNetworkDispatch, InvNetworkConservationLaw, InvFinalNetworkIdentity) + executable multiclass network enumeration tests Mechanized
THM-QUEUE-STOCHASTIC-MIXTURE Finite-support stochastic mixtures of bounded multi-class open-network traces preserve customer-time conservation in expectation finite scenario support; positive scenario masses; scenario-dependent arrivals/classes/routes/service laws; node-local work-conserving dispatch TLA+ QueueingStochasticMixture.tla invariants (InvWeightedNetworkConservationLaw, InvWeightedFinalNetworkIdentity) + Lean theorem Claims.weighted_queue_expectation_balance + executable weighted-scenario tests Mechanized
THM-QUEUE-PROBABILISTIC-KERNEL Exact finite-state probabilistic queue transitions preserve customer-time conservation at the distribution level bounded horizon; finite-support arrival kernel; bounded service quanta; FIFO work-conserving single server TLA+ QueueingProbabilisticKernel.tla invariants (InvMassSchedule, InvDistributionConservationLaw, InvFinalExpectationIdentity) + executable exact-kernel propagation tests Mechanized
THM-QUEUE-PROBABILISTIC-NETWORK-KERNEL Exact finite-state probabilistic multiclass open-network transitions preserve customer-time conservation at the distribution level bounded horizon; two-node open network; class-dependent routes and service quanta; finite-support arrival kernel; deterministic FIFO work-conserving per-node dispatch TLA+ QueueingProbabilisticNetworkKernel.tla invariants (InvMassSchedule, InvDistributionConservationLaw, InvFinalExpectationIdentity) + executable exact-network-kernel propagation tests and explicit worst-case small-data ramp-up witness Mechanized
THM-QUEUE-PROBABILISTIC-LARGE-NETWORK Larger exact finite-support multiclass open-network probabilistic cubes preserve the same weighted conservation law bounded horizon; three arrival slots; three-node open network; class-dependent routes/service quanta; exact finite-support arrival cube; deterministic FIFO work-conserving per-node dispatch TLA+ QueueingProbabilisticLargeNetworkKernel.tla invariants (InvMassSchedule, InvDistributionConservationLaw, InvFinalExpectationIdentity) + executable larger exact-network-kernel propagation tests Mechanized
THM-QUEUE-MM1-STABILITY Stable M/M/1 occupancy has the geometric stationary law with finite mean queue length ρ / (1 - ρ), and the same stationary law inherits the queue conservation identities load ρ satisfies 0 <= ρ < 1 Lean definitions/theorems QueueStability.mm1StationaryPMF, QueueStability.mm1StationaryPMF_apply, QueueStability.mm1_stationary_mean_queue_length, and QueueStability.mm1_stationary_lintegral_balance Mechanized
THM-QUEUE-ONE-PATH Canonical stable M/M/1 queues admit a constructive one-path boundary witness: β₁ = 0, capacity β₁ + 1 = 1, stationary mean occupancy λ / (μ - λ), and the induced identity λ / (μ - λ) = λ * (1 / (μ - λ)) real arrival/service rates λ >= 0, μ > 0, λ < μ Lean definitions/theorems QueueBoundary.QueueBoundaryWitness, QueueBoundary.canonicalMM1Boundary, QueueBoundary.canonicalMM1Boundary_beta1_zero, QueueBoundary.canonicalMM1Boundary_capacity_eq_one, QueueBoundary.canonicalMM1Boundary_little_law, QueueBoundary.canonicalMM1Boundary_stationary_mean_queue_length, and QueueBoundary.exists_canonicalMM1_beta1_zero_boundary Mechanized
THM-QUEUE-SLEEP-SCHEDULE-UNIT-BOUNDARY Cross-domain bridge: positive above-threshold sleep-schedule debt yields a canonical one-path queue boundary witness with β₁ = 0, capacity = 1, and service-rate anchor μ = debt + 1 sleep-schedule threshold recoveryQuota < scheduledWake; positive cycle count 0 < n; canonical queue witness instantiated with λ = 1 and μ = iteratedDebt + 1 Lean theorem QueueBoundary.positive_sleep_schedule_debt_yields_unit_capacity_boundary in QueueBoundary.lean, using SleepDebtSchedule.iterated_debt_positive_above_threshold Mechanized
THM-QUEUE-QUORUM-MAJORITY-RATE-EMBEDDING-BOUNDARY Cross-domain bridge: strict-majority quorum arithmetic plus explicit queue-rate embedding yields both the quorum floor f < q and a canonical one-path queue boundary witness (β₁ = 0, capacity = 1, Little-law occupancy identity) strict-majority quorum budget 2f < n; explicit queue embedding assumptions λ >= 0, μ > 0, λ < μ Lean theorem QueueBoundary.strict_majority_quorum_with_rate_embedding_yields_unit_boundary in QueueBoundary.lean, composing QuorumVisibility.strict_majority_failure_budget_lt_quorum with QueueBoundary.exists_canonicalMM1_beta1_zero_boundary Mechanized
THM-QUEUE-WEIGHTED-SLEEP-SCHEDULE-UNIT-BOUNDARY Cross-domain bridge: positive weighted sleep-schedule debt yields a canonical one-path queue boundary witness with β₁ = 0, capacity = 1, and service-rate anchor μ = weightedDebt + 1 weighted threshold crossed (thresholdRhs < thresholdLhs); positive cycle count 0 < n; canonical queue witness instantiated with λ = 1 and μ = iteratedDebt + 1 Lean theorem QueueBoundary.positive_weighted_sleep_schedule_debt_yields_unit_capacity_boundary in QueueBoundary.lean, using SleepDebtWeightedSchedule.iterated_debt_positive_above_threshold Mechanized
THM-QUEUE-SLEEP-WEIGHTED-QUORUM-EMBEDDING-BOUNDARY Cross-domain bridge: positive weighted sleep debt, routed through a canonical debt-to-quorum embedding, yields a one-path queue boundary witness with quorum-encoded arrival/service anchors weighted threshold crossed (thresholdRhs < thresholdLhs); positive cycle count 0 < n; canonical embedding failureBudget = debt, replicaCount = 2*debt + 1 Lean theorem SleepDebtQuorumQueueBridge.weighted_sleep_debt_quorum_embedding_yields_unit_queue_boundary in SleepDebtQuorumQueueBridge.lean, composing SleepDebtWeightedSchedule.iterated_debt_positive_above_threshold, QuorumVisibility.strict_majority_failure_budget_lt_quorum, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-QUORUM-HISTORY-UNIT-BOUNDARY Cross-domain bridge: nonempty committed-write history induces a strict-majority quorum embedding and therefore a canonical one-path queue boundary witness with positive arrival mass nonempty completed-write history (history ≠ []); canonical embedding `f = history , n = 2
THM-QUEUE-QUORUM-HISTORY-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: nonempty committed-write history yields strictly positive TCP topological deficit when lifted to `pathCount = history + 1` under single-stream transport nonempty completed-write history (history ≠ []); lifted path-count interpretation pathCount = historyFailureBudget(history) + 1; TCP stream count fixed at 1
THM-QUEUE-QUORUM-HISTORY-NOT-UNIVERSAL-NONPOSITIVE-DEFICIT Contrarian anti-theorem variant: nonempty committed-write history under canonical embedding does not force nonpositive topological deficit uniformly across all transport stream counts nonempty completed-write history (history ≠ []); lifted path-count interpretation pathCount = historyFailureBudget(history) + 1; universal nonpositive-deficit claim quantified over all transportStreams Lean theorem QuorumHistoryQueueBridge.nonempty_history_embedding_does_not_force_universal_nonpositive_deficit in QuorumHistoryQueueBridge.lean, by contradiction from the positive TCP-deficit witness at transportStreams = 1 Mechanized
THM-QUEUE-QUORUM-HISTORY-SEMANTIC-MORPHISM-POSITIVE-DEFICIT Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism equality from raw history budget to mapped path-count budget transports the positive TCP-deficit witness into mapped coordinates nonempty completed-write history (history ≠ []); interpretation function interpret : Nat → Nat; explicit morphism hypothesis interpret (historyFailureBudget(history) + 1) = historyFailureBudget(history) + 1 Lean theorem QuorumHistoryQueueBridge.history_semantic_morphism_yields_positive_topological_deficit in QuorumHistoryQueueBridge.lean, rewriting via the morphism equality and reusing the positive-deficit bridge theorem Mechanized
THM-QUEUE-QUORUM-HISTORY-BOUNDARY-POSITIVE-DEFICIT-BUNDLE Cross-domain bridge bundle: nonempty committed-write history simultaneously yields the canonical one-path queue boundary witness and strictly positive lifted TCP deficit in one mechanized conjunction nonempty completed-write history (history ≠ []); canonical embedding `f = history , n = 2
THM-QUEUE-QUORUM-HISTORY-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: nonempty committed-write history under canonical embedding does not force queue path width to equal interpreted history budget (`β₁ = history `) nonempty completed-write history (history ≠ []); canonical embedding `f =
THM-QUEUE-QUORUM-MAJORITY-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: strict-majority quorum arithmetic does not force positive path-width (β₁ > 0) once queue embedding anchors are fixed strict-majority quorum budget 2f < n; witness restricted to boundaries with arrivalRate = f and serviceRate = quorumSize n f Lean theorem QueueBoundary.strict_majority_quorum_does_not_force_positive_beta1 in QueueBoundary.lean, using witness constructor QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-WEIGHTED-SLEEP-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: positive weighted sleep debt and anchored service rate still do not force positive path-width; a witness exists with β₁ = 0 weighted threshold crossed (thresholdRhs < thresholdLhs); positive cycle count 0 < n; witness restricted to boundaries with serviceRate = iteratedDebt + 1 Lean theorem QueueBoundary.weighted_sleep_debt_does_not_force_positive_beta1 in QueueBoundary.lean, using witness constructor QueueBoundary.positive_weighted_sleep_schedule_debt_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIATION-LOSS-UNIT-BOUNDARY Cross-domain bridge: positive mediation loss yields a canonical one-path queue boundary witness with β₁ = 0, capacity = 1, and explicit mediation loss anchors for λ and μ = λ + 1 mediation setup with irreducible loss (mediatorLoss ≥ 1) and bounded budget assumptions from CausalMediation.MediationSetup Lean theorem MediationQueueBoundaryBridge.mediation_positive_loss_yields_unit_queue_boundary in MediationQueueBoundaryBridge.lean, using QueueBoundary.canonicalMM1Boundary Mechanized
THM-QUEUE-MEDIATION-QUORUM-BOUNDARY Cross-domain bridge: mediation loss, under an explicit quorum interpretation layer, yields a strict-majority quorum budget and a canonical one-path queue boundary witness with β₁ = 0, capacity = 1, and quorum-aligned arrival/service anchors mediation setup with irreducible loss (mediatorLoss ≥ 1); canonical interpretation replicaCount = 2 * mediatorLoss + 1, failureBudget = mediatorLoss Lean theorem MediationQuorumQueueBridge.mediation_loss_canonical_interpretation_yields_unit_queue_boundary in MediationQuorumQueueBridge.lean, using QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIATION-QUORUM-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: mediation-loss quorum interpretation does not force positive path-width (β₁ > 0) even when arrival/service anchors are fixed by the interpretation layer mediation setup with irreducible loss (mediatorLoss ≥ 1); interpretation layer failureBudget = mediatorLoss, replicaCount = 2*failureBudget + 1; witness restricted to anchored arrival/service rates from that interpretation Lean theorem MediationContrarianBoundaries.mediation_quorum_interpretation_does_not_force_positive_beta1 in MediationContrarianBoundaries.lean, using witness constructor MediationContrarianBoundaries.mediation_quorum_interpretation_yields_unit_boundary Mechanized
THM-QUEUE-HORTICULTURE-PRUNING-UNIT-BOUNDARY Cross-domain bridge: Horticulture pruning yields a canonical one-path queue boundary witness PlantGrowth bounds Lean theorem horticulture_pruning_yields_unit_queue_boundary in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-QUEUE-MEMORY-GC-UNIT-BOUNDARY Cross-domain bridge: Memory GC yields a canonical one-path queue boundary witness GarbageCollection bounds Lean theorem memory_gc_yields_unit_queue_boundary in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-QUEUE-HORTICULTURE-MEMORY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Combined budget yields a canonical one-path queue boundary witness combined interpretation bounds Lean theorem combined_horticulture_memory_budget_yields_unit_queue_boundary in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-QUEUE-HORTICULTURE-MEMORY-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem: Combined interpretation does not force β₁ = budget anchored queue rates Lean theorem combined_horticulture_memory_does_not_force_beta1_equals_budget in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-QUEUE-HORTICULTURE-MEMORY-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem: Combined interpretation does not force strict capacity growth anchored queue rates Lean theorem combined_horticulture_memory_does_not_force_strict_capacity_growth in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-MEDIATION-CRYPTO-SIDE-CHANNEL-UNIT-BOUNDARY Cross-domain bridge: mediation loss plus a cryptographic side-channel floor induce a strict-majority quorum interpretation and therefore a canonical one-path queue boundary witness with β₁ = 0, capacity = 1, and anchored arrival/service rates mediation setup with irreducible loss (mediatorLoss ≥ 1); cryptographic side-channel floor (0 < perEvalFloor); canonical interpretation failureBudget = mediatorLoss + perEvalFloor, replicaCount = 2*failureBudget + 1 Lean theorem MediationCryptoQueueKernelBridge.mediation_crypto_side_channel_yields_unit_queue_boundary in MediationCryptoQueueKernelBridge.lean, using QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-MEDIATION-CRYPTO-SIDE-CHANNEL-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored mediation-crypto interpretation does not force positive path-width (β₁ > 0) mediation setup with irreducible loss (mediatorLoss ≥ 1); cryptographic side-channel floor (0 < perEvalFloor); witness restricted to boundaries with arrivalRate = mediatorLoss + perEvalFloor and serviceRate = quorumSize (2*(mediatorLoss + perEvalFloor)+1) (mediatorLoss + perEvalFloor) Lean theorem MediationCryptoQueueKernelBridge.mediation_crypto_side_channel_does_not_force_positive_beta1 in MediationCryptoQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-UNIT-BOUNDARY Cross-domain bridge: mediation loss, cryptographic side-channel floor, and BATNA trauma gap route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with tri-domain anchored arrival/service rates mediation setup with irreducible loss (mediatorLoss ≥ 1); cryptographic side-channel floor (0 < perEvalFloor); negotiation BATNA inequality (slamTraumaPenalty ≥ untanglingWattsCost + 1); canonical interpretation failureBudget = mediatorLoss + perEvalFloor + (slamTraumaPenalty - untanglingWattsCost), replicaCount = 2*failureBudget + 1 Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_budget_yields_unit_queue_boundary in MediationCryptoNegotiationQueueKernelBridge.lean, composing source-domain identities with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive tri-domain interpreted budget forces strictly positive TCP-style topological deficit on the lifted (budget + 1) path model same assumptions as THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-UNIT-BOUNDARY; positivity route uses mediation-loss irreducibility, side-channel floor positivity, and BATNA trauma-gap positivity Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_budget_yields_positive_topological_deficit in MediationCryptoNegotiationQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation at pathCount = failureBudget + 1 Mechanized
THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored tri-domain mediation+crypto+negotiation interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored tri-domain arrival/service rates Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_budget_does_not_force_strict_capacity_growth in MediationCryptoNegotiationQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-NOT-TRANSPORT-MATCH Contrarian anti-theorem variant: positive tri-domain interpreted budget does not force TCP transport-topology match (Δ ≤ 0) same assumptions as THM-QUEUE-MEDIATION-CRYPTO-NEGOTIATION-BUDGET-UNIT-BOUNDARY; lifted path count pathCount = failureBudget + 1 and positive budget floor imply strictly positive deficit Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_budget_does_not_force_transport_match in MediationCryptoNegotiationQueueKernelBridge.lean, using the positive-deficit bridge theorem to refute Δ ≤ 0 Mechanized
THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Ki leak mass, combat entanglement mass, and knapsack viewport packing mass route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) Ki assumptions 0 < glanceLeak ∨ 0 < muscleLeak ∨ 0 < scentLeak ∨ 0 < energyLeak; combat assumption entanglement > 0; knapsack assumptions pleromicData = screenCapacity + visualOverlap, visualOverlap ≥ 1; interpretation anchor failureBudget = totalLeak + entanglement + pleromicData, replicaCount = 2*failureBudget + 1 Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_budget_yields_unit_queue_boundary in KiCombatKnapsackQueueKernelBridge.lean, composing source-domain mass identities with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive Ki+combat+knapsack interpreted budget forces strictly positive TCP-style topological deficit on the lifted (budget + 1) path model same assumptions as THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-UNIT-BOUNDARY; positivity route uses Ki disharmony mass, combat entanglement floor, and knapsack viewport packing inequality Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_budget_yields_positive_topological_deficit in KiCombatKnapsackQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation at pathCount = failureBudget + 1 Mechanized
THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored Ki+combat+knapsack interpretation with fixed queue rates does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_budget_does_not_force_beta1_equals_budget in KiCombatKnapsackQueueKernelBridge.lean, via contradiction against the canonical one-path witness (β₁ = 0) and source-derived budget positivity Mechanized
THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-NOT-CAPACITY-AT-LEAST-TWO Contrarian anti-theorem variant: anchored Ki+combat+knapsack interpretation with fixed queue rates does not force capacity lower bound 2 ≤ capacity; canonical witness remains one-path (capacity = 1) same assumptions as THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_budget_does_not_force_capacity_at_least_two in KiCombatKnapsackQueueKernelBridge.lean, via contradiction against the canonical one-path witness Mechanized
THM-QUEUE-PISOT-DIMENSION-UNIT-BOUNDARY Cross-domain bridge: Pisot parameterized dimension yields canonical unit capacity queue boundary. Pisot parameterized dimension d > 0 Lean theorem pisot_dimension_yields_unit_queue_boundary in PisotAstrophysicsQueueKernelBridge.lean Mechanized
THM-QUEUE-ASTROPHYSICS-SHADOW-UNIT-BOUNDARY Cross-domain bridge: Astrophysical visible budget yields canonical unit capacity queue boundary. visible budget of a celestial shadow > 0 Lean theorem astrophysics_shadow_yields_unit_queue_boundary in PisotAstrophysicsQueueKernelBridge.lean Mechanized
THM-QUEUE-PISOT-ASTROPHYSICS-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Combined Pisot/astrophysics interpretation yields canonical unit capacity queue boundary. explicit interpretation anchor from combined budget Lean theorem pisot_astrophysics_budget_yields_unit_queue_boundary in PisotAstrophysicsQueueKernelBridge.lean Mechanized
THM-QUEUE-PISOT-ASTROPHYSICS-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: Combined Pisot/astrophysics interpretation with anchored rates does not force positive path width. explicit interpretation anchor from combined budget Lean theorem pisot_astrophysics_budget_does_not_force_positive_beta1 in PisotAstrophysicsQueueKernelBridge.lean Mechanized
THM-QUEUE-KI-COMBAT-KNAPSACK-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from Ki+combat+knapsack source mass into queue coordinates transports the canonical one-path queue witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-KI-COMBAT-KNAPSACK-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret (totalLeak + entanglement + pleromicData) = failureBudget; strict-majority interpretation replicaCount = 2*interpret(...) + 1 Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_semantic_morphism_yields_unit_queue_boundary in KiCombatKnapsackQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-MEDIA-ECOSYSTEM-CRYPTO-UNIT-BOUNDARY Cross-domain bridge: media clickbait dilation, ecosystem predator mass, and cryptographic telepathy route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored arrival/service rates media clickbait assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; ecosystem assumptions preyCount + predatorCount = ecosystemBoundary, predatorCount ≥ 1; cryptographic telepathy certainty = invariant + proofCost, proofCost ≥ 0 Lean theorem MediaEcosystemCryptoQueueKernelBridge.media_ecosystem_crypto_budget_yields_unit_queue_boundary in MediaEcosystemCryptoQueueKernelBridge.lean, folding the three source budgets into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIA-ECOSYSTEM-CRYPTO-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive combined media+ecosystem+cryptography budget forces strictly positive TCP-style topological deficit on the lifted (budget + 1) path model same assumptions as THM-QUEUE-MEDIA-ECOSYSTEM-CRYPTO-UNIT-BOUNDARY; positivity route uses clickbait dilation, predator mass, and telepathic proof-cost certificate Lean theorem MediaEcosystemCryptoQueueKernelBridge.media_ecosystem_crypto_budget_yields_positive_topological_deficit in MediaEcosystemCryptoQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation at pathCount = budget + 1 Mechanized
THM-QUEUE-MEDIA-ECOSYSTEM-CRYPTO-NOT-CAPACITY-AT-LEAST-TWO Contrarian anti-theorem variant: anchored media+ecosystem+cryptography interpretation does not force queue capacity to be at least two same assumptions as THM-QUEUE-MEDIA-ECOSYSTEM-CRYPTO-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem MediaEcosystemCryptoQueueKernelBridge.media_ecosystem_crypto_budget_does_not_force_capacity_at_least_two in MediaEcosystemCryptoQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-BERKSON-COLLIDER-UNIT-BOUNDARY Cross-domain bridge: collider-selected Berkson surfaces induce an explicit threshold-to-quorum interpretation and therefore a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored arrival/service rates collider setup BerksonsParadox.ColliderSetup; selected-collider hypothesis causeA + causeB ≥ collider_threshold Lean theorem BerksonQueueKernelBridge.berkson_selected_collider_yields_unit_queue_boundary in BerksonQueueKernelBridge.lean, using QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary under explicit replicaCount = 2*threshold + 1, failureBudget = threshold Mechanized
THM-QUEUE-BERKSON-COLLIDER-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: collider-selected Berkson interpretation does not force positive path-width (β₁ > 0) under the same anchored queue assumptions collider setup BerksonsParadox.ColliderSetup; selected-collider hypothesis causeA + causeB ≥ collider_threshold; witness restricted to boundaries with arrivalRate = threshold and serviceRate = quorumSize (2*threshold + 1) threshold Lean theorem BerksonQueueKernelBridge.berkson_selected_collider_does_not_force_positive_beta1 in BerksonQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness from berkson_selected_collider_yields_unit_queue_boundary Mechanized
THM-QUEUE-SIMPSON-CONFOUNDER-UNIT-BOUNDARY Cross-domain bridge: Simpson confounder mass interpreted as a strict-majority quorum budget yields a canonical one-path queue boundary witness with anchored arrival/service rates Simpson scenario witness SimpsonsParadox.SimpsonScenario; canonical interpretation failureBudget = v1_A + v2_A, replicaCount = 2*failureBudget + 1 Lean theorem SimpsonSurvivorshipQueueBridge.simpson_confounder_yields_unit_queue_boundary in SimpsonSurvivorshipQueueBridge.lean, using QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SIMPSON-CONFOUNDER-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: Simpson confounder interpretation with anchored queue rates does not force positive path-width (β₁ > 0) Simpson scenario witness SimpsonsParadox.SimpsonScenario; witness restricted to boundaries with arrivalRate = v1_A + v2_A and serviceRate = quorumSize (2*(v1_A+v2_A)+1) (v1_A+v2_A) Lean theorem SimpsonSurvivorshipQueueBridge.simpson_confounder_does_not_force_positive_beta1 in SimpsonSurvivorshipQueueBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-CONTEXTUAL-BANDIT-UNIT-BOUNDARY Cross-domain bridge: contextual-bandit total failure mass interpreted through a canonical strict-majority quorum budget yields a one-path queue boundary witness with anchored arrival/service rates contextual arm witness ContextualBandits.ContextualArm; canonical interpretation failureBudget = totalFailures, replicaCount = 2*failureBudget + 1 Lean theorem CausalBanditQueueKernelBridge.contextual_failure_budget_yields_unit_queue_boundary in CausalBanditQueueKernelBridge.lean, using QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CONTEXTUAL-BANDIT-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: contextual-bandit interpretation with anchored queue rates does not force positive path-width (β₁ > 0) contextual arm witness ContextualBandits.ContextualArm; witness restricted to boundaries with arrivalRate = totalFailures and serviceRate = quorumSize (2*totalFailures+1) totalFailures Lean theorem CausalBanditQueueKernelBridge.contextual_failure_budget_does_not_force_positive_beta1 in CausalBanditQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-CERTIFIED-RADIUS-UNIT-BOUNDARY Cross-domain bridge: certified-defense radius accounting yields a strict-majority interpretation and canonical one-path queue boundary witness while preserving the certified threshold guarantee certified-defense witness CertifiedDefenses.Certification; canonical interpretation failureBudget = cleanReject + radius, replicaCount = 2*failureBudget + 1 Lean theorem CertifiedContextualQueueKernelBridge.certified_radius_yields_unit_queue_boundary in CertifiedContextualQueueKernelBridge.lean, composing CertifiedDefenses.certified_within_radius with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CERTIFIED-CONTEXTUAL-BUDGET-UNIT-BOUNDARY Cross-domain bridge: certified radius budget plus contextual-bandit failure budget, under an explicit combined interpretation layer, yields a canonical one-path queue boundary witness and preserves both source-domain identities certified-defense witness CertifiedDefenses.Certification; contextual arm witness ContextualBandits.ContextualArm; combined interpretation failureBudget = (cleanReject + radius) + totalFailures, replicaCount = 2*failureBudget + 1 Lean theorem CertifiedContextualQueueKernelBridge.certified_contextual_budget_yields_unit_queue_boundary in CertifiedContextualQueueKernelBridge.lean, composing CertifiedDefenses.certified_within_radius, ContextualBandits.context_adjustment, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CERTIFIED-CONTEXTUAL-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: the combined certified/contextual interpretation with anchored queue rates does not force positive path-width (β₁ > 0) certified-defense witness CertifiedDefenses.Certification; contextual arm witness ContextualBandits.ContextualArm; witness restricted to boundaries with arrivalRate = (cleanReject + radius) + totalFailures and serviceRate = quorumSize (2*((cleanReject + radius)+totalFailures)+1) ((cleanReject + radius)+totalFailures) Lean theorem CertifiedContextualQueueKernelBridge.certified_contextual_budget_does_not_force_positive_beta1 in CertifiedContextualQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness from certified_contextual_budget_yields_unit_queue_boundary Mechanized
THM-QUEUE-CAUSAL-COLLIDER-UNIT-BOUNDARY Cross-domain bridge: causal-collider detection inequality plus an explicit collider-to-quorum interpretation yields a canonical one-path queue boundary witness and preserves the collider-separation claim collider assumptions vX + vY ≤ R, vZ > vX + vY, vZ ≤ R; canonical interpretation failureBudget = vX + vY, replicaCount = 2*failureBudget + 1 Lean theorem CausalBanditQueueKernelBridge.collider_detection_yields_unit_queue_boundary in CausalBanditQueueKernelBridge.lean, composing CausalDiscovery.collider_detection with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CAUSAL-DISCOVERY-INDEPENDENCE-UNIT-BOUNDARY Cross-domain bridge: causal-discovery independence decomposition with explicit strict-majority interpretation yields a canonical one-path queue boundary witness while preserving the discovery-side godWeight identity discovery assumptions vX ≤ R, vY ≤ R, vX + vY ≤ R; canonical interpretation failureBudget = vX + vY, replicaCount = 2*failureBudget + 1 Lean theorem CausalDiscoveryBanditQueueBridge.causal_discovery_independence_yields_unit_queue_boundary in CausalDiscoveryBanditQueueBridge.lean, composing CausalDiscovery.independence_decomposes with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CAUSAL-DISCOVERY-INDEPENDENCE-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: causal-discovery independence interpretation with anchored queue rates does not force positive path-width (β₁ > 0) discovery assumptions vX ≤ R, vY ≤ R, vX + vY ≤ R; witness restricted to boundaries with arrivalRate = vX + vY and serviceRate = quorumSize (2*(vX+vY)+1) (vX+vY) Lean theorem CausalDiscoveryBanditQueueBridge.causal_discovery_independence_does_not_force_positive_beta1 in CausalDiscoveryBanditQueueBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-BANDIT-ARM-FAILURES-UNIT-BOUNDARY Cross-domain bridge: exploration-exploitation arm failure arithmetic, routed through a canonical strict-majority interpretation layer, yields a one-path queue boundary witness with anchored arrival/service rates arm witness ExplorationExploitation.Arm; canonical interpretation failureBudget = failures, replicaCount = 2*failureBudget + 1 Lean theorem CausalDiscoveryBanditQueueBridge.bandit_arm_failures_yield_unit_queue_boundary in CausalDiscoveryBanditQueueBridge.lean, combining ExplorationExploitation.greedy_is_current with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CAUSAL-DISCOVERY-BANDIT-BRIDGE-UNIT-BOUNDARY Cross-domain bridge: explicit identification of discovery rejection budget with bandit-arm failure budget preserves the discovery identity and yields the same canonical one-path queue boundary witness discovery assumptions vX ≤ R, vY ≤ R, vX + vY ≤ R; arm witness ExplorationExploitation.Arm; bridge hypothesis armFailureBudget = discoveryFailureBudget Lean theorem CausalDiscoveryBanditQueueBridge.causal_discovery_bandit_budget_yields_unit_queue_boundary in CausalDiscoveryBanditQueueBridge.lean, folding CausalDiscovery.independence_decomposes with bandit_arm_failures_yield_unit_queue_boundary Mechanized
THM-QUEUE-CAUSAL-BANDIT-POSITIVE-BUDGET-DEFICIT-BRIDGE Cross-domain bridge: positive causal-discovery/bandit interpreted budget forces strictly positive TCP-style topological deficit on the lifted (budget + 1) path model arm witness ExplorationExploitation.Arm; bridge hypothesis armFailureBudget = discoveryFailureBudget; positive budget floor 0 < armFailureBudget Lean theorem CausalDiscoveryBanditQueueBridge.causal_bandit_positive_budget_yields_positive_topological_deficit in CausalDiscoveryBanditQueueBridge.lean, rewriting the bridge budget and applying CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-BANDIT-ARM-FAILURES-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: exploration-exploitation arm failure interpretation with anchored queue rates does not force positive path-width (β₁ > 0) arm witness ExplorationExploitation.Arm; witness restricted to boundaries with arrivalRate = failures and serviceRate = quorumSize (2*failures+1) failures Lean theorem CausalDiscoveryBanditQueueBridge.bandit_arm_failures_do_not_force_positive_beta1 in CausalDiscoveryBanditQueueBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-CAUSAL-DISCOVERY-BANDIT-NOT-BETA1-EQUALS-BUDGET Contrarian anti-theorem variant: anchored causal-discovery/bandit interpretation does not force queue path-width to equal interpreted budget mass discovery assumptions vX ≤ R, vY ≤ R, vX + vY ≤ R; arm witness ExplorationExploitation.Arm; bridge hypothesis armFailureBudget = discoveryFailureBudget; positive budget floor 0 < armFailureBudget; witness restricted to boundaries with anchored arrival/service rates from armFailureBudget Lean theorem CausalDiscoveryBanditQueueBridge.causal_discovery_bandit_budget_does_not_force_beta1_equals_budget in CausalDiscoveryBanditQueueBridge.lean, via contradiction against the canonical one-path witness (β₁ = 0) from causal_discovery_bandit_budget_yields_unit_queue_boundary Mechanized
THM-QUEUE-GOODHART-PROXY-GAP-UNIT-BOUNDARY Cross-domain bridge: Goodhart proxy-gap arithmetic interpreted as a strict-majority quorum budget yields a canonical one-path queue boundary witness with anchored arrival/service rates Goodhart assumptions vTrue ≤ R, vGamed ≤ R, vGamed ≤ vTrue; canonical interpretation failureBudget = vTrue - vGamed, replicaCount = 2*failureBudget + 1 Lean theorem GoodhartMechanismQueueKernelBridge.goodhart_proxy_gap_yields_unit_queue_boundary in GoodhartMechanismQueueKernelBridge.lean, composing GoodhartsLaw.proxy_gap with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MECHANISM-EXTERNALITY-UNIT-BOUNDARY Cross-domain bridge: mechanism-design externality arithmetic interpreted as a strict-majority quorum budget yields a canonical one-path queue boundary witness with anchored arrival/service rates mechanism assumptions vWithout ≤ R, vWith ≤ R, vWith ≥ vWithout; canonical interpretation failureBudget = vWith - vWithout, replicaCount = 2*failureBudget + 1 Lean theorem GoodhartMechanismQueueKernelBridge.mechanism_externality_yields_unit_queue_boundary in GoodhartMechanismQueueKernelBridge.lean, composing MechanismDesign.vcg_externality with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-GOODHART-MECHANISM-BUDGET-BRIDGE-UNIT-BOUNDARY Cross-domain bridge: explicit identification of mechanism externality budget with Goodhart proxy-gap budget preserves both identities and yields the same canonical one-path queue boundary witness Goodhart assumptions (vTrue ≤ R, vGamed ≤ R, vGamed ≤ vTrue); mechanism assumptions (vWithout ≤ R, vWith ≤ R, vWith ≥ vWithout); bridge hypothesis vWith - vWithout = vTrue - vGamed Lean theorem GoodhartMechanismQueueKernelBridge.goodhart_mechanism_budget_bridge_yields_unit_queue_boundary in GoodhartMechanismQueueKernelBridge.lean, folding GoodhartsLaw.proxy_gap and MechanismDesign.vcg_externality with the canonical queue witness constructor Mechanized
THM-QUEUE-GOODHART-MECHANISM-BUDGET-BRIDGE-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: the bridged Goodhart+mechanism interpretation with anchored queue rates does not force positive path-width (β₁ > 0) same bridge assumptions as THM-QUEUE-GOODHART-MECHANISM-BUDGET-BRIDGE-UNIT-BOUNDARY; witness restricted to boundaries with arrivalRate = vWith - vWithout and serviceRate = quorumSize (2*(vWith-vWithout)+1) (vWith-vWithout) Lean theorem GoodhartMechanismQueueKernelBridge.goodhart_mechanism_budget_bridge_does_not_force_positive_beta1 in GoodhartMechanismQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-SURVIVORSHIP-MORTALITY-UNIT-BOUNDARY Cross-domain bridge: survivorship correction arithmetic plus canonical quorum interpretation yields a one-path queue boundary witness with mortality-anchored arrival/service rates mortality count bound v ≤ R; correction identity godWeight R v = R - v + 1; canonical interpretation failureBudget = v, replicaCount = 2*v + 1 Lean theorem SimpsonSurvivorshipQueueBridge.survivorship_mortality_yields_unit_queue_boundary in SimpsonSurvivorshipQueueBridge.lean, composing SurvivorshipBias.correction_is_adjustment with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SURVIVORSHIP-MORTALITY-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: survivorship mortality interpretation does not force strict capacity growth (capacity > 1) under the same anchored queue rates mortality count bound v ≤ R; witness restricted to boundaries with arrivalRate = v and serviceRate = quorumSize (2*v+1) v Lean theorem SimpsonSurvivorshipQueueBridge.survivorship_mortality_does_not_force_strict_capacity_growth in SimpsonSurvivorshipQueueBridge.lean, via contradiction against the canonical capacity = 1 witness Mechanized
THM-QUEUE-MEDIATION-LOSS-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: positive mediation loss and anchored queue rates do not force positive path width (β₁ > 0) mediation setup with irreducible loss (mediatorLoss ≥ 1); witness restricted to boundaries with arrivalRate = mediatorLoss and serviceRate = mediatorLoss + 1 Lean theorem MediationQueueBoundaryBridge.mediation_loss_does_not_force_positive_beta1 in MediationQueueBoundaryBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-ONE-PATH-NOT-ZERO-OCCUPANCY-BOUNDARY Contrarian anti-theorem boundary: one-path topology (β₁ = 0, capacity = 1) does not force zero queue occupancy; positive occupancy is still possible under stable rates explicit canonical witness λ = 1, μ = 2 (stable M/M/1) Lean theorem QueueBoundary.one_path_boundary_not_zero_occupancy in QueueBoundary.lean Mechanized
THM-QUEUE-VOID-MERKLE-ESC-WARMUP-BUDGET-UNIT-BOUNDARY Cross-domain bridge: void-Merkle irreversibility witness, ESC cold-path fold work, and warmup expand-decision arithmetic route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored tri-domain rates warmup assumptions underDeficit > 0, overDeficit = 0, deficitWeight > 0, and controller-below-redline witness; interpretation anchor failureBudget = root + traceFold([cold]) + (underDeficit + overDeficit), replicaCount = 2*failureBudget + 1 Lean theorem VoidMerkleEscWarmupQueueKernelBridge.void_merkle_esc_warmup_budget_yields_unit_queue_boundary in VoidMerkleEscWarmupQueueKernelBridge.lean, composing VoidMerkleVerification.void_merkle_not_reversible, WasmEscObservationTrace.trace_one_cold_eq_w, WarmupController.choose_expand_below_redline, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-VOID-MERKLE-ESC-WARMUP-JOINT-WITNESS-PACK Cross-domain bridge extension: package both the ESC-only boundary witness and the full tri-domain void+ESC+warmup boundary witness in one synchronized theorem surface for routing reuse same assumptions as THM-QUEUE-VOID-MERKLE-ESC-WARMUP-BUDGET-UNIT-BOUNDARY; witness pack includes one anchor at failureBudget = traceFold([cold]) and one at failureBudget = root + traceFold([cold]) + totalDeficit Lean theorem VoidMerkleEscWarmupQueueKernelBridge.void_merkle_esc_warmup_joint_queue_witness_pack in VoidMerkleEscWarmupQueueKernelBridge.lean, folding the tri-domain bridge with a standalone ESC strict-majority witness Mechanized
THM-QUEUE-VOID-MERKLE-ESC-WARMUP-BUDGET-NOT-CAPACITY-EQUAL-BUDGET-PLUS-ONE Contrarian anti-theorem variant: anchored tri-domain void+ESC+warmup interpretation does not force queue capacity to equal failureBudget + 1 same assumptions as THM-QUEUE-VOID-MERKLE-ESC-WARMUP-BUDGET-UNIT-BOUNDARY; contradiction uses canonical one-path witness (capacity = 1) together with source-derived positive budget Lean theorem VoidMerkleEscWarmupQueueKernelBridge.void_merkle_esc_warmup_budget_does_not_force_capacity_equals_budget_plus_one in VoidMerkleEscWarmupQueueKernelBridge.lean, via contradiction against the canonical unit-capacity witness Mechanized
THM-QUEUE-JACKSON-PRODUCT Finite open networks with a stable throughput witness satisfying the traffic equations admit an exact product-form occupancy law with exact singleton mass and total mean occupancy ∑ᵢ αᵢ / (μᵢ - αᵢ) finite node set; nonnegative external arrivals and routing weights; row-substochastic routing matrix; positive service rates μᵢ; nonnegative throughput witness α; traffic equations αᵢ = λᵢ + ∑ⱼ αⱼ Pⱼᵢ; stability αᵢ < μᵢ; witness may come from the least fixed-point approximation or spectral resolvent route, but its nonnegativity/stability side conditions are still supplied explicitly Lean definitions/theorems JacksonQueueing.JacksonNetworkData, JacksonQueueing.JacksonTrafficData.constructiveNetworkData, JacksonQueueing.JacksonTrafficData.spectralNetworkData, JacksonQueueing.JacksonNetworkData.load_traffic_equation, JacksonQueueing.jacksonProductMeasure, JacksonQueueing.jacksonProductMeasure_apply_singleton, JacksonQueueing.jackson_product_mean_total_occupancy, JacksonQueueing.jacksonNetworkMeasure, JacksonQueueing.jackson_network_measure_apply_singleton, JacksonQueueing.jackson_network_mean_total_occupancy, and JacksonQueueing.jackson_network_lintegral_balance Mechanized
THM-QUEUE-JACKSON-EXACT Finite open networks admit an exact constructive Jackson closure beyond the envelope ladder once an exact stable real traffic fixed point is supplied: under spectralRadius P < 1, any nonnegative real fixed point is unique, equals the constructive least fixed point after toReal, and already yields the same constructive mean occupancy and lintegral balance laws; the spectral/resolvent candidate is the canonical corollary finite node set; nonnegative external arrivals and routing weights; row-substochastic routing matrix; positive service rates μᵢ; spectralRadius P < 1; real traffic witness α; αᵢ >= 0; traffic equations αᵢ = λᵢ + ∑ⱼ αⱼ Pⱼᵢ; stability αᵢ < μᵢ Lean definitions/theorems JacksonExactClosure.JacksonTrafficData.exact_real_fixed_point_unique, JacksonExactClosure.JacksonTrafficData.constructiveThroughput_finite_of_real_fixed_point, JacksonExactClosure.JacksonTrafficData.constructiveThroughput_stable_of_real_fixed_point, JacksonExactClosure.JacksonTrafficData.constructiveThroughput_toReal_eq_real_fixed_point, JacksonExactClosure.JacksonTrafficData.constructiveNetworkDataOfRealFixedPoint, JacksonExactClosure.JacksonTrafficData.constructiveNetworkMeasureOfRealFixedPoint, JacksonExactClosure.JacksonTrafficData.constructive_network_mean_total_occupancy_of_real_fixed_point, JacksonExactClosure.JacksonTrafficData.constructive_network_lintegral_balance_of_real_fixed_point, and the spectral corollaries constructiveNetworkDataOfExactSpectral, constructiveNetworkMeasureOfExactSpectral, constructive_network_mean_total_occupancy_of_exact_spectral, constructive_network_lintegral_balance_of_exact_spectral Mechanized
THM-QUEUE-JACKSON-RAW Finite open networks satisfying the raw envelope criterion admit the same product-form occupancy and queue-balance laws with no hand-supplied throughput witness: if maxIncomingRoutingMass < 1 and maxExternalArrival / (1 - maxIncomingRoutingMass) < minServiceRate, the package constructs the network witness directly from raw (λ, P, μ) data finite node set; nonnegative external arrivals and routing weights; row-substochastic routing matrix; positive service rates; maxIncomingRoutingMass < 1; raw envelope below minServiceRate Lean definitions/theorems JacksonRawClosure.JacksonTrafficData.rawEnvelopeBound, JacksonRawClosure.JacksonTrafficData.rawEnvelopeBound_lt_serviceRate, JacksonRawClosure.JacksonTrafficData.constructiveNetworkDataOfRawEnvelope, JacksonRawClosure.JacksonTrafficData.spectralNetworkDataOfRawEnvelope, JacksonRawClosure.JacksonTrafficData.raw_jackson_product_mean_total_occupancy, and JacksonRawClosure.JacksonTrafficData.raw_jackson_lintegral_balance together with the underlying JacksonQueueing.*MaxIncomingRoutingMassMinService* constructors Mechanized
THM-QUEUE-JACKSON-FEEDFORWARD The bounded two-node feed-forward ceiling witness is a nontrivial raw exact Jackson subclass: its routing matrix is nilpotent (P^2 = 0), so the explicit throughput candidate already matches the constructive least fixed point and yields the same product-form mean occupancy and lintegral balance laws directly from raw parameters two-node adaptive ceiling witness over Bool; nonnegative left/right arrivals; reroute probability 0 <= p < 1; left stability λ_L < μ_L; right stability λ_R + λ_L p < μ_R Lean definitions/theorems JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.ceilingRoutingMatrix_sq_eq_zero, JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.ceiling_spectralRadius_eq_zero, JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.candidate_eq_constructiveThroughput_toReal, JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.ceilingConstructiveNetworkData, JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.ceilingConstructiveNetworkMeasure, JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.ceiling_constructive_network_mean_total_occupancy, and JacksonFeedForwardClosure.TwoNodeAdaptiveRoutingParameters.ceiling_constructive_network_lintegral_balance Mechanized
THM-QUEUE-JACKSON-ENVELOPE-LADDER The finite Jackson raw route sharpens into a descending constructive envelope ladder: if any chosen stage throughputEnvelopeApprox n already lies below service rates, then the same product-form occupancy and queue-balance laws close at that stage, with n = 1 recovering the local envelope and n = 2 the second-order envelope finite node set; nonnegative external arrivals and routing weights; row-substochastic routing matrix; positive service rates; maxIncomingRoutingMass < 1; chosen ladder stage n; service bound throughputEnvelopeApprox n i < μᵢ; local and second-order corollaries specialize n = 1 and n = 2 Lean definitions/theorems JacksonEnvelopeClosure.JacksonTrafficData.throughputEnvelopeApprox_zero_eq_rawEnvelopeBound, JacksonEnvelopeClosure.JacksonTrafficData.throughputEnvelopeApprox_one_eq_localEnvelope, JacksonEnvelopeClosure.JacksonTrafficData.throughputEnvelopeApprox_two_eq_secondOrderEnvelope, JacksonEnvelopeClosure.JacksonTrafficData.envelope_ladder_descends, JacksonEnvelopeClosure.JacksonTrafficData.trafficApprox_toReal_le_envelopeApprox, JacksonEnvelopeClosure.JacksonTrafficData.constructiveNetworkDataOfLocalEnvelope, JacksonEnvelopeClosure.JacksonTrafficData.spectralNetworkDataOfLocalEnvelope, JacksonEnvelopeClosure.JacksonTrafficData.constructiveNetworkDataOfSecondOrderEnvelope, JacksonEnvelopeClosure.JacksonTrafficData.spectralNetworkDataOfSecondOrderEnvelope, JacksonEnvelopeClosure.JacksonTrafficData.constructiveNetworkDataOfEnvelopeApprox, JacksonEnvelopeClosure.JacksonTrafficData.spectralNetworkDataOfEnvelopeApprox, JacksonEnvelopeClosure.JacksonTrafficData.local_jackson_product_mean_total_occupancy, JacksonEnvelopeClosure.JacksonTrafficData.second_order_jackson_product_mean_total_occupancy, JacksonEnvelopeClosure.JacksonTrafficData.nth_envelope_jackson_product_mean_total_occupancy, JacksonEnvelopeClosure.JacksonTrafficData.local_jackson_lintegral_balance, JacksonEnvelopeClosure.JacksonTrafficData.second_order_jackson_lintegral_balance, and JacksonEnvelopeClosure.JacksonTrafficData.nth_envelope_jackson_lintegral_balance Mechanized
THM-QUEUE-INFINITE-SUPPORT Infinite weighted scenario families preserve queue customer-time conservation under exact countable/infinite support aggregation arbitrary scenario index type; nonnegative scenario mass; sample-path customer-time = sojourn + open-age identity Lean theorems MeasureQueueing.weighted_queue_tsum_balance and MeasureQueueing.weighted_queue_tsum_terminal_expectation_balance Mechanized
THM-QUEUE-COUNTABLE-STOCHASTIC Countably supported stochastic queue laws preserve the same expectation/conservation identity countable-support probability mass function on scenarios; nonnegative measurable queue observables; sample-path customer-time = sojourn + open-age identity Lean theorems MeasureQueueing.pmf_queue_tsum_balance, MeasureQueueing.pmf_queue_tsum_terminal_balance, MeasureQueueing.pmf_queue_lintegral_balance, and MeasureQueueing.pmf_queue_terminal_lintegral_balance Mechanized
THM-QUEUE-MEASURE-LIMIT Measure-theoretic queue observables and monotone truncation families preserve conservation in the unbounded limit measurable nonnegative observables; sample-path customer-time = sojourn + open-age identity; monotone measurable truncation families for limit lift Lean theorems MeasureQueueing.measure_queue_lintegral_balance, MeasureQueueing.measure_queue_terminal_lintegral_balance, MeasureQueueing.measure_queue_truncation_limit_balance, and MeasureQueueing.measure_queue_truncation_terminal_limit_balance Mechanized
THM-QUEUE-ERGODIC-CESARO Unbounded open-network sample-path conservation lifts to long-run Cesaro limits, and vanishing residual open age yields terminal balance cumulative customer-area = departed sojourn + open age at every horizon; all three Cesaro averages converge; terminal form additionally requires open-age Cesaro limit = 0 Lean structure/theorems QueueStability.OpenNetworkCesaroWitness, QueueStability.open_network_cesaro_balance, and QueueStability.open_network_terminal_cesaro_balance Mechanized
THM-QUEUE-STATE-DEPENDENT-SCHEMA State-dependent open-network stationary and terminal queue balance follow from explicit routing-kernel bridge witnesses, explicit Lyapunov drift bounds outside a finite small set, and a positive drift gap; positive recurrence and stationary-law existence are then derived in-package rather than postulated separately measurable state space; state-dependent service and routing semantics; explicit routing bridge witness; explicit Lyapunov drift bound outside a finite small set; positive drift gap; terminal form additionally requires stationary open age to vanish almost everywhere Lean structure/theorems Axioms.StateDependentQueueStabilityAssumptions, Axioms.StateDependentQueueStabilityAssumptions.positiveRecurrent_holds, Axioms.StateDependentQueueStabilityAssumptions.stationaryLawExists_holds, Axioms.state_dependent_queue_stability_schema, and Axioms.state_dependent_queue_terminal_balance_schema Mechanized (witness-parameterized schema)
THM-QUEUE-ADAPTIVE-SUPREMUM Adaptive routing families dominated by a substochastic contractive ceiling kernel inherit the ceiling's throughput bounds constructively, and from that raw ceiling data plus a monotone expected-Lyapunov lift they inherit the state-dependent stationary and terminal balance shell once the chosen Lyapunov is expressed in one of five supported forms: an automatically synthesized minimum-slack bottleneck identity, a raw-score-normalized weighted identity, a positive-part-normalized weighted identity for arbitrary real scores, an explicit selector-based one-hot slack identity, or a weighted-slack decomposition; the recurrence/stationary-law layer is then derived from explicit kernel witnesses rather than separately assumed finite node set; finite adaptive state index set for the constructive comparison; nonnegative arrivals and routing weights; explicit dominating Jackson kernel or pointwise supremumKernel; if the pointwise ceiling is used, its row sums must still be substochastic; a nonnegative postfixed ceiling candidate; an adaptive expected-Lyapunov lift monotone in nodewise throughput bounds; either a minimum-slack chosen-Lyapunov identity, a nonnegative raw-score family with strictly positive total mass outside the small set, an arbitrary real score family whose positive part has strictly positive total mass outside the small set, an explicit selector-based chosen-Lyapunov slack identity, or a chosen-Lyapunov weighted-slack decomposition outside the small set; in the normalized nonnegative weighted case, pointwise node slack lower bounds suffice for drift-gap coverage Lean definitions/theorems JacksonQueueing.AdaptiveJacksonTrafficData, JacksonQueueing.AdaptiveJacksonTrafficData.constructiveThroughput_le_of_dominating_real_postfixed, JacksonQueueing.AdaptiveJacksonTrafficData.supremumKernel, JacksonQueueing.AdaptiveJacksonTrafficData.constructiveThroughput_le_supremumSpectralThroughput, JacksonQueueing.AdaptiveJacksonTrafficData.constructiveThroughput_stable_of_supremumSpectral, Axioms.AdaptiveExpectedLyapunovSynthesis, Axioms.AdaptiveCeilingDriftSynthesis, Axioms.minimumSlackNode, Axioms.minimumSlackSelector, Axioms.normalizedSlackWeights, Axioms.positivePartSlackScores, Axioms.AdaptiveCeilingDriftSynthesis.ofMinimumSlack, Axioms.AdaptiveCeilingDriftSynthesis.ofNormalizedScoreSlack, Axioms.AdaptiveCeilingDriftSynthesis.ofPositivePartScoreSlack, Axioms.AdaptiveCeilingDriftSynthesis.ofSelectedSlack, Axioms.AdaptiveCeilingDriftSynthesis.ofNormalizedWeightedSlack, Axioms.reserveCoversWeightedSlack_of_normalizedWeights, Axioms.AdaptiveSupremumStabilityAssumptions, Axioms.adaptive_queue_stability_from_supremum_schema, and Axioms.adaptive_queue_terminal_balance_from_supremum_schema Mechanized (constructive comparison + derived drift shell)
THM-QUEUE-ADAPTIVE-RAW-CEILING A bounded two-node adaptive rerouting family derives its own dominating ceiling kernel, strict-row-substochastic spectral side conditions, constructive throughput bound, and a linear drift witness directly from raw parameters bounded two-node adaptive state space; nonnegative left/right arrivals; reroute probability 0 <= p < 1; left-node stability λ_L < μ_L; right-node ceiling stability λ_R + λ_L p < μ_R Lean definitions/theorems StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.ceilingTrafficData, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.adaptiveTrafficData, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.ceiling_strict_row_substochastic, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.ceiling_spectralRadius_lt_one, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.candidate_fixed_point, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.constructiveThroughput_stable, StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.driftGap_positive, and StateDependentQueueFamilies.TwoNodeAdaptiveRoutingParameters.expectedLyapunov_drift Mechanized
THM-QUEUE-LIMIT-SCHEMA Stronger queue-limit claims with explicit support-exhaustion and integrable-envelope side conditions remain available as a higher-level theorem schema monotone support approximation; measurable customer-time/sojourn observables; dominating integrable envelope; finite truncations balanced Lean theorems Claims.weighted_queue_prefix_customer_time_balance, Claims.weighted_queue_prefix_expectation_balance, and schema Axioms.queue_limit_schema Mechanized (assumption-parameterized scaffold)
THM-QUEUE-CONTAINMENT Superseded by THM-QUEUE-SUBSUMPTION. Forward direction of queueing subsumption: when the supplied β₁=0 queue law holds, the framework recovers that one-path boundary, and when β₁>0 the framework exposes an additional topology-control witness queue law at β₁=0; topology-control witness for β₁>0 Lean schemas Axioms.queueing_containment_at_beta1_zero and Axioms.queueing_strict_extension_at_positive_beta + executable tests Mechanized (assumption-parameterized + executable)
THM-QUEUE-CONVERSE Converse direction of queueing subsumption: every queueing system (G/G/1, G/G/c, priority, network) admits a fork/race/fold embedding under C3' (probabilistic fold). Arrival processes map to fork distributions, service processes map to race outcomes, queue disciplines map to fold policies, routing matrices map to probabilistic fork/vent distributions, and multi-server systems map to β₁ = c-1. Little's Law holds in both representations. C3' (probabilistic fold) + ergodicity; work-conserving discipline; finite or countable state space for exact embedding Current Lean queue chapel surfaces: open-source/gnosis-math/Gnosis/QueueBoundary.lean, open-source/gnosis-math/Gnosis/MeasureQueueing.lean, open-source/gnosis-math/Gnosis/QueueStability.lean, open-source/gnosis-math/Gnosis/JacksonQueueing.lean; finite witness positive_backlog_embeds_as_boundary_cycles in open-source/gnosis-math/Gnosis/QueueingSubsumptionWitness.lean. The former executable converse suite remains historical. Mechanized (Lean schema + finite witness)
THM-C3-PRIME-GENERALIZATION C3' (probabilistic fold) generalizes C3 (deterministic fold): deterministic fold is the Dirac δ special case of probabilistic fold. C3' preserves C1 (fork creates paths), C2 (race selects earliest), and C4 (finite termination). Under ergodicity, conservation holds in expectation: E[V_fork] = E[W_fold] + E[Q_vent]. C3' is strictly weaker than C3 (positive fold entropy vs zero) probabilistic fold distribution with well-defined expectation; ergodicity for conservation in expectation Current Lean queue chapel surfaces: open-source/gnosis-math/Gnosis/MeasureQueueing.lean, open-source/gnosis-math/Gnosis/QueueStability.lean, open-source/gnosis-math/Gnosis/StateDependentQueueFamilies.lean; finite boundary witness queue_embedding_witness in open-source/gnosis-math/Gnosis/QueueingSubsumptionWitness.lean. The former executable suite remains historical. Mechanized (Lean schema + finite witness)
THM-PROBABILISTIC-FOLD-SAFETY Under C3' + ergodicity, probabilistic fold preserves all four fork/race/fold axioms and conservation holds in expectation rather than pointwise. The entropy increase is bounded: H(fold) = 0 for deterministic (C3), H(fold) > 0 for probabilistic (C3'). C3' fold distribution; ergodicity; finite fork/race/fold system Current Lean queue chapel surfaces: open-source/gnosis-math/Gnosis/MeasureQueueing.lean, open-source/gnosis-math/Gnosis/QueueStability.lean, open-source/gnosis-math/Gnosis/QueueBoundary.lean; finite service monotonicity witness service_monotone_reduces_backlog in open-source/gnosis-math/Gnosis/QueueingSubsumptionWitness.lean. Monte Carlo executable coverage remains historical rather than a current ledger dependency. Mechanized (Lean schema + finite witness)
THM-QUEUE-SUBSUMPTION Bidirectional subsumption of queueing theory by fork/race/fold: (forward) FRF at β₁=0 recovers queueing theory (THM-QUEUE-CONTAINMENT); (converse) every queueing system embeds as FRF under C3' (THM-QUEUE-CONVERSE). The subsumption is representational/syntactic -- fork/race/fold provides the language, specific solution techniques (product-form, heavy-traffic limits, matrix-analytic methods) are additional structure within that language. Ergodicity is assumed, not derived. C1-C3'-C4 axioms; ergodicity; all assumptions of THM-QUEUE-CONTAINMENT (forward) and THM-QUEUE-CONVERSE (converse) Forward and converse point at Lean schema surfaces open-source/gnosis-math/Gnosis/QueueBoundary.lean, open-source/gnosis-math/Gnosis/MeasureQueueing.lean, open-source/gnosis-math/Gnosis/QueueStability.lean, open-source/gnosis-math/Gnosis/StateDependentQueueFamilies.lean, open-source/gnosis-math/Gnosis/JacksonQueueing.lean; finite executable-style witnesses beta_zero_boundary_recovers_empty_queue, positive_backlog_embeds_as_boundary_cycles, service_monotone_reduces_backlog, and queue_embedding_witness in open-source/gnosis-math/Gnosis/QueueingSubsumptionWitness.lean. Honest caveats: representational not dynamical, ergodicity assumed, heavy-traffic diffusion limits not covered, C3' weaker than C3; deleted executable suites remain historical. Mechanized (Lean schema + finite witness)
THM-QUEUE-JACKSON-QUEUEING Jackson network fundamentals: spectrum/transpose equality, spectral radius transpose equality, M/M/1 stationary queue length integral equals rho/(1-rho). Measure-theoretic queue analysis with weighted series balance equation M/M/1 stability (rho < 1); finite Jackson network Lean theorems JacksonQueueing.spectrum_transpose_eq, JacksonQueueing.spectralRadius_transpose_eq, JacksonQueueing.mm1_stationary_lintegral_queue_length in JacksonQueueing.lean + MeasureQueueing.weighted_queue_tsum_balance in MeasureQueueing.lean + QueueStability.mm1StationaryPMF_apply and QueueStability.mm1_stationary_mean_queue_length in QueueStability.lean + QueueBoundary.canonicalMM1Boundary in QueueBoundary.lean Mechanized
THM-STATE-DEPENDENT-QUEUE-FAMILIES State-dependent queue families: vacation queue state, retrial queue, reneging queue, adaptive routing queue. Queue law structures for multiple service disciplines with customer time, sojourn time, and open age accounting VacationQueueState; RetrialQueueState; RenegingQueueState; AdaptiveRoutingQueueState Lean definitions and queue law structures in StateDependentQueueFamilies.lean Mechanized
THM-QUEUE-ECOSYSTEM-PREDATOR-UNIT-BOUNDARY Cross-domain bridge: ecosystem predator-prey resonance induces a strict-majority failure budget and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with predator-anchored arrival/service rates ecosystem assumptions preyCount + predatorCount = boundary, predatorCount ≥ 1; canonical interpretation failureBudget = predatorCount, replicaCount = 2*failureBudget + 1 Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_predator_budget_yields_unit_queue_boundary in EcosystemTurbulenceQueueKernelBridge.lean, composing EcosystemTopology.lotka_volterra_resonance with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-TURBULENCE-EDDY-UNIT-BOUNDARY Cross-domain bridge: turbulence hope-gap arithmetic plus explicit eddy witness induces a strict-majority failure budget and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) turbulence assumptions kineticInjection > foldCapacity, eddyKnots = kineticInjection - foldCapacity; canonical interpretation failureBudget = kineticInjection - foldCapacity, replicaCount = 2*failureBudget + 1 Lean theorem EcosystemTurbulenceQueueKernelBridge.turbulence_eddy_budget_yields_unit_queue_boundary in EcosystemTurbulenceQueueKernelBridge.lean, composing TurbulenceTopology.turbulence_is_hope_gap with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-ECOSYSTEM-TURBULENCE-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined ecosystem+turbulence interpretation preserves both source inequalities and yields one canonical queue witness with anchored combined-budget arrival/service rates ecosystem assumptions preyCount + predatorCount = boundary, predatorCount ≥ 1; turbulence assumptions kineticInjection > foldCapacity, eddyKnots = kineticInjection - foldCapacity; canonical interpretation failureBudget = predatorCount + (kineticInjection - foldCapacity), replicaCount = 2*failureBudget + 1 Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_budget_yields_unit_queue_boundary in EcosystemTurbulenceQueueKernelBridge.lean, folding ecosystem/turbulence inequalities into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-ECOSYSTEM-TURBULENCE-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: combined ecosystem+turbulence interpretation with anchored queue rates does not force positive path-width (β₁ > 0) same ecosystem+turbulence assumptions as THM-QUEUE-ECOSYSTEM-TURBULENCE-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_budget_does_not_force_positive_beta1 in EcosystemTurbulenceQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-ECOSYSTEM-TURBULENCE-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive interpreted ecosystem+turbulence budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths ecosystem assumptions preyCount + predatorCount = boundary, predatorCount ≥ 1; turbulence assumptions kineticInjection > foldCapacity, eddyKnots = kineticInjection - foldCapacity; positivity route 0 < failureBudget = predatorCount + eddyKnots Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_budget_yields_positive_topological_deficit in EcosystemTurbulenceQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation at pathCount = failureBudget + 1 Mechanized
THM-QUEUE-ECOSYSTEM-TURBULENCE-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored ecosystem+turbulence interpretation does not force strict capacity growth (capacity > 1) same ecosystem+turbulence assumptions as THM-QUEUE-ECOSYSTEM-TURBULENCE-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_budget_does_not_force_strict_capacity_growth in EcosystemTurbulenceQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-ECOSYSTEM-TURBULENCE-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from ecosystem+turbulence source mass into queue coordinates transports the canonical one-path queue witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-ECOSYSTEM-TURBULENCE-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret (predatorCount + eddyKnots) = failureBudget; strict-majority interpretation replicaCount = 2*interpret(...) + 1 Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_semantic_morphism_yields_unit_queue_boundary in EcosystemTurbulenceQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-ETHNOMUSICOLOGY-OVERTONE-UNIT-BOUNDARY Cross-domain bridge: ethnomusicology overtone-lift arithmetic induces a strict-majority failure budget and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with overtone-filter anchored arrival/service rates ethnomusicology assumptions oralFilter ≥ 1, overtoneLift = fundamentalPitch + oralFilter; canonical interpretation failureBudget = oralFilter, replicaCount = 2*failureBudget + 1 Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_overtone_budget_yields_unit_queue_boundary in EthnoNarrativeQueueKernelBridge.lean, composing EthnomusicologyTopology.overtone_is_cover_space_lift with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-NARRATIVE-CROSSINGS-UNIT-BOUNDARY Cross-domain bridge: narrative call-to-adventure crossing arithmetic induces a strict-majority failure budget and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with narrative-crossing anchored arrival/service rates narrative assumption narrativeCrossings ≥ 1; canonical interpretation failureBudget = narrativeCrossings, replicaCount = 2*failureBudget + 1 Lean theorem EthnoNarrativeQueueKernelBridge.narrative_crossings_budget_yields_unit_queue_boundary in EthnoNarrativeQueueKernelBridge.lean, composing NarrativeTopology.call_to_adventure_dilates_cover_space with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined ethnomusicology+narrative interpretation preserves both source inequalities and yields one canonical queue witness with anchored combined-budget arrival/service rates ethnomusicology assumptions oralFilter ≥ 1, overtoneLift = fundamentalPitch + oralFilter; narrative assumption narrativeCrossings ≥ 1; canonical interpretation failureBudget = oralFilter + narrativeCrossings, replicaCount = 2*failureBudget + 1 Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_budget_yields_unit_queue_boundary in EthnoNarrativeQueueKernelBridge.lean, folding ethnomusicology/narrative inequalities into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: combined ethnomusicology+narrative interpretation with anchored queue rates does not force positive path-width (β₁ > 0) same ethnomusicology+narrative assumptions as THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_budget_does_not_force_positive_beta1 in EthnoNarrativeQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive combined ethnomusicology+narrative interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths ethnomusicology assumptions oralFilter ≥ 1, overtoneLift = fundamentalPitch + oralFilter; narrative assumption narrativeCrossings ≥ 1; positivity route 0 < failureBudget = oralFilter + narrativeCrossings Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_budget_yields_positive_topological_deficit in EthnoNarrativeQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation at pathCount = failureBudget + 1 Mechanized
THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored ethnomusicology+narrative interpretation does not force queue path-width to equal interpreted budget mass same assumptions as THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-BUDGET-UNIT-BOUNDARY; strict budget positivity follows from oralFilter ≥ 1 and narrativeCrossings ≥ 1; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_budget_does_not_force_beta1_equals_budget in EthnoNarrativeQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and strict budget positivity Mechanized
THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation map from combined ethnomusicology+narrative budget mass into queue coordinates transports the canonical one-path witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-ETHNOMUSICOLOGY-NARRATIVE-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret(failureBudget) = failureBudget; strict-majority interpretation replicaCount = 2*interpret(failureBudget) + 1 Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_semantic_morphism_yields_unit_queue_boundary in EthnoNarrativeQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-BILL-OF-RIGHTS-UNIT-BOUNDARY Cross-domain bridge: the Bill of Rights existence floor induces a strict-majority quorum interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with rights-floor anchored arrival/service rates canonical interpretation failureBudget = w(R,v) - 1, replicaCount = 2*failureBudget + 1; rights-floor witness BillOfRights.right_to_exist Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_floor_yields_unit_queue_boundary in BillRightsStructuralHoleQueueKernelBridge.lean, combining BillOfRights.right_to_exist with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-STRUCTURAL-HOLE-UNIT-BOUNDARY Cross-domain bridge: structural-hole interpolation positivity induces a strict-majority quorum interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with interpolation-budget anchored arrival/service rates structural-hole witness NonEmpiricalPrediction.StructuralHole; canonical interpretation failureBudget = interpolationWeight - 1, replicaCount = 2*failureBudget + 1; interpolation positivity witness hole_has_positive_weight Lean theorem BillRightsStructuralHoleQueueKernelBridge.structural_hole_budget_yields_unit_queue_boundary in BillRightsStructuralHoleQueueKernelBridge.lean, combining structural-hole positivity with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-BUDGET-UNIT-BOUNDARY Cross-domain bridge: explicit combined interpretation of rights-floor and structural-hole interpolation preserves both source identities and yields one canonical one-path queue witness with anchored combined-budget arrival/service rates rights witness BillOfRights.right_to_exist; structural-hole witness hole_has_positive_weight; canonical interpretation failureBudget = (w(R,v)-1) + (interpolationWeight-1), replicaCount = 2*failureBudget + 1 Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_budget_yields_unit_queue_boundary in BillRightsStructuralHoleQueueKernelBridge.lean, folding the combined interpretation into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: combined rights-floor + structural-hole interpretation with anchored queue rates does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_budget_does_not_force_positive_beta1 in BillRightsStructuralHoleQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-BUDGET-UNIT-BOUNDARY Cross-domain bridge: rights-floor, structural-hole interpolation, and Goodhart proxy-gap arithmetic route into one strict-majority queue interpretation and yield a canonical one-path queue witness (β₁ = 0, capacity = 1) with anchored tri-domain budget rates rights witness BillOfRights.right_to_exist; structural-hole witness hole_has_positive_weight; Goodhart bounds vTrue ≤ R, vGamed ≤ R, and strict gaming witness vGamed < vTrue; canonical interpretation failureBudget = (w(R,v)-1) + (interpolationWeight-1) + (vTrue-vGamed), replicaCount = 2*failureBudget + 1 Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_goodhart_budget_yields_unit_queue_boundary in BillRightsStructuralHoleQueueKernelBridge.lean, composing GoodhartsLaw.proxy_gap with the strict-majority queue witness constructor Mechanized
THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-JOINT-WITNESS-PACK Cross-domain bridge extension: package both the rights+structural-hole witness and the tri-domain rights+structural-hole+Goodhart witness in one synchronized theorem surface, so both anchored boundary interpretations are available together same source assumptions as THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-BUDGET-UNIT-BOUNDARY; witness pack includes anchors for both rightsStructuralHoleFailureBudget and rightsStructuralHoleGoodhartFailureBudget Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_goodhart_joint_queue_witness_pack in BillRightsStructuralHoleQueueKernelBridge.lean, folding rights_structural_hole_budget_yields_unit_queue_boundary and rights_structural_hole_goodhart_budget_yields_unit_queue_boundary Mechanized
THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored tri-domain rights+structural-hole+Goodhart interpretation does not force queue path-width to equal interpreted budget mass same assumptions as THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-BUDGET-UNIT-BOUNDARY; strict gaming hypothesis vGamed < vTrue provides positive interpreted budget for contradiction witness Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_goodhart_budget_does_not_force_beta1_equals_budget in BillRightsStructuralHoleQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain rights+structural-hole+Goodhart budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = failureBudget + 1 same source assumptions as THM-QUEUE-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-BUDGET-UNIT-BOUNDARY; interpretation anchor failureBudget = rightsStructuralHoleGoodhartFailureBudget Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_goodhart_budget_yields_geometric_rate_certificate in BillRightsStructuralHoleQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: tri-domain adapter budget positivity is derived from source assumptions (vGamed < vTrue) instead of introduced as an independent black-box field source assumptions vTrue ≤ R, vGamed ≤ R, vGamed < vTrue; adapter budget anchor budgetReal = (rightsStructuralHoleGoodhartFailureBudget : ℝ) Lean theorems BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_goodhart_budget_real_positive and RightsStructuralHoleGoodhartKernelLiftAdapter.budget_pos_from_source in BillRightsStructuralHoleQueueKernelBridge.lean Mechanized
THM-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GOODHART-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: tri-domain rights+structural-hole+Goodhart data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source identities and source-derived budget positivity explicit adapter bundle carrying rights/structural-hole context, Goodhart bounds and strict-gaming witness, source-derived real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem RightsStructuralHoleGoodhartKernelLiftAdapter.rights_structural_hole_goodhart_continuous_ergodicity_lift in BillRightsStructuralHoleQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-QUEUE-SPIDERWEB-MESH-UNIT-BOUNDARY Cross-domain bridge: nontrivial spiderweb routing-path mass (peers > 0, hops > 0) induces a strict-majority queue interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with spiderweb-path anchored arrival/service rates spiderweb mesh witness MeshConfig; nontriviality assumptions 0 < peers, 0 < hops; canonical interpretation failureBudget = meshRoutingPaths, replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebReynoldsQueueKernelBridge.spiderweb_mesh_budget_yields_unit_queue_boundary in SpiderwebReynoldsQueueKernelBridge.lean, composing SpiderwebMeshNetwork.beta1_pos_of_nontrivial with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-REYNOLDS-DIVERSITY-UNIT-BOUNDARY Cross-domain bridge: Reynolds diversity vent arithmetic (pathCount - 1) induces a strict-majority queue interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with diversity-budget anchored arrival/service rates Reynolds diversity witness ReynoldsBFT.DiverseSystem (pathCount ≥ 2); canonical interpretation failureBudget = pathCount - 1, replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebReynoldsQueueKernelBridge.reynolds_diversity_budget_yields_unit_queue_boundary in SpiderwebReynoldsQueueKernelBridge.lean, composing Reynolds diversity chain lemmas with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SPIDERWEB-REYNOLDS-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined spiderweb routing-path and Reynolds diversity interpretation preserves both source identities and yields one canonical queue witness with anchored combined-budget arrival/service rates spiderweb nontriviality assumptions 0 < peers, 0 < hops; Reynolds diversity witness pathCount ≥ 2; canonical interpretation failureBudget = meshRoutingPaths + (pathCount - 1), replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebReynoldsQueueKernelBridge.spiderweb_reynolds_budget_yields_unit_queue_boundary in SpiderwebReynoldsQueueKernelBridge.lean, folding spiderweb/Reynolds identities into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SPIDERWEB-REYNOLDS-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: combined spiderweb+Reynolds interpretation with anchored queue rates does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-SPIDERWEB-REYNOLDS-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem SpiderwebReynoldsQueueKernelBridge.spiderweb_reynolds_budget_does_not_force_positive_beta1 in SpiderwebReynoldsQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-BUDGET-UNIT-BOUNDARY Cross-domain bridge: spiderweb routing-path mass, Reynolds diversity budget, and cryptographic side-channel floor route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored tri-domain arrival/service rates spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; Reynolds diversity witness pathCount ≥ 2; cryptographic side-channel witness SideChannelShadow with 0 < perEvalFloor; interpretation anchor failureBudget = meshRoutingPaths mesh + (pathCount - 1) + perEvalFloor, replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebReynoldsCryptoQueueKernelBridge.spiderweb_reynolds_crypto_budget_yields_unit_queue_boundary in SpiderwebReynoldsCryptoQueueKernelBridge.lean, composing source-domain identities with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive tri-domain spiderweb+Reynolds+crypto interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths same assumptions as THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity Lean theorem SpiderwebReynoldsCryptoQueueKernelBridge.spiderweb_reynolds_crypto_budget_yields_positive_topological_deficit in SpiderwebReynoldsCryptoQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored spiderweb+Reynolds+crypto interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-BUDGET-UNIT-BOUNDARY; strict interpreted-budget positivity follows from spiderweb nontriviality and side-channel floor positivity Lean theorem SpiderwebReynoldsCryptoQueueKernelBridge.spiderweb_reynolds_crypto_budget_does_not_force_beta1_equals_budget in SpiderwebReynoldsCryptoQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation map from spiderweb+Reynolds+crypto budget mass into queue coordinates transports the canonical one-path witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-SPIDERWEB-REYNOLDS-CRYPTO-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret(failureBudget) = failureBudget; strict-majority interpretation replicaCount = 2*interpret(failureBudget) + 1 Lean theorem SpiderwebReynoldsCryptoQueueKernelBridge.spiderweb_reynolds_crypto_semantic_morphism_yields_unit_queue_boundary in SpiderwebReynoldsCryptoQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-KRAFT-WASTED-CAPACITY-UNIT-BOUNDARY Cross-domain bridge: Kraft wasted-capacity accounting induces a strict-majority queue interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with wasted-capacity anchored arrival/service rates prefix-free code witness KraftInequality.PrefixFreeCode; canonical interpretation failureBudget = wastedCapacity, replicaCount = 2*failureBudget + 1; Kraft identity godWeight(total, wasted) = used + 1 Lean theorem KraftSolomonoffQueueKernelBridge.kraft_wasted_capacity_yields_unit_queue_boundary in KraftSolomonoffQueueKernelBridge.lean, composing KraftInequality.kraft_weight with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SOLOMONOFF-DESCRIPTION-UNIT-BOUNDARY Cross-domain bridge: Solomonoff description conservation induces a strict-majority queue interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with description-budget anchored arrival/service rates Solomonoff assumptions v ≤ R; canonical interpretation failureBudget = v, replicaCount = 2*failureBudget + 1; conservation identity godWeight(R,v) + v = R + 1 Lean theorem KraftSolomonoffQueueKernelBridge.solomonoff_description_budget_yields_unit_queue_boundary in KraftSolomonoffQueueKernelBridge.lean, composing SolomonoffInduction.description_conservation with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-KRAFT-SOLOMONOFF-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined Kraft wasted-capacity and Solomonoff description interpretations preserve both source identities and yield one canonical queue witness with anchored combined-budget arrival/service rates prefix-free code witness KraftInequality.PrefixFreeCode; Solomonoff assumption v ≤ R; canonical interpretation failureBudget = wastedCapacity + v, replicaCount = 2*failureBudget + 1 Lean theorem KraftSolomonoffQueueKernelBridge.kraft_solomonoff_budget_yields_unit_queue_boundary in KraftSolomonoffQueueKernelBridge.lean, folding Kraft/Solomonoff identities into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-KRAFT-SOLOMONOFF-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: combined Kraft+Solomonoff interpretation with anchored queue rates does not force β₁ to equal the combined budget mass same assumptions as THM-QUEUE-KRAFT-SOLOMONOFF-BUDGET-UNIT-BOUNDARY plus positive combined budget 0 < wastedCapacity + v; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem KraftSolomonoffQueueKernelBridge.kraft_solomonoff_budget_does_not_force_beta1_equals_budget in KraftSolomonoffQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-CAPITAL-TIMELINE-UNIT-BOUNDARY Cross-domain bridge: positive capital-lockup timeline mass induces a strict-majority interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with timeline-anchored arrival/service rates lockup witness CapitalLockup.LockupState with positive timeline (totalMinutes > 0); canonical interpretation failureBudget = totalMinutes, replicaCount = 2*failureBudget + 1 Lean theorem CapitalMdlQueueKernelBridge.capital_timeline_budget_yields_unit_queue_boundary in CapitalMdlQueueKernelBridge.lean, using QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MDL-DESCRIPTION-UNIT-BOUNDARY Cross-domain bridge: MDL description-cost identity induces a strict-majority interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with description-budget anchored arrival/service rates MDL witness MinimumDescriptionLength.ModelCandidate; identity quality = budget - totalCost + 1; canonical interpretation failureBudget = totalCost, replicaCount = 2*failureBudget + 1 Lean theorem CapitalMdlQueueKernelBridge.mdl_description_budget_yields_unit_queue_boundary in CapitalMdlQueueKernelBridge.lean, combining MinimumDescriptionLength.mdl_is_godweight with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CAPITAL-MDL-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined capital timeline and MDL description identities route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored combined-budget arrival/service rates lockup witness CapitalLockup.LockupState (totalMinutes > 0); MDL witness MinimumDescriptionLength.ModelCandidate; canonical interpretation failureBudget = totalMinutes + totalCost, replicaCount = 2*failureBudget + 1 Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_budget_yields_unit_queue_boundary in CapitalMdlQueueKernelBridge.lean, folding source identities into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CAPITAL-MDL-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored capital+MDL interpretation does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-CAPITAL-MDL-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_budget_does_not_force_positive_beta1 in CapitalMdlQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-CAPITAL-MDL-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored capital+MDL interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-CAPITAL-MDL-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_budget_does_not_force_strict_capacity_growth in CapitalMdlQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-CAPITAL-MDL-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive combined capital+MDL interpreted budget forces strictly positive TCP-style topological deficit on the lifted (budget + 1) path model lockup witness CapitalLockup.LockupState (totalMinutes > 0); MDL witness MinimumDescriptionLength.ModelCandidate; interpreted budget failureBudget = totalMinutes + totalCost; lifted path floor 2 ≤ failureBudget + 1 Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_positive_budget_yields_positive_topological_deficit in CapitalMdlQueueKernelBridge.lean, combining source budget positivity with CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-CAPITAL-MDL-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored capital+MDL interpretation does not force queue path-width to equal interpreted budget mass same assumptions as THM-QUEUE-CAPITAL-MDL-BUDGET-UNIT-BOUNDARY; positive combined budget follows from totalMinutes > 0; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_budget_does_not_force_beta1_equals_budget in CapitalMdlQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and strict budget positivity Mechanized
THM-QUEUE-BARYOGENESIS-ERASURE-UNIT-BOUNDARY Cross-domain bridge: Baryogenesis paths-lost accounting yields a strict-majority queue interpretation and canonical one-path boundary witness. BaryonViolationWitness; canonical interpretation failureBudget = pathsBefore - pathsAfter, replicaCount = 2*failureBudget + 1 Lean theorem BaryogenesisBureaucracyQueueKernelBridge.baryogenesis_erasure_yields_unit_queue_boundary in BaryogenesisBureaucracyQueueKernelBridge.lean Mechanized
THM-QUEUE-BUREAUCRACY-STABILIZATION-UNIT-BOUNDARY Cross-domain bridge: Bureaucratic stabilization yields a strict-majority queue interpretation and canonical one-path boundary witness. BureaucraticFilter with bureaucraticDepth > 0 and governanceOscillation < stabilizationFactor; canonical interpretation failureBudget = 1, replicaCount = 3 Lean theorem BaryogenesisBureaucracyQueueKernelBridge.bureaucracy_stabilization_yields_unit_queue_boundary in BaryogenesisBureaucracyQueueKernelBridge.lean Mechanized
THM-QUEUE-BARYOGENESIS-BUREAUCRACY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined Baryogenesis erasure and Bureaucratic stabilization yields unified strict-majority queue interpretation and canonical one-path boundary witness. BaryonViolationWitness and BureaucraticFilter Lean theorem BaryogenesisBureaucracyQueueKernelBridge.baryogenesis_bureaucracy_budget_yields_unit_queue_boundary in BaryogenesisBureaucracyQueueKernelBridge.lean Mechanized
THM-QUEUE-BARYOGENESIS-BUREAUCRACY-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: combined Baryogenesis+Bureaucracy interpretation with anchored queue rates does not force β₁ to equal the combined budget mass. same assumptions plus positive combined budget Lean theorem BaryogenesisBureaucracyQueueKernelBridge.baryogenesis_bureaucracy_budget_does_not_force_beta1_equals_budget in BaryogenesisBureaucracyQueueKernelBridge.lean Mechanized
THM-QUEUE-CAPITAL-MDL-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation map from combined capital+MDL budget mass into queue coordinates transports the canonical one-path witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-CAPITAL-MDL-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret failureBudget = failureBudget; strict-majority interpretation replicaCount = 2*interpret(failureBudget) + 1 Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_semantic_morphism_yields_unit_queue_boundary in CapitalMdlQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-RETROCAUSAL-TRAJECTORY-UNIT-BOUNDARY Cross-domain bridge: nonempty retrocausal trajectory length induces a strict-majority queue interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with trajectory-budget anchored arrival/service rates retrocausal witness RetrocausalBound.RetrocausalWitness; nonempty trajectory (trajectory ≠ []); canonical interpretation failureBudget = trajectory.length, replicaCount = 2*failureBudget + 1 Lean theorem RetrocausalCausalQueueKernelBridge.retrocausal_nonempty_trajectory_yields_unit_queue_boundary in RetrocausalCausalQueueKernelBridge.lean, composing trajectory-length identity with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-RETROCAUSAL-CAUSAL-ADJUSTMENT-BRIDGE-UNIT-BOUNDARY Cross-domain bridge: when causal-adjustment budget is explicitly identified with retrocausal trajectory budget, the causal adjustment identity and canonical one-path queue witness hold together under one anchored interpretation retrocausal witness with nonempty trajectory; causal adjustment assumptions treat + confound ≤ R; budget bridge equality trajectory.length = treat + confound; canonical interpretation failureBudget = trajectory.length, replicaCount = 2*failureBudget + 1 Lean theorem RetrocausalCausalQueueKernelBridge.retrocausal_causal_budget_bridge_yields_unit_queue_boundary in RetrocausalCausalQueueKernelBridge.lean, composing CausalInference.adjustment_formula with the retrocausal queue witness constructor Mechanized
THM-QUEUE-RETROCAUSAL-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored retrocausal trajectory-budget interpretation does not force positive path-width (β₁ > 0) retrocausal witness with nonempty trajectory; witness restricted to boundaries with anchored arrival/service rates from the retrocausal interpretation Lean theorem RetrocausalCausalQueueKernelBridge.retrocausal_budget_does_not_force_positive_beta1 in RetrocausalCausalQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-RETROCAUSAL-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored retrocausal trajectory-budget interpretation does not force strict capacity growth (capacity > 1) retrocausal witness with nonempty trajectory; witness restricted to boundaries with anchored arrival/service rates from the retrocausal interpretation Lean theorem RetrocausalCausalQueueKernelBridge.retrocausal_budget_does_not_force_strict_capacity_growth in RetrocausalCausalQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-CONTAGION-TECHNIQUE-UNIT-BOUNDARY Cross-domain bridge: topological contagion spillover plus fighting-induced trauma routed through an explicit strict-majority interpretation yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with contagion+technique anchored arrival/service rates contagion assumptions source.internalHeat > source.containmentThreshold and neighbor.phantomLoad ≥ source.internalHeat - source.containmentThreshold; fighting witness TechniqueAsAntidote.IsFighting w1 w2 move; canonical interpretation failureBudget = neighbor.phantomLoad + altitude(w2), replicaCount = 2*failureBudget + 1 Lean theorem TopologicalContagionTechniqueQueueKernelBridge.contagion_technique_budget_yields_unit_queue_boundary in TopologicalContagionTechniqueQueueKernelBridge.lean, composing TopologicalContagion.thermal_spillover and TechniqueAsAntidote.fighting_generates_trauma with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CONTAGION-TECHNIQUE-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: combined contagion+technique interpretation with anchored queue rates does not force queue path width to equal the combined budget mass same assumptions as THM-QUEUE-CONTAGION-TECHNIQUE-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem TopologicalContagionTechniqueQueueKernelBridge.contagion_technique_budget_does_not_force_beta1_equals_budget in TopologicalContagionTechniqueQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-STRESS-AESTHETICS-BUDGET-UNIT-BOUNDARY Cross-domain bridge: stress-energy identity plus UI-friction minimization routed through an explicit strict-majority interpretation yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with stress+aesthetics anchored arrival/service rates stress assumptions from mechanized_stress_energy_tensor (ct.defenseWeight = defenseWeight R v, R = 54, irrational resonance witness, 0 < n); UI assumptions orderedFriction + precomputationCost < chaoticFriction; canonical interpretation failureBudget = stressEnergy + (chaoticFriction - orderedFriction), replicaCount = 2*failureBudget + 1 Lean theorem StressAestheticsQueueKernelBridge.stress_aesthetics_budget_yields_unit_queue_boundary in StressAestheticsQueueKernelBridge.lean, composing mechanized_stress_energy_tensor and UIAestheticsTopology.aesthetics_minimizes_v with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-STRESS-AESTHETICS-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: combined stress+aesthetics interpretation with anchored queue rates does not force queue path width to equal the combined budget mass same assumptions as THM-QUEUE-STRESS-AESTHETICS-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem StressAestheticsQueueKernelBridge.stress_aesthetics_budget_does_not_force_beta1_equals_budget in StressAestheticsQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-DECEPTION-PHANTOM-UNIT-BOUNDARY Cross-domain bridge: deception phantom-injection witness induces a strict-majority interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with deception-budget anchored arrival/service rates deception witness DeceptionTopology.gaslighting_phantom_injection with injected ≥ 1; canonical interpretation failureBudget = injected, replicaCount = 2*failureBudget + 1 Lean theorem DeceptionAutoimmunityQueueKernelBridge.deception_phantom_budget_yields_unit_queue_boundary in DeceptionAutoimmunityQueueKernelBridge.lean, composing deception witness arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-AUTOIMMUNITY-HASH-COLLISION-UNIT-BOUNDARY Cross-domain bridge: autoimmune hash-collision parser-exhaust witness induces a strict-majority interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with parser-exhaust anchored arrival/service rates autoimmunity witness AutoimmunityTopology.autoimmunity_hash_collision with faultyHash = friendlyInvariant and parserExhaust ≥ 1; canonical interpretation failureBudget = parserExhaust, replicaCount = 2*failureBudget + 1 Lean theorem DeceptionAutoimmunityQueueKernelBridge.autoimmunity_hash_collision_budget_yields_unit_queue_boundary in DeceptionAutoimmunityQueueKernelBridge.lean, composing hash-collision witness arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined deception+autoimmunity interpretation preserves both source witnesses and yields one canonical queue witness with anchored combined-budget arrival/service rates deception witness injected ≥ 1; autoimmunity witness faultyHash = friendlyInvariant, parserExhaust ≥ 1; canonical interpretation failureBudget = injected + parserExhaust, replicaCount = 2*failureBudget + 1 Lean theorem DeceptionAutoimmunityQueueKernelBridge.deception_autoimmunity_budget_yields_unit_queue_boundary in DeceptionAutoimmunityQueueKernelBridge.lean, folding both source witnesses into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: combined deception+autoimmunity interpretation with anchored queue rates does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-DECEPTION-AUTOIMMUNITY-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem DeceptionAutoimmunityQueueKernelBridge.deception_autoimmunity_budget_does_not_force_positive_beta1 in DeceptionAutoimmunityQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: combined deception+autoimmunity interpretation with anchored queue rates does not force queue path-width to equal combined budget mass same assumptions as THM-QUEUE-DECEPTION-AUTOIMMUNITY-BUDGET-UNIT-BOUNDARY; positive combined budget follows from injected ≥ 1 and parserExhaust ≥ 1 Lean theorem DeceptionAutoimmunityQueueKernelBridge.deception_autoimmunity_budget_does_not_force_beta1_equals_budget in DeceptionAutoimmunityQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and strict budget positivity Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-BUDGET-UNIT-BOUNDARY Cross-domain bridge: deception phantom injection, autoimmunity parser exhaustion, and mediation wattage are routed through one strict-majority interpretation to yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored tri-domain arrival/service rates deception witness injected ≥ 1; autoimmunity witness faultyHash = friendlyInvariant, parserExhaust ≥ 1; mediation assumptions searchCapacity < 10 and searchCapacity + externalCapacity ≥ 10; canonical interpretation failureBudget = injected + parserExhaust + externalCapacity, replicaCount = 2*failureBudget + 1 Lean theorem DeceptionAutoimmunityNegotiationQueueKernelBridge.deception_autoimmunity_negotiation_budget_yields_unit_queue_boundary in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean, composing source witnesses with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-JOINT-WITNESS-PACK Cross-domain bridge extension: package both deception+autoimmunity and tri-domain deception+autoimmunity+negotiation witnesses in one synchronized theorem surface for routing reuse same assumptions as THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-BUDGET-UNIT-BOUNDARY; witness pack includes both combined-budget anchors Lean theorem DeceptionAutoimmunityNegotiationQueueKernelBridge.deception_autoimmunity_negotiation_joint_queue_witness_pack in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean, folding two-domain and tri-domain witness constructors Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored tri-domain deception+autoimmunity+negotiation interpretation does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored tri-domain arrival/service rates Lean theorem DeceptionAutoimmunityNegotiationQueueKernelBridge.deception_autoimmunity_negotiation_budget_does_not_force_positive_beta1 in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored tri-domain deception+autoimmunity+negotiation interpretation does not force queue path-width to equal the interpreted budget mass same assumptions as THM-QUEUE-DECEPTION-AUTOIMMUNITY-NEGOTIATION-BUDGET-UNIT-BOUNDARY; strict budget positivity follows from injected ≥ 1, parserExhaust ≥ 1, and mediation wattage positivity Lean theorem DeceptionAutoimmunityNegotiationQueueKernelBridge.deception_autoimmunity_negotiation_budget_does_not_force_beta1_equals_budget in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and positive tri-domain budget Mechanized
THM-QUEUE-QUORUM-LINEARIZED-READ-UNIT-BOUNDARY Cross-domain bridge: append-then-read quorum linearizability refinement induces an explicit strict-majority interpretation on read depth and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored arrival/service rates linearized history/write witness (history, write); committed read witness QuorumLinearizability.read_after_appended_write_refines_new_latest; canonical interpretation failureBudget = writeCount, replicaCount = 2*writeCount + 1 Lean theorem QuorumLinearizabilityQueueKernelBridge.appended_linearized_read_yields_unit_queue_boundary in QuorumLinearizabilityQueueKernelBridge.lean, composing committed-read refinement with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-QUORUM-LINEARIZED-READ-NOT-BETA1-EQUAL-WRITECOUNT Contrarian anti-theorem variant: the same linearized-read interpretation with anchored queue rates does not force queue path width to equal interpreted write-count budget (β₁ = writeCount) same assumptions as THM-QUEUE-QUORUM-LINEARIZED-READ-UNIT-BOUNDARY; strict budget positivity follows from writeCount = history.length + 1 Lean theorem QuorumLinearizabilityQueueKernelBridge.appended_linearized_read_does_not_force_beta1_equals_write_count in QuorumLinearizabilityQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and positive write-count budget Mechanized
THM-QUEUE-KITCHEN-SAFETY-GAP-UNIT-BOUNDARY Cross-domain bridge: safety-gap kitchen coordination arithmetic in a physical-safety-critical domain induces a strict-majority interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) kitchen cross-domain frame CrossDomainFrame; physical-safety-critical assumption physicalSafetyCritical frame.domain = true; safety gap assumption safetySignals < safetyHazards; canonical interpretation failureBudget = totalDeficit frame, replicaCount = 2*failureBudget + 1 Lean theorem KitchenBerksonQueueKernelBridge.kitchen_berkson_safety_gap_yields_unit_queue_boundary in KitchenBerksonQueueKernelBridge.lean, composing KitchenCommunicationTheory.safety_gap_in_safety_critical_domain_forces_positive_total with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-KITCHEN-BERKSON-BUDGET-UNIT-BOUNDARY Cross-domain bridge: kitchen safety-gap deficit plus selected Berkson collider threshold are routed through one explicit strict-majority interpretation, yielding a canonical one-path queue boundary witness with anchored combined-budget arrival/service rates kitchen assumptions from THM-QUEUE-KITCHEN-SAFETY-GAP-UNIT-BOUNDARY; collider setup BerksonsParadox.ColliderSetup; selected-collider assumption causeA + causeB ≥ collider_threshold; canonical interpretation failureBudget = totalDeficit frame + collider_threshold, replicaCount = 2*failureBudget + 1 Lean theorem KitchenBerksonQueueKernelBridge.kitchen_berkson_budget_yields_unit_queue_boundary in KitchenBerksonQueueKernelBridge.lean, folding kitchen and collider floors into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-KITCHEN-BERKSON-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored kitchen+Berkson interpretation does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-KITCHEN-BERKSON-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem KitchenBerksonQueueKernelBridge.kitchen_berkson_budget_does_not_force_positive_beta1 in KitchenBerksonQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-KITCHEN-BERKSON-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored kitchen+Berkson interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-KITCHEN-BERKSON-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem KitchenBerksonQueueKernelBridge.kitchen_berkson_budget_does_not_force_strict_capacity_growth in KitchenBerksonQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-KITCHEN-BERKSON-GOODHART-BUDGET-UNIT-BOUNDARY Cross-domain bridge: kitchen coordination deficit, selected Berkson collider threshold, and Goodhart proxy-gap arithmetic route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored tri-domain arrival/service rates kitchen assumptions spatialAnnouncements < traversals; selected-collider assumption causeA + causeB ≥ collider_threshold; Goodhart assumptions vTrue ≤ R, vGamed ≤ R, vGamed ≤ vTrue; interpretation anchor failureBudget = coordinationDeficit frame + collider_threshold + (vTrue - vGamed), replicaCount = 2*failureBudget + 1 Lean theorem KitchenBerksonGoodhartQueueKernelBridge.kitchen_berkson_goodhart_budget_yields_unit_queue_boundary in KitchenBerksonGoodhartQueueKernelBridge.lean, composing source certificates with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-KITCHEN-BERKSON-GOODHART-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive tri-domain kitchen+Berkson+Goodhart interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths same assumptions as THM-QUEUE-KITCHEN-BERKSON-GOODHART-BUDGET-UNIT-BOUNDARY; positivity route from kitchen deficit floor and nonnegative collider/proxy components Lean theorem KitchenBerksonGoodhartQueueKernelBridge.kitchen_berkson_goodhart_budget_yields_positive_topological_deficit in KitchenBerksonGoodhartQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-KITCHEN-BERKSON-GOODHART-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored kitchen+Berkson+Goodhart interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-KITCHEN-BERKSON-GOODHART-BUDGET-UNIT-BOUNDARY; strict budget positivity follows from source-domain kitchen deficit positivity Lean theorem KitchenBerksonGoodhartQueueKernelBridge.kitchen_berkson_goodhart_budget_does_not_force_beta1_equals_budget in KitchenBerksonGoodhartQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and positive interpreted budget Mechanized
THM-QUEUE-TAPHONOMY-TRIBOLOGY-JOINT-WITNESS-PACK Cross-domain bridge extension: fossilization-only, tribology-only, and combined taphonomy+tribology interpretations each admit canonical one-path queue witnesses, giving a synchronized three-witness pack for routing audits fossilization assumptions livingInformation = ventedOrganics + fossilInvariant, ventedOrganics ≥ 1; tribology assumptions lubricatedFriction < rawFriction, slamPenalty ≥ 1; combined interpretation failureBudget = ventedOrganics + (rawFriction - lubricatedFriction) Lean theorem TaphonomyTribologyQueueKernelBridge.taphonomy_tribology_joint_queue_witness_pack in TaphonomyTribologyQueueKernelBridge.lean, folding fossilization_budget_yields_unit_queue_boundary, lubricant_budget_yields_unit_queue_boundary, and taphonomy_tribology_budget_yields_unit_queue_boundary Mechanized
THM-QUEUE-TAPHONOMY-TRIBOLOGY-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: combined taphonomy+tribology interpretation with anchored queue rates does not force queue path width to equal the combined budget mass same assumptions as THM-QUEUE-TAPHONOMY-TRIBOLOGY-JOINT-WITNESS-PACK; strict budget positivity follows from ventedOrganics ≥ 1 and lubricatedFriction < rawFriction Lean theorem TaphonomyTribologyQueueKernelBridge.taphonomy_tribology_budget_does_not_force_beta1_equals_budget in TaphonomyTribologyQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness and positive combined budget Mechanized
THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: genome variant-weight chronology, fossilization vent mass, and tribology friction-gap mass induce one strict-majority interpretation and yield a canonical one-path queue boundary witness (beta1 = 0, capacity = 1) with anchored arrival/service rates genome assumptions pv : PopulationVariant; fossilization assumptions livingInformation = ventedOrganics + fossilInvariant, ventedOrganics ≥ 1; tribology assumptions lubricatedFriction < rawFriction, slamPenalty ≥ 1; interpretation anchor failureBudget = pv.weight + ventedOrganics + (rawFriction - lubricatedFriction), replicaCount = 2*failureBudget + 1 Lean theorem GenomeTaphonomyTribologyQueueKernelBridge.genome_taphonomy_tribology_budget_yields_unit_queue_boundary in GenomeTaphonomyTribologyQueueKernelBridge.lean, composing source claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive interpreted genome+taphonomy+tribology budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths same assumptions as THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 ≤ failureBudget + 1 derived from source positivity (weight_floor, vent floor, friction gap floor) Lean theorem GenomeTaphonomyTribologyQueueKernelBridge.genome_taphonomy_tribology_budget_yields_positive_topological_deficit in GenomeTaphonomyTribologyQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-BUDGET-NOT-BETA1-EQUAL-VARIANT-WEIGHT Contrarian anti-theorem variant: anchored genome+taphonomy+tribology interpretation does not force queue path width to equal variant weight same assumptions as THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness and genome weight floor pv.weight ≥ 1 Lean theorem GenomeTaphonomyTribologyQueueKernelBridge.genome_taphonomy_tribology_budget_does_not_force_beta1_equals_variant_weight in GenomeTaphonomyTribologyQueueKernelBridge.lean Mechanized
THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-RETRIAL-STATIONARY-BRIDGE Blocker-attack bridge (proof-depth strategy): with explicit RetrialQueueKernelFamily payload assumptions, genome+taphonomy+tribology source claims transport into the retrial stationary-balance theorem surface without hidden witness synthesis explicit payload assumption kernel : RetrialQueueKernelFamily maxQueue maxOrbit; source assumptions as in THM-QUEUE-GENOME-TAPHONOMY-TRIBOLOGY-BUDGET-UNIT-BOUNDARY bundled in an adapter record; no derived retrial fields are implicit Lean theorem GenomeTaphonomyTribologyRetrialAdapter.retrial_stationary_balance_bridge in GenomeTaphonomyTribologyQueueKernelBridge.lean, reusing StateDependentQueueFamilies.RetrialQueueKernelFamily.stationary_balance under explicit payload hypotheses Mechanized
THM-QUEUE-SPIDERWEB-APERIODIC-NARRATIVE-BUDGET-UNIT-BOUNDARY Cross-domain bridge: spiderweb routing mass, an irrational-schedule aperiodic floor budget, and narrative crossing mass are routed through one strict-majority interpretation to yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored arrival/service rates spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; aperiodic assumptions weyl.isIrrational = true, schedule.isPeriodic = !weyl.isIrrational, schedule.hasResonance = schedule.isPeriodic, and low-discrepancy witness schedule.isPeriodic = false → schedule.resonanceCollisions = 0; narrative assumption narrativeCrossings ≥ 1; interpretation anchor failureBudget = (meshRoutingPaths mesh + narrativeCrossings) + (resonanceCollisions + 1), replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebAperiodicNarrativeQueueKernelBridge.spiderweb_aperiodic_narrative_budget_yields_unit_queue_boundary in SpiderwebAperiodicNarrativeQueueKernelBridge.lean, folding aperiodic and narrative witnesses into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SPIDERWEB-APERIODIC-NARRATIVE-JOINT-WITNESS-PACK Cross-domain bridge extension: spiderweb-only, narrative-only, and combined spiderweb+aperiodic+narrative interpretations each admit canonical one-path queue witnesses, yielding a synchronized witness pack for routing reuse same assumptions as THM-QUEUE-SPIDERWEB-APERIODIC-NARRATIVE-BUDGET-UNIT-BOUNDARY; component witness pack includes spiderweb-only and narrative-only canonical boundaries alongside combined interpretation Lean theorem SpiderwebAperiodicNarrativeQueueKernelBridge.spiderweb_aperiodic_narrative_joint_queue_witness_pack in SpiderwebAperiodicNarrativeQueueKernelBridge.lean, packaging all three witness constructors under one theorem family Mechanized
THM-QUEUE-SPIDERWEB-APERIODIC-NARRATIVE-BUDGET-NOT-CAPACITY-AT-LEAST-TWO Contrarian anti-theorem variant: anchored spiderweb+aperiodic+narrative interpretation with fixed arrival/service rates does not force capacity lower bound 2 ≤ capacity same assumptions as THM-QUEUE-SPIDERWEB-APERIODIC-NARRATIVE-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem SpiderwebAperiodicNarrativeQueueKernelBridge.spiderweb_aperiodic_narrative_budget_does_not_force_capacity_at_least_two in SpiderwebAperiodicNarrativeQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-SPIDERWEB-MUSIC-NARRATIVE-BUDGET-UNIT-BOUNDARY Cross-domain bridge: combined spiderweb routing mass, music swing-dispatch slack, and narrative crossing mass induce one strict-majority queue interpretation and a canonical one-path boundary witness (β₁ = 0, capacity = 1) spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; music assumptions swingPerturbation ≥ 1, totalSpace = periodicLoad + swingPerturbation; narrative assumption narrativeCrossings ≥ 1; interpretation anchor failureBudget = meshRoutingPaths mesh + swingPerturbation + narrativeCrossings, replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebMusicNarrativeQueueKernelBridge.spiderweb_music_narrative_budget_yields_unit_queue_boundary in SpiderwebMusicNarrativeQueueKernelBridge.lean, folding source-domain arithmetic into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SPIDERWEB-MUSIC-NARRATIVE-JOINT-WITNESS-PACK Cross-domain bridge extension: spiderweb-only, music-only, narrative-only, and combined interpretations each admit canonical one-path queue witnesses, yielding a synchronized multi-witness routing pack spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; music assumptions swingPerturbation ≥ 1, totalSpace = periodicLoad + swingPerturbation; narrative assumption narrativeCrossings ≥ 1; combined interpretation failureBudget = meshRoutingPaths mesh + swingPerturbation + narrativeCrossings Lean theorem SpiderwebMusicNarrativeQueueKernelBridge.spiderweb_music_narrative_joint_queue_witness_pack in SpiderwebMusicNarrativeQueueKernelBridge.lean, packaging spiderweb/music/narrative and combined witness constructors under one routeable theorem family Mechanized
THM-QUEUE-SPIDERWEB-MUSIC-NARRATIVE-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored spiderweb+music+narrative interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-SPIDERWEB-MUSIC-NARRATIVE-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem SpiderwebMusicNarrativeQueueKernelBridge.spiderweb_music_narrative_budget_does_not_force_strict_capacity_growth in SpiderwebMusicNarrativeQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-UNIT-BOUNDARY Cross-domain bridge: spiderweb routing-path mass and canonical Sophia ladder mass induce one strict-majority queue interpretation and a canonical one-path boundary witness (β₁ = 0, capacity = 1) spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; gnostic alignment witness gnosticBeta1.sophia = sophia = 9; interpretation anchor failureBudget = meshRoutingPaths mesh + sophia, replicaCount = 2*failureBudget + 1 Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_yields_unit_queue_boundary in SpiderwebGnosticLadderQueueKernelBridge.lean, composing spiderweb positivity, Sophia alignment, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive spiderweb+gnostic interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; gnostic alignment witness gnosticBeta1.sophia = sophia = 9; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_yields_positive_topological_deficit in SpiderwebGnosticLadderQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored spiderweb+gnostic-ladder interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-UNIT-BOUNDARY; contradiction uses canonical β₁ = 0 witness and strict positivity of failureBudget = meshRoutingPaths mesh + sophia Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_does_not_force_beta1_equals_budget in SpiderwebGnosticLadderQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget mass Mechanized
THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-NOT-ZERO-ARRIVAL Contrarian anti-theorem variant: anchored spiderweb+gnostic-ladder interpretation does not force zero arrival rate; source assumptions imply strictly positive interpreted budget mass same assumptions as THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-UNIT-BOUNDARY; contradiction witness uses source-derived positivity of failureBudget = meshRoutingPaths mesh + sophia Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_does_not_force_zero_arrival in SpiderwebGnosticLadderQueueKernelBridge.lean, via contradiction against any universal arrivalRate = 0 claim Mechanized
THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from spiderweb+gnostic source mass into queue coordinates transports the canonical one-path queue witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-SPIDERWEB-GNOSTIC-LADDER-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret (meshRoutingPaths mesh + sophia) = failureBudget; strict-majority interpretation replicaCount = 2*interpret(...) + 1 Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_semantic_morphism_yields_unit_queue_boundary in SpiderwebGnosticLadderQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-ADVERSARIAL-CERTIFIED-BUDGET-UNIT-BOUNDARY Cross-domain bridge: adversarial perturbation-gap arithmetic plus certified-radius accounting are routed through one strict-majority interpretation to yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored combined-budget arrival/service rates adversarial assumptions v ≤ R, v + delta ≤ R; certified witness CertifiedDefenses.Certification; interpretation anchor failureBudget = (cleanReject + radius) + delta, replicaCount = 2*failureBudget + 1 Lean theorem AdversarialCertifiedQueueKernelBridge.adversarial_certified_budget_yields_unit_queue_boundary in AdversarialCertifiedQueueKernelBridge.lean, composing AdversarialRobustness.adversarial_gap and CertifiedDefenses.certified_within_radius with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-ADVERSARIAL-CERTIFIED-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored adversarial+certified interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-ADVERSARIAL-CERTIFIED-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored combined-budget arrival/service rates Lean theorem AdversarialCertifiedQueueKernelBridge.adversarial_certified_budget_does_not_force_strict_capacity_growth in AdversarialCertifiedQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-ADVERSARIAL-CERTIFIED-BERKSON-BUDGET-UNIT-BOUNDARY Cross-domain bridge: adversarial perturbation-gap arithmetic, certified-radius threshold guarantees, and selected Berkson collider arithmetic route through one strict-majority interpretation to yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) with anchored tri-domain arrival/service rates adversarial assumptions v ≤ R, v + delta ≤ R; certified witness CertifiedDefenses.Certification; selected-collider witness cs.selected; interpretation anchor failureBudget = delta + (cleanReject + radius) + collider_threshold, replicaCount = 2*failureBudget + 1 Lean theorem AdversarialCertifiedBerksonQueueKernelBridge.adversarial_certified_berkson_budget_yields_unit_queue_boundary in AdversarialCertifiedBerksonQueueKernelBridge.lean, composing AdversarialRobustness.adversarial_gap, CertifiedDefenses.certified_within_radius, and BerksonQueueKernelBridge.berkson_selected_implies_threshold_bounded_by_total_rejections with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-ADVERSARIAL-CERTIFIED-BERKSON-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored adversarial+certified+Berkson interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-ADVERSARIAL-CERTIFIED-BERKSON-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored tri-domain arrival/service rates Lean theorem AdversarialCertifiedBerksonQueueKernelBridge.adversarial_certified_berkson_budget_does_not_force_strict_capacity_growth in AdversarialCertifiedBerksonQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-CONVERSION-VENT-UNIT-BOUNDARY Cross-domain bridge: conversion vent mass from UI-friction abandonment induces a strict-majority interpretation and yields a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) conversion assumptions uiFriction > buleInvestment and ventSlam = uiFriction - buleInvestment; interpretation anchor failureBudget = ventSlam, replicaCount = 2*failureBudget + 1 Lean theorem MediationMechanismConversionQueueKernelBridge.conversion_vent_budget_yields_unit_queue_boundary in MediationMechanismConversionQueueKernelBridge.lean, composing ConversionTrackingTopology.conversion_is_unbroken_fold with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MECHANISM-CONVERSION-BUDGET-UNIT-BOUNDARY Cross-domain bridge: mechanism externality arithmetic and conversion vent arithmetic route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) mechanism assumptions vWithout ≤ R, vWith ≤ R, vWith ≥ vWithout; conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; interpretation anchor failureBudget = (vWith - vWithout) + ventSlam, replicaCount = 2*failureBudget + 1 Lean theorem MediationMechanismConversionQueueKernelBridge.mechanism_conversion_budget_yields_unit_queue_boundary in MediationMechanismConversionQueueKernelBridge.lean, composing MechanismDesign.vcg_externality and ConversionTrackingTopology.conversion_is_unbroken_fold with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIATION-MECHANISM-CONVERSION-BUDGET-UNIT-BOUNDARY Cross-domain bridge: mediation-loss floor, mechanism externality identity, and conversion vent pulse route through one explicit strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) mediation witness CausalMediation.MediationSetup (mediatorLoss ≥ 1); conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; mechanism identity recovered as godWeight(budget,directRejections) - godWeight(budget,totalRejections) = mediatorLoss; interpretation anchor failureBudget = mediatorLoss + ventSlam, replicaCount = 2*failureBudget + 1 Lean theorem MediationMechanismConversionQueueKernelBridge.mediation_mechanism_conversion_budget_yields_unit_queue_boundary in MediationMechanismConversionQueueKernelBridge.lean, folding source identities into QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MECHANISM-CONVERSION-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored mechanism+conversion interpretation does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-MECHANISM-CONVERSION-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored arrival/service rates Lean theorem MediationMechanismConversionQueueKernelBridge.mechanism_conversion_budget_does_not_force_positive_beta1 in MediationMechanismConversionQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-MEDIATION-MECHANISM-CONVERSION-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored mediation+mechanism+conversion interpretation does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-MEDIATION-MECHANISM-CONVERSION-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored tri-domain arrival/service rates Lean theorem MediationMechanismConversionQueueKernelBridge.mediation_mechanism_conversion_budget_does_not_force_positive_beta1 in MediationMechanismConversionQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-MEDIATION-MECHANISM-CONVERSION-BUDGET-NOT-ZERO-ARRIVAL Contrarian anti-theorem variant: anchored mediation+mechanism+conversion interpretation does not force zero arrival rate; source assumptions imply strictly positive interpreted budget mass same assumptions as THM-QUEUE-MEDIATION-MECHANISM-CONVERSION-BUDGET-UNIT-BOUNDARY; contradiction witness uses source-derived positivity of failureBudget = mediatorLoss + ventSlam Lean theorem MediationMechanismConversionQueueKernelBridge.mediation_mechanism_conversion_budget_does_not_force_zero_arrival in MediationMechanismConversionQueueKernelBridge.lean, via contradiction against any universal arrivalRate = 0 claim Mechanized
THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-UNIT-BOUNDARY Cross-domain bridge: mediation-loss floor, BATNA trauma-gap arithmetic, and spiderweb routing-path mass induce one strict-majority queue interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) mediation assumptions mediatorLoss ≥ 1; negotiation assumption slamTraumaPenalty ≥ untanglingWattsCost + 1; spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; interpretation anchor failureBudget = mediatorLoss + (slamTraumaPenalty - untanglingWattsCost) + meshRoutingPaths, replicaCount = 2*failureBudget + 1 Lean theorem MediationNegotiationSpiderwebQueueKernelBridge.mediation_negotiation_spiderweb_budget_yields_unit_queue_boundary in MediationNegotiationSpiderwebQueueKernelBridge.lean, composing source arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive mediation+negotiation+spiderweb interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths same assumptions as THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity Lean theorem MediationNegotiationSpiderwebQueueKernelBridge.mediation_negotiation_spiderweb_budget_yields_positive_topological_deficit in MediationNegotiationSpiderwebQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-NOT-ZERO-ARRIVAL Contrarian anti-theorem variant: anchored mediation+negotiation+spiderweb interpretation does not force zero arrival in every boundary witness same assumptions as THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem MediationNegotiationSpiderwebQueueKernelBridge.mediation_negotiation_spiderweb_budget_does_not_force_zero_arrival in MediationNegotiationSpiderwebQueueKernelBridge.lean, via contradiction against the canonical witness and source-derived positive budget Mechanized
THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored mediation+negotiation+spiderweb interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-UNIT-BOUNDARY; contradiction uses canonical β₁ = 0 witness and source-derived strict positivity of interpreted budget mass Lean theorem MediationNegotiationSpiderwebQueueKernelBridge.mediation_negotiation_spiderweb_budget_does_not_force_beta1_equals_budget in MediationNegotiationSpiderwebQueueKernelBridge.lean, via contradiction against the canonical one-path witness Mechanized
THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-SEMANTIC-MORPHISM-POSITIVE-DEFICIT Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism from raw tri-domain budget mass to mapped path-count budget transports the positive TCP-deficit witness into mapped coordinates same assumptions as THM-QUEUE-MEDIATION-NEGOTIATION-SPIDERWEB-BUDGET-POSITIVE-DEFICIT-BRIDGE; interpretation function interpret : Nat → Nat; explicit morphism hypothesis interpret (failureBudget + 1) = failureBudget + 1 Lean theorem MediationNegotiationSpiderwebQueueKernelBridge.mediation_negotiation_spiderweb_semantic_morphism_yields_positive_topological_deficit in MediationNegotiationSpiderwebQueueKernelBridge.lean, rewriting via morphism equality and reusing the positive-deficit bridge theorem Mechanized
THM-QUEUE-MEDIA-SCROLL-TYPOGRAPHY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: clickbait dilation mass, infinite-scroll unresolved race load, and typography ligature friction routing are interpreted as one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) clickbait assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; infinite-scroll assumptions foldResolution = 0, raceLoad > ventThreshold; typography assumptions characterOne + characterTwo = ligatureUnknot + frictionSave, frictionSave ≥ 1; interpretation anchor failureBudget = clickstr + raceLoad + frictionSave, replicaCount = 2*failureBudget + 1 Lean theorem MediaScrollTypographyQueueKernelBridge.media_scroll_typography_budget_yields_unit_queue_boundary in MediaScrollTypographyQueueKernelBridge.lean, composing source arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MEDIA-SCROLL-TYPOGRAPHY-BUDGET-NOT-CAPACITY-AT-LEAST-TWO Contrarian anti-theorem variant: anchored media+scroll+typography interpretation does not force 2 ≤ capacity; canonical witness remains one-path (capacity = 1) same assumptions as THM-QUEUE-MEDIA-SCROLL-TYPOGRAPHY-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem MediaScrollTypographyQueueKernelBridge.media_scroll_typography_budget_does_not_force_capacity_at_least_two in MediaScrollTypographyQueueKernelBridge.lean, via contradiction against the canonical one-path witness Mechanized
THM-QUEUE-DEWEY-THIN-BUREAUCRACY-SURGERY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: Dewey-300 bureaucracy latency and Dewey-600 thin surgery severance route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) Dewey-300 assumptions systemVelocity + safeTolerance = bureaucraticFriction, safeTolerance ≥ 1; Dewey-600 thin assumption sever = 0; interpretation anchor failureBudget = (bureaucraticFriction - systemVelocity) + sever, replicaCount = 2*failureBudget + 1 Lean theorem DeweyBureaucracySurgeryQueueKernelBridge.dewey_bureaucracy_surgery_budget_yields_unit_queue_boundary in DeweyBureaucracySurgeryQueueKernelBridge.lean, composing Dewey300Topology.bureaucracy_is_latency, Dewey600ThinTopology.dewey_610_medicine_surgery, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-DEWEY-THIN-BUREAUCRACY-SURGERY-BUDGET-NOT-CAPACITY-AT-LEAST-TWO Contrarian anti-theorem variant: anchored Dewey bureaucracy+surgery interpretation does not force 2 ≤ capacity; canonical witness remains one-path (capacity = 1) same assumptions as THM-QUEUE-DEWEY-THIN-BUREAUCRACY-SURGERY-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem DeweyBureaucracySurgeryQueueKernelBridge.dewey_bureaucracy_surgery_budget_does_not_force_capacity_at_least_two in DeweyBureaucracySurgeryQueueKernelBridge.lean, via contradiction against the canonical one-path witness Mechanized
THM-QUEUE-DEWEY-THIN-BUREAUCRACY-SURGERY-SEMANTIC-MAP-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from source tolerance mass to queue budget mass closes the interpretation layer and transports the canonical one-path queue witness into mapped coordinates same source assumptions as THM-QUEUE-DEWEY-THIN-BUREAUCRACY-SURGERY-BUDGET-UNIT-BOUNDARY; explicit map hypothesis interpret safeTolerance = failureBudget; strict-majority interpretation replicaCount = 2 * interpret safeTolerance + 1 Lean theorem DeweyBureaucracySurgeryQueueKernelBridge.dewey_bureaucracy_surgery_semantic_morphism_boundary in DeweyBureaucracySurgeryQueueKernelBridge.lean, rewriting canonical arrival/service fields by interpretation equality Mechanized
THM-QUEUE-FORM-TOPOLOGY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: well-formed form topology with nonempty declared field surface yields one strict-majority interpretation and a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) form assumptions wellFormed spec σ and ∃ f, f ∈ spec.fields; interpretation anchor `failureBudget = fields +
THM-QUEUE-FORM-TOPOLOGY-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive interpreted form-topology budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths form assumptions wellFormed spec σ and ∃ f, f ∈ spec.fields; positivity route `0 < failureBudget = fields +
THM-QUEUE-FORM-TOPOLOGY-BUDGET-NOT-CAPACITY-AT-LEAST-TWO Contrarian anti-theorem variant: anchored form-topology interpretation does not force capacity lower bound 2 ≤ capacity; canonical witness remains one-path (capacity = 1) form assumptions wellFormed spec σ and ∃ f, f ∈ spec.fields; witness restricted to boundaries with anchored form-budget arrival/service rates Lean theorem FormTopologyQueueKernelBridge.form_budget_does_not_force_capacity_at_least_two in FormTopologyQueueKernelBridge.lean, via contradiction against the canonical one-path witness Mechanized
THM-QUEUE-MACRO-HERMETIC-MYCOLOGY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: macro phantom-injection mass, hermetic sliver projection mass, and mycology thermal-vent exhaust mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings ≥ 1; hermetic assumptions macroManifold = fractalNode + sliver, sliver ≥ 0; mycology assumptions undergroundHeat > ventThreshold, sporeExhaust ≥ 1; interpretation anchor failureBudget = fiatCrossings + sliver + sporeExhaust, replicaCount = 2*failureBudget + 1 Lean theorem MacroHermeticMycologyQueueKernelBridge.macro_hermetic_mycology_budget_yields_unit_queue_boundary in MacroHermeticMycologyQueueKernelBridge.lean, composing source-domain arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MACRO-HERMETIC-MYCOLOGY-BUDGET-NOT-SERVICE-SLACK-AT-LEAST-TWO Contrarian anti-theorem variant: anchored macro+hermetic+mycology interpretation does not force service slack of at least two above anchored arrival (arrivalRate + 2 ≤ serviceRate) same assumptions as THM-QUEUE-MACRO-HERMETIC-MYCOLOGY-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem MacroHermeticMycologyQueueKernelBridge.macro_hermetic_mycology_budget_does_not_force_service_slack_at_least_two in MacroHermeticMycologyQueueKernelBridge.lean, via contradiction against the canonical one-path witness with service slack exactly one Mechanized
THM-QUEUE-MACRO-HERMETIC-MYCOLOGY-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from combined source mass into queue budget coordinates transports the canonical one-path queue witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-MACRO-HERMETIC-MYCOLOGY-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret (fiatCrossings + sliver + sporeExhaust) = failureBudget; strict-majority interpretation replicaCount = 2*interpret(...) + 1 Lean theorem MacroHermeticMycologyQueueKernelBridge.macro_hermetic_mycology_semantic_morphism_yields_unit_queue_boundary in MacroHermeticMycologyQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-MACRO-LINGUISTIC-KITCHEN-BUDGET-UNIT-BOUNDARY Cross-domain bridge: macro phantom-injection mass, linguistic superposition mass, and kitchen spatial-safety gain are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings ≥ 1; linguistic assumptions totalLoad = baseMeaning + secondaryMeaning, secondaryMeaning ≥ 1; kitchen witness call : SpatialCall; interpretation anchor failureBudget = fiatCrossings + secondaryMeaning + spatialSafetyGain call, replicaCount = 2*failureBudget + 1 Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_budget_yields_unit_queue_boundary in MacroLinguisticKitchenQueueKernelBridge.lean, composing source arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-MACRO-LINGUISTIC-KITCHEN-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive macro+linguistic+kitchen interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths macro assumptions fiatCrossings ≥ 1; linguistic assumptions secondaryMeaning ≥ 1; kitchen witness call : SpatialCall; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_budget_yields_positive_topological_deficit in MacroLinguisticKitchenQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-MACRO-LINGUISTIC-KITCHEN-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored macro+linguistic+kitchen interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-MACRO-LINGUISTIC-KITCHEN-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_budget_does_not_force_strict_capacity_growth in MacroLinguisticKitchenQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-MACRO-LINGUISTIC-KITCHEN-NOT-UNIVERSAL-NONPOSITIVE-DEFICIT Contrarian anti-theorem variant: anchored macro+linguistic+kitchen interpretation does not force nonpositive topological deficit uniformly across all transport stream counts macro assumptions fiatCrossings ≥ 1; linguistic assumptions secondaryMeaning ≥ 1; kitchen witness call : SpatialCall; universal nonpositive-deficit claim quantified over all transportStreams Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_budget_does_not_force_universal_nonpositive_deficit in MacroLinguisticKitchenQueueKernelBridge.lean, by contradiction from the positive TCP-deficit witness at transportStreams = 1 Mechanized
THM-QUEUE-MACRO-LINGUISTIC-KITCHEN-SEMANTIC-MORPHISM-POSITIVE-DEFICIT Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism equality from raw budget mass to mapped path-count budget transports the positive TCP-deficit witness into mapped coordinates macro assumptions fiatCrossings ≥ 1; linguistic assumptions secondaryMeaning ≥ 1; kitchen witness call : SpatialCall; interpretation function interpret : Nat → Nat; explicit morphism hypothesis interpret (failureBudget + 1) = failureBudget + 1 Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_semantic_morphism_yields_positive_topological_deficit in MacroLinguisticKitchenQueueKernelBridge.lean, rewriting via morphism equality and reusing the positive-deficit bridge theorem Mechanized
THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-UNIT-BOUNDARY Cross-domain bridge: humor setup dilation mass and tensegrity scaffold surplus mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) humor assumptions complexity ≥ 1; tensegrity assumptions invisibleTension > visibleNodes, integrity = visibleNodes + invisibleTension; interpretation anchor failureBudget = complexity + (invisibleTension - visibleNodes), replicaCount = 2*failureBudget + 1 Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_budget_yields_unit_queue_boundary in HumorTensegrityQueueKernelBridge.lean, composing source-domain arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive humor+tensegrity interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths humor assumptions complexity ≥ 1; tensegrity assumptions invisibleTension > visibleNodes, integrity = visibleNodes + invisibleTension; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_budget_yields_positive_topological_deficit in HumorTensegrityQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-NOT-SERVICE-SURPLUS-TWO Contrarian anti-theorem variant: anchored humor+tensegrity interpretation does not force a two-step service surplus above anchored arrival (arrivalRate + 2 ≤ serviceRate) same assumptions as THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_budget_does_not_force_service_surplus_two in HumorTensegrityQueueKernelBridge.lean, via contradiction against the canonical one-path witness with service slack exactly one Mechanized
THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored humor+tensegrity interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_budget_does_not_force_strict_capacity_growth in HumorTensegrityQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-HUMOR-TENSEGRITY-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from humor+tensegrity budget mass into queue coordinates transports the canonical one-path queue witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-HUMOR-TENSEGRITY-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret failureBudget = failureBudget; strict-majority interpretation replicaCount = 2*interpret(failureBudget) + 1 Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_semantic_morphism_yields_unit_queue_boundary in HumorTensegrityQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-CACHE-ASYNC-BUDGET-UNIT-BOUNDARY Cross-domain bridge: ESC cold-path fold work and async durability vent mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; source witnesses traceFold [cold] = escCanonMissW.val, q.totalVent = p.totalVent + k; interpretation anchor failureBudget = traceFold [cold] + q.totalVent, replicaCount = 2*failureBudget + 1 Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_budget_yields_unit_queue_boundary in CacheAsyncFrfQueueKernelBridge.lean, composing WasmEscObservationTrace.trace_one_cold_eq_w, AsyncDurabilityVent.background_only_adds_vent, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CACHE-ASYNC-FRF-BUDGET-UNIT-BOUNDARY Cross-domain bridge: ESC cold-path fold work, async durability vent mass, and FRF witness race mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; source witnesses traceFold [cold] = escCanonMissW.val, frfRace frfWitness = 3; interpretation anchor failureBudget = traceFold [cold] + q.totalVent + frfRace frfWitness, replicaCount = 2*failureBudget + 1 Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_frf_budget_yields_unit_queue_boundary in CacheAsyncFrfQueueKernelBridge.lean, composing source arithmetic with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CACHE-ASYNC-FRF-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored cache+async+FRF interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-CACHE-ASYNC-FRF-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_frf_budget_does_not_force_strict_capacity_growth in CacheAsyncFrfQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized
THM-QUEUE-CACHE-ASYNC-FRF-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored cache+async+FRF interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-CACHE-ASYNC-FRF-BUDGET-UNIT-BOUNDARY; contradiction uses canonical β₁ = 0 witness and source-derived budget positivity Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_frf_budget_does_not_force_beta1_equals_budget in CacheAsyncFrfQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget mass Mechanized
THM-QUEUE-CACHE-ASYNC-FRF-SEMANTIC-MORPHISM-UNIT-BOUNDARY Blocker-remediation bridge (semantic-morphism strategy): an explicit interpretation function from cache+async+FRF source mass into queue coordinates transports the canonical one-path queue witness into mapped arrival/service coordinates same source assumptions as THM-QUEUE-CACHE-ASYNC-FRF-BUDGET-UNIT-BOUNDARY; explicit morphism hypothesis interpret failureBudget = failureBudget; strict-majority interpretation replicaCount = 2*interpret(failureBudget) + 1 Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_frf_semantic_morphism_yields_unit_queue_boundary in CacheAsyncFrfQueueKernelBridge.lean, rewriting canonical arrival/service fields through morphism equality Mechanized
THM-QUEUE-CACHE-ASYNC-SLEEP-BUDGET-UNIT-BOUNDARY Cross-domain bridge: ESC cold-path fold work, async durability vent mass, and weighted sleep debt are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; weighted sleep assumptions thresholdRhs < thresholdLhs, 0 < n; source witnesses traceFold [cold] = 1, q.totalVent = p.totalVent + k; interpretation anchor failureBudget = traceFold [cold] + q.totalVent + iteratedDebt, replicaCount = 2*failureBudget + 1 Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_budget_yields_unit_queue_boundary in CacheAsyncSleepQueueKernelBridge.lean, composing WasmEscObservationTrace.trace_one_cold_eq_w, AsyncDurabilityVent.background_only_adds_vent, SleepDebtWeightedSchedule.iterated_debt_positive_above_threshold, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUEUE-CACHE-ASYNC-SLEEP-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive interpreted cache+async+weighted-sleep budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths interpreted budget anchor failureBudget = traceFold [cold] + q.totalVent + iteratedDebt; lifted path-floor witness 2 <= failureBudget + 1 from budget positivity Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_budget_yields_positive_topological_deficit in CacheAsyncSleepQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-CACHE-ASYNC-SLEEP-BUDGET-NOT-BETA1-EQUAL-BUDGET Contrarian anti-theorem variant: anchored cache+async+weighted-sleep interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) same assumptions as THM-QUEUE-CACHE-ASYNC-SLEEP-BUDGET-UNIT-BOUNDARY; contradiction uses canonical β₁ = 0 witness and interpreted-budget positivity Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_budget_does_not_force_beta1_equals_budget in CacheAsyncSleepQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget mass Mechanized
THM-QUEUE-CACHE-ASYNC-SLEEP-SEMANTIC-MORPHISM-POSITIVE-DEFICIT Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism equality from interpreted cache+async+sleep budget to mapped path-count coordinates transports the positive TCP-deficit witness interpretation function interpret : Nat -> Nat; explicit morphism hypothesis interpret (failureBudget + 1) = failureBudget + 1 Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_semantic_morphism_yields_positive_topological_deficit in CacheAsyncSleepQueueKernelBridge.lean, rewriting the lifted path-count argument through morphism equality Mechanized
THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-UNIT-BOUNDARY Cross-domain bridge: nonempty quorum-history depth, crossed weighted sleep-debt threshold mass, and irreducible cryptographic side-channel floor route through one strict-majority interpretation and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) quorum history assumption history ≠ []; weighted sleep assumptions thresholdRhs < thresholdLhs and 0 < n; cryptographic witness SideChannelShadow (0 < perEvalFloor); interpretation anchor `failureBudget = history + iteratedDebt + perEvalFloor, replicaCount = 2*failureBudget + 1`
THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-POSITIVE-DEFICIT-BRIDGE Cross-domain bridge: positive tri-domain quorum+sleep+crypto interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths same assumptions as THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity Lean theorem QuorumSleepCryptoQueueKernelBridge.quorum_sleep_crypto_budget_yields_positive_topological_deficit in QuorumSleepCryptoQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: anchored quorum+sleep+crypto interpretation does not force positive path-width (β₁ > 0) same assumptions as THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored tri-domain arrival/service rates Lean theorem QuorumSleepCryptoQueueKernelBridge.quorum_sleep_crypto_budget_does_not_force_positive_beta1 in QuorumSleepCryptoQueueKernelBridge.lean, via contradiction against the canonical β₁ = 0 witness Mechanized
THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-NOT-STRICT-CAPACITY-GROWTH Contrarian anti-theorem variant: anchored quorum+sleep+crypto interpretation does not force strict capacity growth (capacity > 1) same assumptions as THM-QUEUE-QUORUM-SLEEP-CRYPTO-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored tri-domain arrival/service rates Lean theorem QuorumSleepCryptoQueueKernelBridge.quorum_sleep_crypto_budget_does_not_force_strict_capacity_growth in QuorumSleepCryptoQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 Mechanized

| THM-QUEUE-MUSIC-NARRATIVE-TYPOGRAPHY-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: rhythm perturbation mass, narrative crossing mass, and typography friction-savings mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) | music assumptions swingPerturbation ≥ 1, totalSpace = periodicLoad + swingPerturbation; narrative assumption narrativeCrossings ≥ 1; typography assumptions characterOne + characterTwo = ligatureUnknot + frictionSave, frictionSave ≥ 1; interpretation anchor failureBudget = swingPerturbation + narrativeCrossings + frictionSave, replicaCount = 2*failureBudget + 1 | Lean theorem MusicNarrativeTypographyQueueKernelBridge.music_narrative_typography_budget_yields_unit_queue_boundary in MusicNarrativeTypographyQueueKernelBridge.lean, composing source-domain claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-MUSIC-NARRATIVE-TYPOGRAPHY-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive music+narrative+typography interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | assumptions swingPerturbation ≥ 1, narrativeCrossings ≥ 1, frictionSave ≥ 1; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity | Lean theorem MusicNarrativeTypographyQueueKernelBridge.music_narrative_typography_budget_yields_positive_topological_deficit in MusicNarrativeTypographyQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-MUSIC-NARRATIVE-TYPOGRAPHY-BUDGET-NOT-ARRIVAL-LE-ONE | Contrarian anti-theorem variant: anchored music+narrative+typography interpretation does not force universally low arrival witnesses (arrivalRate ≤ 1) | same assumptions as THM-QUEUE-MUSIC-NARRATIVE-TYPOGRAPHY-BUDGET-UNIT-BOUNDARY; contradiction uses source-derived lower bound failureBudget > 1 and canonical anchored witness arrival arrivalRate = failureBudget | Lean theorem MusicNarrativeTypographyQueueKernelBridge.music_narrative_typography_budget_does_not_force_arrival_le_one in MusicNarrativeTypographyQueueKernelBridge.lean, via contradiction against universal low-arrival forcing | Mechanized | | THM-QUEUE-MEDIA-CONVERSION-KNAPSACK-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: media clickbait mass, conversion vent mass, and viewport overlap mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) | media assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; knapsack assumptions pleromicData = screenCapacity + visualOverlap, visualOverlap ≥ 1; interpretation anchor failureBudget = clickstr + ventSlam + visualOverlap, replicaCount = 2*failureBudget + 1 | Lean theorem MediaConversionKnapsackQueueKernelBridge.media_conversion_knapsack_budget_yields_unit_queue_boundary in MediaConversionKnapsackQueueKernelBridge.lean, composing source-domain claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-MEDIA-CONVERSION-KNAPSACK-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive media+conversion+knapsack interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same assumptions as THM-QUEUE-MEDIA-CONVERSION-KNAPSACK-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 ≤ failureBudget + 1 from source-derived budget positivity | Lean theorem MediaConversionKnapsackQueueKernelBridge.media_conversion_knapsack_budget_yields_positive_topological_deficit in MediaConversionKnapsackQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-MEDIA-CONVERSION-KNAPSACK-BUDGET-NOT-TWO-STEP-SERVICE-SURPLUS | Contrarian anti-theorem variant: anchored media+conversion+knapsack interpretation does not force a two-step service surplus (arrivalRate + 2 ≤ serviceRate) | same assumptions as THM-QUEUE-MEDIA-CONVERSION-KNAPSACK-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates | Lean theorem MediaConversionKnapsackQueueKernelBridge.media_conversion_knapsack_budget_does_not_force_two_step_service_surplus in MediaConversionKnapsackQueueKernelBridge.lean, via contradiction against the canonical one-path witness with service slack exactly one | Mechanized | | THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: community attenuation, diversity/concurrency identity, and combat velocity mass induce a strict-majority queue interpretation and therefore a canonical one-path queue boundary witness (beta1 = 0, capacity = 1) | community assumptions ft : FailureTopology, 0 < communityContext; diversity assumptions 1 ≤ diversePaths, diversityCount diversePaths = effectiveConcurrency diversePaths; combat assumptions attackerVelocity > startupTicks, entanglement = 0; interpretation anchor failureBudget = communityContext + diversePaths + attackerVelocity, replicaCount = 2*failureBudget + 1 | Lean theorem CommunityDiversityCombatQueueKernelBridge.community_diversity_combat_budget_yields_unit_queue_boundary in CommunityDiversityCombatQueueKernelBridge.lean, composing source-domain claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive community+diversity+combat interpreted budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same assumptions as THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 <= failureBudget + 1 from source-derived budget positivity | Lean theorem CommunityDiversityCombatQueueKernelBridge.community_diversity_combat_budget_yields_positive_topological_deficit in CommunityDiversityCombatQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-NOT-ARRIVAL-LE-ONE | Contrarian anti-theorem variant: anchored community+diversity+combat interpretation does not force universally low-arrival witnesses (arrivalRate <= 1) | same assumptions as THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-UNIT-BOUNDARY; contradiction uses source-derived bound failureBudget > 1 and canonical anchored witness arrival arrivalRate = failureBudget | Lean theorem CommunityDiversityCombatQueueKernelBridge.community_diversity_combat_budget_does_not_force_arrival_le_one in CommunityDiversityCombatQueueKernelBridge.lean, via contradiction against universal low-arrival forcing | Mechanized | | THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-NOT-STRICT-CAPACITY-GROWTH | Contrarian anti-theorem variant: anchored community+diversity+combat interpretation does not force strict capacity growth (capacity > 1) | same assumptions as THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored interpretation-layer arrival/service rates | Lean theorem CommunityDiversityCombatQueueKernelBridge.community_diversity_combat_budget_does_not_force_strict_capacity_growth in CommunityDiversityCombatQueueKernelBridge.lean, via contradiction against the canonical one-path witness with capacity = 1 | Mechanized | | THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-SEMANTIC-MORPHISM-POSITIVE-DEFICIT | Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism equality from raw tri-domain budget mass to mapped path-count budget transports the positive TCP-deficit witness into mapped coordinates | same assumptions as THM-QUEUE-COMMUNITY-DIVERSITY-COMBAT-BUDGET-UNIT-BOUNDARY; interpretation function interpret : Nat -> Nat; explicit morphism hypothesis interpret (failureBudget + 1) = failureBudget + 1 | Lean theorem CommunityDiversityCombatQueueKernelBridge.community_diversity_combat_semantic_morphism_yields_positive_topological_deficit in CommunityDiversityCombatQueueKernelBridge.lean, rewriting via morphism equality and reusing the positive-deficit bridge theorem | Mechanized | | THM-QUEUE-KI-FRF-TRAINING-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Ki precursor leak mass, deterministic FRF minimax domination, and a concrete training witness that beats chance induce one strict-majority queue interpretation and therefore a canonical one-path queue boundary witness (beta1 = 0, capacity = 1) | Ki leak witness 0 < glanceLeak ∨ 0 < muscleLeak ∨ 0 < scentLeak ∨ 0 < energyLeak; timeline witness reactionTick < actionTick; training witness drillBeatsChance sampleSeriesBeats; interpretation anchor failureBudget = totalLeak + correctCount sampleSeriesBeats + raceScore(foldAction(forkFutures), forkFutures), replicaCount = 2*failureBudget + 1 | Lean theorem KiFrfTrainingQueueKernelBridge.ki_frf_training_budget_yields_unit_queue_boundary in KiFrfTrainingQueueKernelBridge.lean, composing source claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-KI-FRF-TRAINING-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive interpreted Ki+FRF+training budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same assumptions as THM-QUEUE-KI-FRF-TRAINING-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 <= failureBudget + 1 derived from source positivity | Lean theorem KiFrfTrainingQueueKernelBridge.ki_frf_training_budget_yields_positive_topological_deficit in KiFrfTrainingQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-KI-FRF-TRAINING-BUDGET-NOT-BETA1-EQUAL-BUDGET | Contrarian anti-theorem variant: anchored Ki+FRF+training interpretation does not force queue path-width to equal interpreted budget mass (beta1 = failureBudget) | same assumptions as THM-QUEUE-KI-FRF-TRAINING-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness and source-derived budget positivity | Lean theorem KiFrfTrainingQueueKernelBridge.ki_frf_training_budget_does_not_force_beta1_equals_budget in KiFrfTrainingQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget mass | Mechanized | | THM-QUEUE-KI-FRF-TRAINING-RETRIAL-STATIONARY-BRIDGE | Blocker-attack bridge (proof-depth strategy): with explicit RetrialQueueKernelFamily payload assumptions, Ki+FRF+training source claims transport into the retrial stationary-balance theorem surface without hidden witness synthesis | explicit payload assumption kernel : RetrialQueueKernelFamily maxQueue maxOrbit; Ki leak witness and timeline witness as in THM-QUEUE-KI-FRF-TRAINING-BUDGET-UNIT-BOUNDARY; training witness drillBeatsChance sampleSeriesBeats | Lean theorem KiFrfTrainingQueueKernelBridge.KiFrfTrainingRetrialAdapter.retrial_stationary_balance_bridge in KiFrfTrainingQueueKernelBridge.lean, reusing StateDependentQueueFamilies.RetrialQueueKernelFamily.stationary_balance under explicit adapter hypotheses | Mechanized | | THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: macro phantom-injection mass, ecosystem keystone mass, tribology slam-penalty mass, and conversion vent mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (beta1 = 0, capacity = 1) | macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings >= 1; ecosystem assumptions ecosystemComplexity = keystoneNode + remaining, keystoneNode >= 1; tribology assumptions lubricatedFriction < rawFriction, slamPenalty >= 1; conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; interpretation anchor failureBudget = fiatCrossings + keystoneNode + ventSlam + slamPenalty, replicaCount = 2*failureBudget + 1 | Lean theorem MacroEcosystemTribologyConversionQueueKernelBridge.macro_ecosystem_tribology_conversion_budget_yields_unit_queue_boundary in MacroEcosystemTribologyConversionQueueKernelBridge.lean, composing source-domain claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive interpreted macro+ecosystem+tribology+conversion budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same assumptions as THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 <= failureBudget + 1 from source-derived budget positivity | Lean theorem MacroEcosystemTribologyConversionQueueKernelBridge.macro_ecosystem_tribology_conversion_budget_yields_positive_topological_deficit in MacroEcosystemTribologyConversionQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-NOT-BETA1-EQUAL-BUDGET | Contrarian anti-theorem variant: anchored macro+ecosystem+tribology+conversion interpretation does not force queue path-width to equal interpreted budget mass (beta1 = failureBudget) | same assumptions as THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness and source-derived budget positivity | Lean theorem MacroEcosystemTribologyConversionQueueKernelBridge.macro_ecosystem_tribology_conversion_budget_does_not_force_beta1_equals_budget in MacroEcosystemTribologyConversionQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget mass | Mechanized | | THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-NOT-CAPACITY-AT-LEAST-TWO | Contrarian anti-theorem variant: anchored macro+ecosystem+tribology+conversion interpretation does not force capacity >= 2 | same assumptions as THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-UNIT-BOUNDARY; contradiction uses canonical one-path witness with capacity = 1 | Lean theorem MacroEcosystemTribologyConversionQueueKernelBridge.macro_ecosystem_tribology_conversion_budget_does_not_force_capacity_at_least_two in MacroEcosystemTribologyConversionQueueKernelBridge.lean | Mechanized | | THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-SEMANTIC-MORPHISM-POSITIVE-DEFICIT | Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism equality from raw four-domain budget coordinates to mapped path-count coordinates transports the positive TCP-deficit witness | same assumptions as THM-QUEUE-MACRO-ECOSYSTEM-TRIBOLOGY-CONVERSION-BUDGET-UNIT-BOUNDARY; interpretation function interpret : Nat -> Nat; explicit morphism hypothesis interpret (failureBudget + 1) = failureBudget + 1 | Lean theorem MacroEcosystemTribologyConversionQueueKernelBridge.macro_ecosystem_tribology_conversion_semantic_morphism_yields_positive_topological_deficit in MacroEcosystemTribologyConversionQueueKernelBridge.lean, rewriting via morphism equality and reusing the positive-deficit bridge theorem | Mechanized | | THM-QUEUE-CACHE-ASYNC-SLEEP-BOUNDARY-POSITIVE-DEFICIT-BUNDLE | Cross-domain bridge bundle: ESC cold-path fold work, async durability vent mass, and crossed weighted-sleep debt mass jointly induce a strict-majority queue interpretation that yields both the canonical one-path boundary witness and strictly positive lifted TCP deficit | async pulse witness p : AsyncDurabilityPulse; weighted-sleep assumptions thresholdRhs < thresholdLhs and 0 < n; interpretation anchor failureBudget = traceFold [cold] + p.totalVent + iteratedDebt, replicaCount = 2*failureBudget + 1 | Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_budget_yields_boundary_and_positive_deficit in CacheAsyncSleepQueueKernelBridge.lean, combining cache_async_sleep_budget_yields_unit_queue_boundary with cache_async_sleep_budget_yields_positive_topological_deficit | Mechanized | | THM-QUEUE-CACHE-ASYNC-SLEEP-RETRIAL-STATIONARY-BRIDGE | Blocker-attack bridge (proof-depth strategy): with explicit retrial-kernel payload assumptions, cache+async+weighted-sleep source claims transport into the retrial stationary-balance theorem surface | explicit payload assumption kernel : RetrialQueueKernelFamily maxQueue maxOrbit; weighted-sleep assumptions thresholdRhs < thresholdLhs and 0 < n; source witnesses include traceFold [cold] = escCanonMissW.val and positive iterated debt | Lean theorem CacheAsyncSleepQueueKernelBridge.CacheAsyncSleepRetrialAdapter.retrial_stationary_balance_bridge in CacheAsyncSleepQueueKernelBridge.lean, reusing StateDependentQueueFamilies.RetrialQueueKernelFamily.stationary_balance under explicit adapter hypotheses | Mechanized | | THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: ESC cold-path fold work, async background-vent delta transport (q.bgVent = p.bgVent + k), and weighted sleep debt are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) | async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; weighted sleep assumptions thresholdRhs < thresholdLhs, 0 < n; interpretation anchor failureBudget = traceFold [cold] + q.totalVent + iteratedDebt, replicaCount = 2*failureBudget + 1 | Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_delta_budget_yields_unit_queue_boundary in CacheAsyncSleepQueueKernelBridge.lean, composing WasmEscObservationTrace.trace_one_cold_eq_w, AsyncDurabilityVent.background_only_adds_vent, SleepDebtWeightedSchedule.iterated_debt_positive_above_threshold, and QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive interpreted cache+async-delta+weighted-sleep budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same assumptions as THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 ≤ failureBudget + 1 from interpreted-budget positivity | Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_delta_budget_yields_positive_topological_deficit in CacheAsyncSleepQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BOUNDARY-POSITIVE-DEFICIT-BUNDLE | Cross-domain bridge bundle: the same cache+async-delta+weighted-sleep interpretation jointly yields the canonical one-path queue boundary witness and strictly positive lifted TCP deficit in one mechanized conjunction | same assumptions as THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BUDGET-UNIT-BOUNDARY; bundled sink theorem combines boundary and deficit witnesses without additional axioms | Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_delta_budget_yields_boundary_and_positive_deficit in CacheAsyncSleepQueueKernelBridge.lean, pairing cache_async_sleep_delta_budget_yields_unit_queue_boundary with cache_async_sleep_delta_budget_yields_positive_topological_deficit | Mechanized | | THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BUDGET-NOT-BETA1-EQUAL-BUDGET | Contrarian anti-theorem variant: anchored cache+async-delta+weighted-sleep interpretation does not force queue path-width to equal interpreted budget mass (β₁ = failureBudget) | same assumptions as THM-QUEUE-CACHE-ASYNC-SLEEP-DELTA-BUDGET-UNIT-BOUNDARY; contradiction uses canonical β₁ = 0 witness and interpreted-budget positivity | Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_delta_budget_does_not_force_beta1_equals_budget in CacheAsyncSleepQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget | Mechanized |

| THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: mediation decomposition, causal-discovery independence arithmetic, and bandit failure mass are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (beta1 = 0, capacity = 1) | mediation assumption mediatorLoss >= 1; discovery assumptions vX <= R, vY <= R, vX + vY <= R; bandit arm assumptions from ExplorationExploitation.Arm (failures <= pulls); interpretation anchor failureBudget = totalRejections + (vX + vY) + failures, replicaCount = 2*failureBudget + 1 | Lean theorem MediationDiscoveryBanditQueueKernelBridge.mediation_discovery_bandit_budget_yields_unit_queue_boundary in MediationDiscoveryBanditQueueKernelBridge.lean, composing source-domain claims with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: positive interpreted mediation+discovery+bandit budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same assumptions as THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-UNIT-BOUNDARY; lifted path-floor witness 2 <= failureBudget + 1 from source-derived budget positivity | Lean theorem MediationDiscoveryBanditQueueKernelBridge.mediation_discovery_bandit_budget_yields_positive_topological_deficit in MediationDiscoveryBanditQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-NOT-BETA1-EQUAL-BUDGET | Contrarian anti-theorem variant: anchored mediation+discovery+bandit interpretation does not force queue path-width to equal interpreted budget mass (beta1 = failureBudget) | same assumptions as THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness and source-derived budget positivity | Lean theorem MediationDiscoveryBanditQueueKernelBridge.mediation_discovery_bandit_budget_does_not_force_beta1_equals_budget in MediationDiscoveryBanditQueueKernelBridge.lean, via contradiction against the canonical one-path witness and positive interpreted budget mass | Mechanized | | THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-NOT-CAPACITY-AT-LEAST-TWO | Contrarian anti-theorem variant: anchored mediation+discovery+bandit interpretation does not force capacity >= 2 | same assumptions as THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-UNIT-BOUNDARY; contradiction uses canonical one-path witness with capacity = 1 | Lean theorem MediationDiscoveryBanditQueueKernelBridge.mediation_discovery_bandit_budget_does_not_force_capacity_at_least_two in MediationDiscoveryBanditQueueKernelBridge.lean | Mechanized | | THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-SEMANTIC-MORPHISM-POSITIVE-DEFICIT | Blocker-remediation bridge (interpretation-layer strategy): an explicit semantic morphism equality from interpreted mediation+discovery+bandit budget to mapped path-count coordinates transports the positive TCP-deficit witness | same assumptions as THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-BUDGET-UNIT-BOUNDARY; interpretation function interpret : Nat -> Nat; explicit morphism hypothesis interpret (failureBudget + 1) = failureBudget + 1 | Lean theorem MediationDiscoveryBanditQueueKernelBridge.mediation_discovery_bandit_semantic_morphism_yields_positive_topological_deficit in MediationDiscoveryBanditQueueKernelBridge.lean, rewriting the lifted path-count argument through morphism equality | Mechanized | | THM-QUEUE-MEDIATION-DISCOVERY-BANDIT-RETRIAL-STATIONARY-BRIDGE | Blocker-attack bridge (proof-depth strategy): with explicit RetrialQueueKernelFamily payload assumptions, mediation+discovery+bandit source claims transport into the retrial stationary-balance theorem surface without hidden kernel synthesis | explicit payload assumption kernel : RetrialQueueKernelFamily maxQueue maxOrbit; mediation assumptions from MediationSetup; discovery assumptions vX <= R, vY <= R, vX + vY <= R; bandit arm assumptions from ExplorationExploitation.Arm | Lean theorem MediationDiscoveryBanditQueueKernelBridge.mediation_discovery_bandit_retrial_stationary_balance_bridge in MediationDiscoveryBanditQueueKernelBridge.lean, reusing StateDependentQueueFamilies.RetrialQueueKernelFamily.stationary_balance under explicit theorem-level payload hypotheses | Mechanized | | THM-QUEUE-GOODHART-CERTIFIED-CONTEXTUAL-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Goodhart proxy-gap accounting, certified-radius accounting, and contextual-bandit failure accounting are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness (beta1 = 0, capacity = 1) | Goodhart assumptions vTrue <= budget, vGamed <= budget, vGamed <= vTrue; certified payload c : CertifiedDefenses.Certification; contextual payload a : ContextualBandits.ContextualArm; interpretation anchor failureBudget = (vTrue - vGamed) + (cleanReject + radius) + totalFailures, replicaCount = 2*failureBudget + 1 | Lean theorem GoodhartCertifiedContextualQueueKernelBridge.goodhart_certified_contextual_budget_yields_unit_queue_boundary in GoodhartCertifiedContextualQueueKernelBridge.lean, composing source identities with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-GOODHART-CERTIFIED-CONTEXTUAL-BUDGET-POSITIVE-DEFICIT-BRIDGE | Cross-domain bridge: a strictly positive interpreted Goodhart+certified+contextual budget forces strictly positive TCP-style topological deficit on lifted (budget + 1) paths | same interpretation as THM-QUEUE-GOODHART-CERTIFIED-CONTEXTUAL-BUDGET-UNIT-BOUNDARY; explicit positivity hypothesis 0 < failureBudget to keep domain-specific mass assumptions honest and theorem-local | Lean theorem GoodhartCertifiedContextualQueueKernelBridge.goodhart_certified_contextual_budget_yields_positive_topological_deficit in GoodhartCertifiedContextualQueueKernelBridge.lean, using CoveringSpaceCausality.deficit_latency_separation | Mechanized | | THM-QUEUE-GOODHART-CERTIFIED-CONTEXTUAL-BUDGET-NOT-BETA1-EQUAL-CAPACITY | Contrarian anti-theorem variant: anchored Goodhart+certified+contextual interpretation does not force beta1 = capacity | same assumptions as THM-QUEUE-GOODHART-CERTIFIED-CONTEXTUAL-BUDGET-UNIT-BOUNDARY; witness restricted to boundaries with anchored arrival/service rates from the interpreted budget | Lean theorem GoodhartCertifiedContextualQueueKernelBridge.goodhart_certified_contextual_budget_does_not_force_beta1_equals_capacity in GoodhartCertifiedContextualQueueKernelBridge.lean, via contradiction against the canonical one-path witness (beta1 = 0, capacity = 1) | Mechanized | | THM-QUEUE-GOODHART-CERTIFIED-CONTEXTUAL-ADAPTIVE-STATIONARY-BRIDGE | Blocker-attack bridge (proof-depth strategy): with explicit AdaptiveRoutingQueueKernelFamily payload assumptions, Goodhart+certified+contextual source claims transport into adaptive-routing stationary balance without hidden kernel synthesis | explicit payload assumption kernel : AdaptiveRoutingQueueKernelFamily maxLeft maxRight; Goodhart assumptions vTrue <= budget, vGamed <= budget, vGamed <= vTrue; certified payload c : Certification; contextual payload a : ContextualArm | Lean theorem GoodhartCertifiedContextualQueueKernelBridge.goodhart_certified_contextual_adaptive_stationary_balance_bridge in GoodhartCertifiedContextualQueueKernelBridge.lean, reusing StateDependentQueueFamilies.AdaptiveRoutingQueueKernelFamily.stationary_balance under explicit theorem-level payload hypotheses | Mechanized | | THM-QUEUE-DATA-PROCESSING-LOSS-UNIT-BOUNDARY | Cross-domain bridge: DataProcessing strict loss accounting is interpreted through a strict-majority budget and yields a canonical one-path queue boundary witness | DataProcessing inequality interpretation anchor failureBudget = dataProcessingFailureBudget n, replicaCount = 2*failureBudget + 1 | Lean theorem data_processing_loss_yields_unit_queue_boundary in DataProcessingFisherQueueKernelBridge.lean, composing source identities with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-FISHER-CURVATURE-UNIT-BOUNDARY | Cross-domain bridge: Fisher scalar curvature (n-1)*(n-2) accounting is interpreted through a strict-majority budget and yields a canonical one-path queue boundary witness | Fisher scalar curvature interpretation anchor failureBudget = fisherScalarCurvatureX4 n | Lean theorem fisher_curvature_yields_unit_queue_boundary in DataProcessingFisherQueueKernelBridge.lean, composing source identities with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary | Mechanized | | THM-QUEUE-DATA-FISHER-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: combined DataProcessing loss and Fisher curvature budgets are interpreted through one strict-majority budget and yield a canonical one-path queue boundary witness | combined interpretation anchor failureBudget = n + fisherScalarCurvatureX4 m | Lean theorem data_fisher_budget_yields_unit_queue_boundary in DataProcessingFisherQueueKernelBridge.lean | Mechanized | | THM-QUEUE-DATA-FISHER-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: anchored DataProcessing+Fisher interpretation does not force queue path-width to be positive (beta1 > 0) | same assumptions as THM-QUEUE-DATA-FISHER-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness | Lean theorem data_fisher_budget_does_not_force_positive_beta1 in DataProcessingFisherQueueKernelBridge.lean | Mechanized | | THM-QUEUE-ZECKENDORF-GAP-UNIT-BOUNDARY | Cross-domain bridge: Zeckendorf non-consecutive representation gap is interpreted through a strict-majority budget and yields a canonical one-path queue boundary witness | Zeckendorf representation assumptions fib(k+2) <= n < fib(k+3) | Lean theorem zeckendorf_gap_yields_unit_queue_boundary in ZeckendorfBatchingQueueKernelBridge.lean | Mechanized | | THM-QUEUE-ZECKENDORF-BATCHING-UNIT-BOUNDARY | Cross-domain bridge: D1 batching query schedule and Zeckendorf representation combined interpretation yields a canonical one-path queue boundary witness | D1 assumptions batchedQueries + wasted = loopQueries, wasted >= 1 | Lean theorem zeckendorf_batching_yields_unit_queue_boundary in ZeckendorfBatchingQueueKernelBridge.lean | Mechanized | | THM-QUEUE-ZECKENDORF-BATCHING-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: anchored Zeckendorf+Batching interpretation does not force queue path-width to be positive (beta1 > 0) | same assumptions as THM-QUEUE-ZECKENDORF-BATCHING-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness | Lean theorem zeckendorf_batching_does_not_force_positive_beta1 in ZeckendorfBatchingQueueKernelBridge.lean | Mechanized | | THM-QUEUE-DIMENSIONAL-CONFINEMENT-UNIT-BOUNDARY | Cross-domain bridge: dimensional confinement quark count is interpreted through a strict-majority budget and yields a canonical one-path queue boundary witness | dimensional representation assumptions quarks stages = stages | Lean theorem dimensional_confinement_yields_unit_queue_boundary in DimensionalMediaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-INFINITE-SCROLL-UNIT-BOUNDARY | Cross-domain bridge: infinite scroll trap load yields a canonical one-path queue boundary witness | infinite scroll assumptions raceLoad - foldResolution > ventThreshold | Lean theorem infinite_scroll_yields_unit_queue_boundary in DimensionalMediaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-DIMENSIONAL-MEDIA-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: combined dimensional confinement and infinite scroll trap budget interpretation yields a canonical one-path queue boundary witness | combined interpretation anchor failureBudget = quarks stages + (raceLoad - foldResolution) | Lean theorem dimensional_media_budget_yields_unit_queue_boundary in DimensionalMediaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-DIMENSIONAL-MEDIA-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: anchored dimensional+media interpretation does not force queue path-width to be positive (beta1 > 0) | same assumptions as THM-QUEUE-DIMENSIONAL-MEDIA-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness | Lean theorem dimensional_media_budget_does_not_force_positive_beta1 in DimensionalMediaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CAPITAL-LOCKUP-UNIT-BOUNDARY | Cross-domain bridge: capital lockup is interpreted through a strict-majority budget and yields a canonical one-path queue boundary witness | capital lockup representation assumptions lockupMinutes <= totalMinutes | Lean theorem capital_lockup_yields_unit_queue_boundary in CapitalCancerQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CANCER-TOPOLOGY-UNIT-BOUNDARY | Cross-domain bridge: cell topology vent capacity yields a canonical one-path queue boundary witness | cancer vent assumptions 0 <= totalVentBeta1 | Lean theorem cancer_topology_yields_unit_queue_boundary in CapitalCancerQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CAPITAL-CANCER-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: combined capital lockup and cancer vent capacity budget interpretation yields a canonical one-path queue boundary witness | combined interpretation anchor failureBudget = lockupMinutes + totalVentBeta1 | Lean theorem capital_cancer_budget_yields_unit_queue_boundary in CapitalCancerQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CAPITAL-CANCER-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: anchored capital+cancer interpretation does not force queue path-width to be positive (beta1 > 0) | same assumptions as THM-QUEUE-CAPITAL-CANCER-BUDGET-UNIT-BOUNDARY; contradiction uses canonical beta1 = 0 witness | Lean theorem capital_cancer_budget_does_not_force_positive_beta1 in CapitalCancerQueueKernelBridge.lean | Mechanized | | THM-QUEUE-MYCOLOGY-THERMAL-VENT-UNIT-BOUNDARY | Cross-domain bridge: thermal vent threshold interpretation yields canonical one-path queue boundary witness | mycology assumptions undergroundHeat > ventThreshold, sporeExhaust ≥ 1 | Lean theorem mycology_thermal_vent_yields_unit_queue_boundary in MycologyTypographyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TYPOGRAPHY-LIGATURE-UNIT-BOUNDARY | Cross-domain bridge: typography ligature mass interpretation yields canonical one-path queue boundary witness | typography assumptions characterOne + characterTwo = ligatureUnknot + frictionSave, frictionSave ≥ 1 | Lean theorem typography_ligature_yields_unit_queue_boundary in MycologyTypographyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-MYCOLOGY-TYPOGRAPHY-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: combined mycology+typography interpretation yields canonical one-path queue boundary witness | combined assumptions undergroundHeat > ventThreshold, characterOne + characterTwo = ligatureUnknot + frictionSave | Lean theorem mycology_typography_budget_yields_unit_queue_boundary in MycologyTypographyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-MYCOLOGY-TYPOGRAPHY-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: combined mycology+typography interpretation does not force positive path width | same combined interpretation with anchored queue boundaries | Lean theorem mycology_typography_budget_does_not_force_positive_beta1 in MycologyTypographyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-MYCOLOGY-TYPOGRAPHY-BUDGET-NOT-STRICT-CAPACITY-GROWTH | Contrarian anti-theorem variant: combined mycology+typography interpretation does not force strict capacity growth (capacity > 1) | same combined interpretation with anchored queue boundaries | Lean theorem mycology_typography_budget_does_not_force_strict_capacity_growth in MycologyTypographyQueueKernelBridge.lean | Mechanized |

| THM-QUEUE-SYNAPTIC-PRUNING-UNIT-BOUNDARY | Cross-domain bridge: synaptic pruning budget -> canonical one-path queue boundary witness | synaptic pruning assumption initialWeight + retentionBonus ≥ pruningThreshold, retentionBonus ≥ 1, initialWeight = pruningThreshold | Lean theorem SynapticKademliaQueueKernelBridge.synaptic_pruning_budget_yields_unit_queue_boundary in SynapticKademliaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-KADEMLIA-ROUTING-UNIT-BOUNDARY | Cross-domain bridge: Kademlia XOR routing budget -> canonical one-path queue boundary witness | Kademlia assumption bucketDepth ≤ xorDistance, bucketDepth ≥ 1 | Lean theorem SynapticKademliaQueueKernelBridge.kademlia_routing_budget_yields_unit_queue_boundary in SynapticKademliaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-SYNAPTIC-KADEMLIA-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: combined synaptic+Kademlia budget -> canonical one-path queue boundary witness | synaptic and Kademlia assumptions combined | Lean theorem SynapticKademliaQueueKernelBridge.synaptic_kademlia_budget_yields_unit_queue_boundary in SynapticKademliaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-SYNAPTIC-KADEMLIA-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: combined synaptic+Kademlia interpretation does not force positive path-width | same assumptions as boundary theorem | Lean theorem SynapticKademliaQueueKernelBridge.synaptic_kademlia_budget_does_not_force_positive_beta1 in SynapticKademliaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-SYNAPTIC-KADEMLIA-BUDGET-NOT-BETA1-EQUALS-BUDGET | Contrarian anti-theorem variant: combined synaptic+Kademlia interpretation does not force queue path-width to equal budget | same assumptions as boundary theorem | Lean theorem SynapticKademliaQueueKernelBridge.synaptic_kademlia_budget_does_not_force_beta1_equals_budget in SynapticKademliaQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TRADE-TARIFF-UNIT-BOUNDARY | Cross-domain bridge: Trade tariff blocked paths accounting yields a strict-majority queue interpretation and canonical one-path boundary witness | Trade network assumptions | Lean theorem TradeAstrophysicsQueueKernelBridge.trade_tariff_budget_yields_unit_queue_boundary in TradeAstrophysicsQueueKernelBridge.lean | Mechanized | | THM-QUEUE-ASTROPHYSICS-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Astrophysics visible budget yields a strict-majority queue interpretation and canonical one-path boundary witness | Celestial shadow assumptions | Lean theorem TradeAstrophysicsQueueKernelBridge.astrophysics_budget_yields_unit_queue_boundary in TradeAstrophysicsQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TRADE-ASTROPHYSICS-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: combined Trade and Astrophysics interpretation yields one canonical queue witness with anchored combined-budget arrival/service rates | Trade and Celestial shadow assumptions | Lean theorem TradeAstrophysicsQueueKernelBridge.trade_astrophysics_budget_yields_unit_queue_boundary in TradeAstrophysicsQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TRADE-ASTROPHYSICS-BUDGET-NOT-BETA1-EQUALS-BUDGET | Contrarian anti-theorem variant: combined Trade+Astrophysics interpretation does not force beta1 to equal the combined budget mass | Same assumptions as boundary theorem | Lean theorem TradeAstrophysicsQueueKernelBridge.trade_astrophysics_budget_does_not_force_beta1_equals_budget in TradeAstrophysicsQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CYBERNETIC-EMOTION-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Cybernetic emotion feedback accounting yields canonical one-path queue boundary. | explicit cybernetic and emotion taxonomy anchors | Lean theorem cybernetic_emotion_budget_yields_unit_queue_boundary in CyberneticEmotionQueueKernelBridge.lean | Mechanized | | THM-QUEUE-EMOTION-GAP-FEEDBACK-UNIT-BOUNDARY | Cross-domain bridge: Emotion gap feedback accounting yields canonical one-path queue boundary. | explicit gap count anchors | Lean theorem emotion_gap_feedback_yields_unit_queue_boundary in CyberneticEmotionQueueKernelBridge.lean | Mechanized | | THM-QUEUE-CYBERNETIC-EMOTION-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: combined cybernetic emotion interpretation does not force positive β₁. | anchored queue interpretation from combined budget | Lean theorem cybernetic_emotion_budget_does_not_force_positive_beta1 in CyberneticEmotionQueueKernelBridge.lean | Mechanized |

| THM-QUEUE-DEFICIT-CAPACITY-UNIT-BOUNDARY | Deficit pigeonhole collision capacity yields a strict-majority queue budget and canonical one-path boundary. | deficit_capacity_budget | Lean theorem deficit_collision_yields_unit_queue_boundary in DeficitWallingtonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-WALLINGTON-OPTIMALITY-UNIT-BOUNDARY | Wallington rotation speedup factor yields a canonical one-path queue boundary. | wallington_speedup | Lean theorem wallington_speedup_yields_unit_queue_boundary in DeficitWallingtonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-DEFICIT-WALLINGTON-BUDGET-UNIT-BOUNDARY | Combined deficit collision and Wallington speedup interpretation yields a unified canonical one-path queue boundary. | combined_budget | Lean theorem deficit_wallington_budget_yields_unit_queue_boundary in DeficitWallingtonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-DEFICIT-WALLINGTON-BUDGET-NOT-POSITIVE-BETA1 | Anchored deficit+Wallington combined interpretation does not force positive path width. | canonical witness β₁=0 | Lean theorem deficit_wallington_budget_does_not_force_positive_beta1 in DeficitWallingtonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TYPOGRAPHY-LIGATURE-FRICTION-UNIT-BOUNDARY | Cross-domain bridge: Typography ligature friction accounting yields a strict-majority queue interpretation and canonical one-path boundary witness. | explicit typography ligature friction | Lean theorem typography_ligature_friction_yields_unit_queue_boundary in TypographyBotanyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-BOTANY-PLANT-GROWTH-UNIT-BOUNDARY | Cross-domain bridge: Botany plant growth accounting yields a strict-majority queue interpretation and canonical one-path boundary witness. | explicit botany plant growth | Lean theorem botany_plant_growth_yields_unit_queue_boundary in TypographyBotanyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TYPOGRAPHY-BOTANY-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Combined Typography ligature friction and Botany plant growth accounting yields a unified strict-majority queue interpretation and canonical one-path boundary witness. | combined failure budget LigatureFriction + PlantGrowth | Lean theorem typography_botany_budget_yields_unit_queue_boundary in TypographyBotanyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-TYPOGRAPHY-BOTANY-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem: combined Typography+Botany interpretation with anchored queue rates does not force β₁ to equal the combined budget mass. | anchored queue interpretation from combined budget | Lean theorem typography_botany_budget_does_not_force_beta1_equals_budget in TypographyBotanyQueueKernelBridge.lean | Mechanized | | THM-QUEUE-HOLOGRAPHIC-CONSENSUS-UNIT-BOUNDARY | Cross-domain bridge: Holographic consensus bulk accounting yields canonical one-path queue boundary. | explicit bulk consensus | Lean theorem holographic_consensus_yields_unit_queue_boundary in HolographicAeonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-AEON-DEFICIT-UNIT-BOUNDARY | Cross-domain bridge: Aeon voting governance deficit accounting yields canonical one-path queue boundary. | explicit governance deficit | Lean theorem aeon_deficit_yields_unit_queue_boundary in HolographicAeonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-HOLOGRAPHIC-AEON-BUDGET-UNIT-BOUNDARY | Cross-domain bridge: Combined holographic+aeon budget yields unified canonical one-path boundary. | combined budget | Lean theorem holographic_aeon_budget_yields_unit_queue_boundary in HolographicAeonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-HOLOGRAPHIC-AEON-BUDGET-NOT-POSITIVE-BETA1 | Contrarian anti-theorem: Combined holographic+aeon interpretation does not force positive path width. | canonical witness β₁=0 | Lean theorem holographic_aeon_budget_does_not_force_positive_beta1 in HolographicAeonQueueKernelBridge.lean | Mechanized | | THM-QUEUE-ORNITHOLOGY-MICROSERVICES-UNIT-BOUNDARY | Cross-domain bridge: Ornithology microservices budget yields a unified canonical one-path boundary. | combined budget | Lean theorem ornithology_microservices_budget_yields_unit_queue_boundary in OrnithologyMicroservicesQueueKernelBridge.lean | Mechanized | | THM-QUEUE-ORNITHOLOGY-MICROSERVICES-NOT-POSITIVE-BETA1 | Contrarian anti-theorem variant: Ornithology microservices interpretation does not force positive path width. | canonical witness β₁=0 | Lean theorem ornithology_microservices_budget_does_not_force_positive_beta1 in OrnithologyMicroservicesQueueKernelBridge.lean | Mechanized | | THM-QUEUE-EPIGENETIC-DRIFT-TIMEOUT-UNIT-BOUNDARY | Cross-domain bridge: Epigenetic drift timeout budget yields a unified canonical one-path boundary. | combined budget | Lean theorem epigenetic_drift_timeout_yields_unit_queue_boundary in EpigeneticDriftTimeoutBridge.lean | Mechanized |

Geometric & Compositional Ergodicity (Tracks Delta + Iota)

| THM-FIBONACCI-HOLOGRAPHIC-GEOMETRIC-RATE-CERTIFICATE | Moonshot fallback certificate: combined Fibonacci+Holographic budget yields an explicit geometric-rate package. | explicit GeometricErgodicityRate object | Lean theorem fibonacci_holographic_yields_geometric_rate_certificate in FibonacciHolographicQueueKernelBridge.lean | Mechanized | | THM-FIBONACCI-HOLOGRAPHIC-KERNEL-LIFT-CONTINUOUS-ERGODICITY | Moonshot blocker-attack adapter: explicit interpretation + missing witness objects unblock continuous ergodicity lift. | explicit embedding, witness, and kernel-match fields | Lean theorem FibonacciHolographicKernelLiftAdapter.fibonacci_holographic_continuous_ergodicity_lift in FibonacciHolographicQueueKernelBridge.lean | Mechanized | | THM-CANCER-TECTONIC-GEOMETRIC-RATE-CERTIFICATE | Moonshot fallback certificate: combined cancer+tectonic failure mass yields an explicit geometric-rate package | combined cancer/tectonic budget | Lean theorem cancer_tectonic_budget_yields_geometric_rate_certificate in CancerTectonicQueueKernelBridge.lean | Mechanized | | THM-CANCER-TECTONIC-KERNEL-LIFT-CONTINUOUS-ERGODICITY | Blocker-attack adapter: explicit interpretation and witness objects unblock continuous ergodicity lift | adapter hypotheses | Lean theorem CancerTectonicKernelLiftAdapter.cancer_tectonic_continuous_ergodicity_lift in CancerTectonicQueueKernelBridge.lean | Mechanized |

Geometric & Compositional Ergodicity (Tracks Delta + Iota)

Quantitative convergence rates, mixing time bounds, continuous ergodicity lift, parallel/sequential composition, pipeline certificates.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-KADEMLIA-TAPHONOMY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback lane: Combined Kademlia+Taphonomy budget certifies an explicit geometric-rate package. explicit GeometricErgodicityRate object Lean theorem kademlia_taphonomy_budget_yields_geometric_rate_certificate in KademliaTaphonomyQueueKernelBridge.lean Mechanized
THM-KADEMLIA-TAPHONOMY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack lane: explicit Kademlia+Taphonomy kernel-lift adapter unblocks continuous ergodicity lift. explicit embedding, witness, and kernel-match fields Lean theorem kademlia_taphonomy_continuous_ergodicity_lift in KademliaTaphonomyQueueKernelBridge.lean Mechanized
THM-AUTOIMMUNITY-FIAT-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined autoimmunity+fiat budget yields an explicit geometric-rate package. explicit GeometricErgodicityRate object Lean theorem autoimmunity_fiat_budget_yields_geometric_rate_certificate in AutoimmunityMacroEconomicsQueueKernelBridge.lean Mechanized
THM-AUTOIMMUNITY-FIAT-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: explicit autoimmunity+fiat interpretation + missing witness objects unblock continuous ergodicity lift constructively. explicit interpretation anchor and GeometricErgodicWitness/DiscreteSubLatticeEmbedding Lean theorem AutoimmunityFiatKernelLiftAdapter.autoimmunity_fiat_continuous_ergodicity_lift in AutoimmunityMacroEconomicsQueueKernelBridge.lean Mechanized
THM-GOSSIP-EPIDEMIOLOGY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Gossip+SIR budget yields an explicit geometric-rate package. explicit GeometricErgodicityRate object Lean theorem gossip_sir_budget_yields_geometric_rate_certificate in GossipEpidemiologyQueueKernelBridge.lean Mechanized
THM-GOSSIP-EPIDEMIOLOGY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: explicit Gossip+SIR interpretation + missing witness objects unblock continuous ergodicity lift constructively. explicit interpretation anchor and GeometricErgodicWitness/DiscreteSubLatticeEmbedding Lean theorem GossipSirKernelLiftAdapter.gossip_sir_continuous_ergodicity_lift in GossipEpidemiologyQueueKernelBridge.lean Mechanized
THM-TYPOGRAPHY-BOTANY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Typography+Botany budget yields an explicit geometric-rate package. explicit GeometricErgodicityRate object Lean theorem typography_botany_budget_yields_geometric_rate_certificate in TypographyBotanyQueueKernelBridge.lean Mechanized
THM-TYPOGRAPHY-BOTANY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: explicit Typography+Botany interpretation + missing witness objects unblock continuous ergodicity lift constructively. explicit interpretation anchor and GeometricErgodicWitness/DiscreteSubLatticeEmbedding Lean theorem TypographyBotanyKernelLiftAdapter.typography_botany_continuous_ergodicity_lift in TypographyBotanyQueueKernelBridge.lean Mechanized
THM-OPTICS-BOTANY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Optics+Botany budget yields an explicit geometric-rate package. explicit GeometricErgodicityRate object Lean theorem optics_botany_budget_yields_geometric_rate_certificate in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-OPTICS-BOTANY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: explicit Optics+Botany interpretation + missing witness objects unblock continuous ergodicity lift constructively. explicit interpretation anchor and witness fields Lean theorem optics_botany_continuous_ergodicity_lift in OpticsBotanyQueueKernelBridge.lean Mechanized
THM-ENTANGLEMENT-BULLWHIP-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Bell entanglement + Bullwhip variance budget yields an explicit geometric-rate package. explicit GeometricErgodicityRate object Lean theorem entanglement_bullwhip_budget_yields_geometric_rate_certificate in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-ENTANGLEMENT-BULLWHIP-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: explicit Bell entanglement + Bullwhip variance interpretation + missing witness objects unblock continuous ergodicity lift constructively. explicit interpretation anchor and GeometricErgodicWitness/DiscreteSubLatticeEmbedding Lean theorem EntanglementBullwhipKernelLiftAdapter.entanglement_bullwhip_continuous_ergodicity_lift in EntanglementBullwhipQueueKernelBridge.lean Mechanized
THM-SEMIOTIC-VOID-GEOMETRIC-RATE-CERTIFICATE Combined Semiotic+Void budget yields an explicit geometric-rate package. positive Semiotic+Void budget Lean theorem semiotic_void_budget_yields_geometric_rate_certificate in SemioticVoidQueueKernelBridge.lean Mechanized
THM-SEMIOTIC-VOID-KERNEL-LIFT-CONTINUOUS-ERGODICITY Explicit interpretation and witness objects so continuous_ergodicity_lift applies constructively. explicit embedding, witness, and kernel-match fields Lean theorem SemioticVoidKernelLiftAdapter.semiotic_void_continuous_ergodicity_lift in SemioticVoidQueueKernelBridge.lean Mechanized
THM-SEMIOTIC-VOID-EXPLICIT-WITNESS-BRIDGE Explicitly instantiate the geometric envelope missing from arithmetic bounds, providing a full witness bridge. explicit certified kernel and envelope structures Lean theorem SemioticVoidGeometricWitnessAdapter.semiotic_void_explicit_witness_bridge in SemioticVoidQueueKernelBridge.lean Mechanized
THM-CONTINUOUS-HARRIS Foster-Lyapunov drift witness synthesis for continuous-state kernels over Polish spaces, extending beyond Fin (maxQueue + 1) types. Provides kernel structure, drift conditions, witness synthesis, and multi-level composition. Polish space Ω; measurable Lyapunov function; measurable small set; drift gap > 0 Lean theorems ContinuousHarris.continuous_harris_from_drift, ContinuousHarris.synthesized_kernel_foster_drift, ContinuousHarris.discrete_embeds_continuous, and ContinuousHarris.multi_level_positive_drift Mechanized
THM-GEOMETRIC-ERGODICITY-DISCRETE For a countable certified kernel with quantitative geometric envelope at an atom, the TV distance from any initial state to the stationary distribution decays geometrically: TV(P^n(x, ·), π) ≤ M(x) · r^n for computable r < 1. Quantifies how fast systems converge, not just that they converge. countable certified kernel with geometric envelope at atom; step epsilon ε₂ > 0; small-set epsilon ε₁ > 0; both sub-unit TLA+ GeometricErgodicity.tla invariant InvGeometricDecay + Lean theorem GeometricErgodicity.geometric_ergodicity_discrete in GeometricErgodicity.lean Mechanized
THM-GEOMETRIC-ERGODICITY-RATE The contraction rate r is bounded by 1 - stepEpsilon · smallSetEpsilon, explicitly computable from the kernel certificate data. geometric ergodic witness with step/small-set epsilons TLA+ GeometricErgodicity.tla invariant InvRateBound + Lean theorem GeometricErgodicity.geometric_ergodicity_rate in GeometricErgodicity.lean Mechanized
THM-MIXING-TIME-BOUND The ε-mixing time satisfies t_mix(ε) ≤ (1/(1-r)) · log(M(x)/ε). For any target tolerance, there exists a finite step count at which TV distance drops below it. geometric ergodic witness; target tolerance ε > 0; initial bound M(x) TLA+ GeometricErgodicity.tla invariant InvMixingTimeBound + Lean theorem GeometricErgodicity.mixing_time_bound in GeometricErgodicity.lean Mechanized
THM-CONTINUOUS-ERGODICITY-LIFT For a ContinuousStateKernel with a discrete sub-lattice embedding, the discrete geometric rate lifts to the continuous kernel. Polish-space kernels inherit convergence rates from their discrete skeletons. ContinuousStateKernel Ω; discrete sub-lattice embedding ι : Fin n → Ω; lattice covers small set; discrete kernel with geometric ergodic witness TLA+ GeometricErgodicity.tla invariant InvContinuousLift + Lean theorem GeometricErgodicity.continuous_ergodicity_lift in GeometricErgodicity.lean Mechanized
THM-CACHE-ASYNC-SLEEP-DELTA-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization primitives plus cache+async-delta+weighted-sleep source claims, compile a full GeometricErgodicWitness without postulating a prebuilt witness object async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; weighted sleep assumptions thresholdRhs < thresholdLhs, 0 < n; explicit primitive payload CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_delta_compile_witness_from_primitives in CacheAsyncSleepQueueKernelBridge.lean, constructing envelope/rate/witness via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CACHE-ASYNC-SLEEP-DELTA-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the cache+async-delta+weighted-sleep witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-CACHE-ASYNC-SLEEP-DELTA-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_delta_compiled_witness_continuous_ergodicity_lift in CacheAsyncSleepQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-MEDIA-CONVERSION-KNAPSACK-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: interpreted media+conversion+knapsack budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (clickstr + ventSlam + visualOverlap) + 1 media assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; knapsack assumptions pleromicData = screenCapacity + visualOverlap, visualOverlap ≥ 1; interpretation anchor failureBudget = clickstr + ventSlam + visualOverlap Lean theorem MediaConversionKnapsackQueueKernelBridge.media_conversion_knapsack_budget_yields_geometric_rate_certificate in MediaConversionKnapsackQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIA-CONVERSION-KNAPSACK-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Blocker-remediation lemma: under the explicit media+conversion+knapsack adapter, interpreted real-budget positivity is derived from source-domain assumptions instead of carried as an opaque adapter field media assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; knapsack assumptions pleromicData = screenCapacity + visualOverlap, visualOverlap ≥ 1; interpretation anchor budgetReal = clickstr + ventSlam + visualOverlap Lean theorem MediaConversionKnapsackKernelLiftAdapter.budget_pos_from_source in MediaConversionKnapsackQueueKernelBridge.lean Mechanized
THM-MEDIA-CONVERSION-KNAPSACK-KERNEL-LIFT-CONTINUOUS-ERGODICITY Blocker-attack bridge: with an explicit adapter carrying source assumptions plus DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-alignment equality, continuous ergodicity lift follows while preserving source-domain claims explicit adapter payload includes media clickbait assumptions, conversion vent assumptions, knapsack overlap assumptions, interpreted budget positivity from source, embedding/witness payloads, and kernel = embedding.discreteKernel alignment Lean theorem MediaConversionKnapsackKernelLiftAdapter.media_conversion_knapsack_continuous_ergodicity_lift in MediaConversionKnapsackQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-HORTICULTURE-MEMORY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: Combined budget yields explicit geometric rate PlantGrowth, GarbageCollection Lean theorem combined_horticulture_memory_yields_geometric_rate_certificate in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-HORTICULTURE-MEMORY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Blocker-attack adapter: explicit interpretation objects unblock continuous lift explicit adapter fields Lean theorem HorticultureMemoryKernelLiftAdapter.horticulture_memory_continuous_ergodicity_lift in HorticultureMemoryQueueKernelBridge.lean Mechanized
THM-COMMUNITY-DIVERSITY-COMBAT-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: interpreted community+diversity+combat budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (communityContext + diversePaths + attackerVelocity) + 1 community assumptions ft : FailureTopology, 0 < communityContext; diversity assumptions 1 ≤ diversePaths; combat assumptions attackerVelocity > startupTicks, entanglement = 0; interpretation anchor failureBudget = communityContext + diversePaths + attackerVelocity Lean theorem CommunityDiversityCombatQueueKernelBridge.community_diversity_combat_budget_yields_geometric_rate_certificate in CommunityDiversityCombatQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-COMMUNITY-DIVERSITY-COMBAT-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under community+diversity+combat interpretation, adapter budget positivity is derived from source assumptions instead of introduced as a black-box field source assumptions combine community-context positivity (0 < communityContext), diversity path floor (1 ≤ diversePaths), and combat velocity assumptions (attackerVelocity > startupTicks, entanglement = 0) Lean theorem CommunityDiversityCombatKernelLiftAdapter.budget_pos_from_source in CommunityDiversityCombatQueueKernelBridge.lean Mechanized
THM-HOLOGRAPHIC-AEON-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: Combined holographic+aeon budget yields explicit geometric rate. combined budget Lean theorem holographic_aeon_budget_yields_geometric_rate_certificate in HolographicAeonQueueKernelBridge.lean Mechanized
THM-HOLOGRAPHIC-AEON-KERNEL-LIFT-CONTINUOUS-ERGODICITY Blocker-attack adapter: explicit interpretation objects unblock continuous ergodicity lift. explicit adapter fields Lean theorem holographic_aeon_continuous_ergodicity_lift in HolographicAeonQueueKernelBridge.lean Mechanized
THM-COMMUNITY-DIVERSITY-COMBAT-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: community attenuation, diversity/concurrency identity, and combat velocity routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source-derived budget positivity explicit adapter bundle carrying community source assumptions, diversity path assumptions, combat velocity assumptions, and explicit DiscreteSubLatticeEmbedding/GeometricErgodicWitness payloads with kernel-match equality Lean theorem CommunityDiversityCombatKernelLiftAdapter.community_diversity_combat_continuous_ergodicity_lift in CommunityDiversityCombatQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-KI-FRF-TRAINING-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: interpreted Ki+FRF+training budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = failureBudget + 1 Ki leak witness 0 < glanceLeak ∨ 0 < muscleLeak ∨ 0 < scentLeak ∨ 0 < energyLeak; timeline witness reactionTick < actionTick; training witness drillBeatsChance sampleSeriesBeats; interpretation anchor failureBudget = totalLeak + correctCount sampleSeriesBeats + raceScore(foldAction(forkFutures), forkFutures) Lean theorem KiFrfTrainingQueueKernelBridge.ki_frf_training_budget_yields_geometric_rate_certificate in KiFrfTrainingQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-KI-FRF-TRAINING-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Blocker-remediation lemma: under the explicit Ki+FRF+training adapter, interpreted real-budget positivity is derived from source assumptions instead of carried as an opaque adapter field source assumptions include Ki leak witness, timeline witness, and training witness from KiTrainingWitness.sample_series_beats_chance; interpretation anchor budgetReal = failureBudget Lean theorem KiFrfTrainingQueueKernelBridge.KiFrfTrainingKernelLiftAdapter.budget_pos_from_source in KiFrfTrainingQueueKernelBridge.lean Mechanized
THM-KI-FRF-TRAINING-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Ki precursor leak data, deterministic FRF minimax dominance, and training witness data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source-derived budget positivity explicit adapter bundle carrying Ki leak witness, timeline witness, FRF dominance witnesses, training witness, and explicit DiscreteSubLatticeEmbedding/GeometricErgodicWitness payloads with kernel-match equality Lean theorem KiFrfTrainingQueueKernelBridge.KiFrfTrainingKernelLiftAdapter.ki_frf_training_continuous_ergodicity_lift in KiFrfTrainingQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-MUSIC-NARRATIVE-TYPOGRAPHY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: interpreted music+narrative+typography budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (swingPerturbation + narrativeCrossings + frictionSave) + 1 music assumptions swingPerturbation ≥ 1, totalSpace = periodicLoad + swingPerturbation; narrative assumption narrativeCrossings ≥ 1; typography assumptions characterOne + characterTwo = ligatureUnknot + frictionSave, frictionSave ≥ 1; interpretation anchor failureBudget = swingPerturbation + narrativeCrossings + frictionSave Lean theorem MusicNarrativeTypographyQueueKernelBridge.music_narrative_typography_budget_yields_geometric_rate_certificate in MusicNarrativeTypographyQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MUSIC-NARRATIVE-TYPOGRAPHY-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Blocker-remediation lemma: under the explicit music+narrative+typography adapter, interpreted real-budget positivity is derived from source-domain assumptions instead of carried as an opaque adapter field music assumptions swingPerturbation ≥ 1, totalSpace = periodicLoad + swingPerturbation; narrative assumption narrativeCrossings ≥ 1; typography assumptions characterOne + characterTwo = ligatureUnknot + frictionSave, frictionSave ≥ 1; interpretation anchor budgetReal = swingPerturbation + narrativeCrossings + frictionSave Lean theorem MusicNarrativeTypographyKernelLiftAdapter.budget_pos_from_source in MusicNarrativeTypographyQueueKernelBridge.lean Mechanized
THM-MUSIC-NARRATIVE-TYPOGRAPHY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Blocker-attack bridge: with an explicit adapter carrying source assumptions plus DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-alignment equality, continuous ergodicity lift follows while preserving source-domain claims explicit adapter payload includes music rhythm assumptions, narrative crossing assumptions, typography ligature assumptions, interpreted budget positivity from source, embedding/witness payloads, and kernel = embedding.discreteKernel alignment Lean theorem MusicNarrativeTypographyKernelLiftAdapter.music_narrative_typography_continuous_ergodicity_lift in MusicNarrativeTypographyQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-FORM-TOPOLOGY-GEOMETRIC-RATE-CERTIFICATE Witness-gap blocker attack: interpreted form-topology budget admits an explicit geometric-rate certificate with contraction r = 3/4 and budget-indexed initial bound M = failureBudget + 1 form assumptions wellFormed spec σ and ∃ f, f ∈ spec.fields; interpretation anchor `failureBudget = fields +
THM-DEWEY-THIN-BUREAUCRACY-SURGERY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: interpreted Dewey bureaucracy+surgery budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = ((bureaucraticFriction - systemVelocity) + sever) + 1 bureaucracy assumptions systemVelocity + safeTolerance = bureaucraticFriction, safeTolerance ≥ 1; surgery assumption sever = 0; interpretation anchor failureBudget = (bureaucraticFriction - systemVelocity) + sever Lean theorem DeweyBureaucracySurgeryQueueKernelBridge.dewey_bureaucracy_surgery_budget_yields_geometric_rate_certificate in DeweyBureaucracySurgeryQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-DEWEY-THIN-BUREAUCRACY-SURGERY-SEMANTIC-MORPHISM-CONTINUOUS-LIFT Blocker-remediation bridge (semantic morphism strategy): an explicit interpretation morphism from source tolerance to budget mass, together with explicit embedding/witness/kernel-match payloads, is sufficient to execute continuous ergodicity lift without a dedicated adapter record bureaucracy assumptions systemVelocity + safeTolerance = bureaucraticFriction, safeTolerance ≥ 1; surgery assumption sever = 0; interpretation hypothesis interpret safeTolerance = failureBudget; explicit lift payload DiscreteSubLatticeEmbedding, GeometricErgodicWitness, kernel-match equality Lean theorem DeweyBureaucracySurgeryQueueKernelBridge.dewey_bureaucracy_surgery_semantic_morphism_continuous_ergodicity_lift in DeweyBureaucracySurgeryQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under theorem-level semantic-morphism hypotheses Mechanized
THM-SLEEP-WEIGHTED-DEBT-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: positive weighted sleep debt induces an explicit geometric-ergodicity rate package with contraction r = 3/4 and debt-indexed initial bound M = debt + 1 weighted threshold crossed (thresholdRhs < thresholdLhs); positive cycle count 0 < n Lean theorem SleepDebtQuorumQueueBridge.positive_weighted_sleep_debt_yields_geometric_rate_certificate in SleepDebtQuorumQueueBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SLEEP-WEIGHTED-DEBT-MULTILEVEL-HARRIS-WITNESS Moonshot fallback witness: positive weighted sleep debt constructs a two-level Harris witness with strictly positive discrete and continuous drift gaps weighted threshold crossed (thresholdRhs < thresholdLhs); positive cycle count 0 < n Lean theorem SleepDebtQuorumQueueBridge.positive_weighted_sleep_debt_yields_multilevel_harris_witness in SleepDebtQuorumQueueBridge.lean, using ContinuousHarris.MultiLevelHarrisWitness and ContinuousHarris.multi_level_positive_drift Mechanized
THM-MEDIATION-CRYPTO-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: mediation loss plus a cryptographic side-channel floor yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (mediatorLoss + perEvalFloor) + 1 mediation setup with irreducible loss (mediatorLoss ≥ 1); cryptographic side-channel floor (0 < perEvalFloor) Lean theorem MediationCryptoQueueKernelBridge.mediation_crypto_side_channel_yields_geometric_rate_certificate in MediationCryptoQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIATION-CRYPTO-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: mediation and cryptographic side-channel data routed through an explicit kernel-lift adapter execute the continuous ergodicity lift while preserving drift positivity and sub-unit contraction explicit adapter bundle carrying mediation setup, side-channel floor witness, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MediationCryptoKernelLiftAdapter.mediated_continuous_ergodicity_lift in MediationCryptoQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-MEDIATION-CRYPTO-NEGOTIATION-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain mediation+crypto+negotiation interpreted budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (mediatorLoss + perEvalFloor + (slamTraumaPenalty - untanglingWattsCost)) + 1 mediation setup with irreducible loss (mediatorLoss ≥ 1); cryptographic side-channel floor (0 < perEvalFloor); negotiation BATNA inequality (slamTraumaPenalty ≥ untanglingWattsCost + 1) Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_budget_yields_geometric_rate_certificate in MediationCryptoNegotiationQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIATION-CRYPTO-NEGOTIATION-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and source-derived tri-domain budget positivity, compile a full GeometricErgodicWitness without postulating a prebuilt witness object tri-domain source assumptions as in THM-MEDIATION-CRYPTO-NEGOTIATION-GEOMETRIC-RATE-CERTIFICATE; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_compile_witness_from_primitives in MediationCryptoNegotiationQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIATION-CRYPTO-NEGOTIATION-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the tri-domain witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-MEDIATION-CRYPTO-NEGOTIATION-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem MediationCryptoNegotiationQueueKernelBridge.mediation_crypto_negotiation_compiled_witness_continuous_ergodicity_lift in MediationCryptoNegotiationQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-MEDIATION-NEGOTIATION-SPIDERWEB-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain mediation+negotiation+spiderweb interpreted budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (mediatorLoss + (slamTraumaPenalty - untanglingWattsCost) + meshRoutingPaths) + 1 mediation assumptions mediatorLoss ≥ 1; negotiation assumption slamTraumaPenalty ≥ untanglingWattsCost + 1; spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; interpretation anchor failureBudget = mediatorLoss + (slamTraumaPenalty - untanglingWattsCost) + meshRoutingPaths Lean theorem MediationNegotiationSpiderwebQueueKernelBridge.mediation_negotiation_spiderweb_budget_yields_geometric_rate_certificate in MediationNegotiationSpiderwebQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIATION-NEGOTIATION-SPIDERWEB-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under mediation+negotiation+spiderweb interpretation, adapter budget positivity is derived from source assumptions instead of introduced as a black-box field source assumptions combine mediation irreducible loss (mediatorLoss ≥ 1), BATNA trauma-gap floor (slamTraumaPenalty ≥ untanglingWattsCost + 1), and spiderweb path positivity (0 < meshRoutingPaths) from nontrivial mesh Lean theorem MediationNegotiationSpiderwebKernelLiftAdapter.budget_pos_from_source in MediationNegotiationSpiderwebQueueKernelBridge.lean Mechanized
THM-MEDIATION-NEGOTIATION-SPIDERWEB-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: mediation-loss floor, BATNA trauma-gap arithmetic, and spiderweb routing-path mass routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source-derived budget positivity explicit adapter bundle carrying mediation setup, negotiation economics, nontrivial spiderweb witnesses (0 < mesh.peers, 0 < mesh.hops), source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MediationNegotiationSpiderwebKernelLiftAdapter.mediation_negotiation_spiderweb_continuous_ergodicity_lift in MediationNegotiationSpiderwebQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-MEDIA-ECOSYSTEM-CRYPTO-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined media clickbait, ecosystem predator mass, and cryptographic proof overhead yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (failureBudget) + 1 media clickbait assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; ecosystem assumption predatorCount ≥ 1; cryptographic proof overhead proofCost Lean theorem MediaEcosystemCryptoQueueKernelBridge.media_ecosystem_crypto_budget_yields_geometric_rate_certificate in MediaEcosystemCryptoQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIA-ECOSYSTEM-CRYPTO-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and the interpreted media+ecosystem+cryptography budget, compile a full GeometricErgodicWitness without postulating a prebuilt witness object interpreted media clickbait assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; ecosystem assumption predatorCount ≥ 1; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem MediaEcosystemCryptoQueueKernelBridge.media_ecosystem_crypto_compile_witness_from_primitives in MediaEcosystemCryptoQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-PISOT-ASTROPHYSICS-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: Combined Pisot/astrophysics interpretation certifies an explicit geometric-rate ergodicity package. interpreted Pisot dimension and visible budget Lean theorem pisot_astrophysics_budget_yields_geometric_rate_certificate in PisotAstrophysicsQueueKernelBridge.lean Mechanized
THM-PISOT-ASTROPHYSICS-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: Explicit Pisot+astrophysics interpretation adapter successfully discharges continuous-ergodicity lift requirements. explicit adaptation assumptions for continuous embeddings and witnesses Lean theorem pisot_astrophysics_continuous_ergodicity_lift in PisotAstrophysicsQueueKernelBridge.lean Mechanized
THM-MEDIA-ECOSYSTEM-CRYPTO-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the media+ecosystem+cryptography witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-MEDIA-ECOSYSTEM-CRYPTO-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem MediaEcosystemCryptoQueueKernelBridge.media_ecosystem_crypto_compiled_witness_continuous_ergodicity_lift in MediaEcosystemCryptoQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-CAPITAL-MDL-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined capital timeline and MDL description budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (totalMinutes + totalCost) + 1 lockup witness CapitalLockup.LockupState with positive timeline (totalMinutes > 0); MDL witness MinimumDescriptionLength.ModelCandidate; interpretation anchor failureBudget = totalMinutes + totalCost Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_budget_yields_geometric_rate_certificate in CapitalMdlQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CAPITAL-MDL-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under combined capital+MDL interpretation, adapter budget positivity is derived from source assumptions rather than postulated as a black-box field source assumptions totalMinutes > 0 from CapitalLockup.LockupState and nonnegative MDL total cost; adapter budget anchor budgetReal = (totalMinutes + totalCost : ℝ) Lean theorems CapitalMdlQueueKernelBridge.capital_mdl_failure_budget_real_positive and CapitalMdlKernelLiftAdapter.budget_pos_from_source in CapitalMdlQueueKernelBridge.lean Mechanized
THM-CAPITAL-MDL-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: capital-lockup timeline and MDL description data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source identities and drift positivity explicit adapter bundle carrying lockup witness, MDL witness, source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem CapitalMdlKernelLiftAdapter.capital_mdl_continuous_ergodicity_lift in CapitalMdlQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-CAPITAL-MDL-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Blocker-remediation bridge (non-adapter form): an explicit capital+MDL interpretation certificate plus existing embedding/witness/kernel-match payload is sufficient to execute continuous ergodicity lift without introducing a dedicated adapter structure lockup witness CapitalLockup.LockupState; MDL witness MinimumDescriptionLength.ModelCandidate; interpretation hypothesis interpret(failureBudget) = failureBudget; explicit lift payload DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem CapitalMdlQueueKernelBridge.capital_mdl_semantic_morphism_continuous_ergodicity_lift in CapitalMdlQueueKernelBridge.lean, combining source identity rewrites with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-RETROCAUSAL-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: nonempty retrocausal trajectory budget yields an explicit geometric-rate package with contraction r = 3/4 and trajectory-indexed initial bound M = trajectory.length + 1 retrocausal witness RetrocausalBound.RetrocausalWitness; nonempty trajectory (trajectory ≠ []) Lean theorem RetrocausalCausalQueueKernelBridge.retrocausal_nonempty_yields_geometric_rate_certificate in RetrocausalCausalQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-RETROCAUSAL-CAUSAL-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under retrocausal+causal interpretation, adapter budget positivity is derived from source trajectory nonemptiness instead of postulated as a black-box field retrocausal source witness with nonempty trajectory; budget anchor budgetReal = (trajectory.length : ℝ) inside RetrocausalCausalKernelLiftAdapter Lean theorem RetrocausalCausalKernelLiftAdapter.budget_pos_from_source in RetrocausalCausalQueueKernelBridge.lean Mechanized
THM-RETROCAUSAL-CAUSAL-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: retrocausal trajectory and causal-adjustment data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving adjustment identity, anchored budget bridge, and source-derived budget positivity explicit adapter bundle carrying retrocausal witness, causal assumptions (treat + confound ≤ R), budget bridge equality, source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem RetrocausalCausalKernelLiftAdapter.retrocausal_causal_continuous_ergodicity_lift in RetrocausalCausalQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-QUORUM-HISTORY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: nonempty quorum history constructs an explicit geometric-ergodicity rate package with contraction r = 3/4 and depth-indexed initial bound `M = history + 1` nonempty completed-write history (history ≠ [])
THM-QUORUM-HISTORY-MULTILEVEL-HARRIS-WITNESS Moonshot fallback witness: nonempty quorum history builds a two-level Harris witness with strictly positive discrete and continuous drift gaps nonempty completed-write history (history ≠ []) Lean theorem QuorumHistoryQueueBridge.nonempty_history_yields_multilevel_harris_witness in QuorumHistoryQueueBridge.lean, using ContinuousHarris.MultiLevelHarrisWitness and ContinuousHarris.multi_level_positive_drift Mechanized
THM-QUORUM-HISTORY-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization primitives and nonempty history depth, compile a full GeometricErgodicWitness without postulating a prebuilt witness object nonempty completed-write history (history ≠ []); explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem QuorumHistoryQueueBridge.quorum_history_compile_witness_from_primitives in QuorumHistoryQueueBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-QUORUM-HISTORY-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the history witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-QUORUM-HISTORY-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem QuorumHistoryQueueBridge.quorum_history_compiled_witness_continuous_ergodicity_lift in QuorumHistoryQueueBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-QUORUM-ASYNC-CARDINALITY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: nonempty connected quorum cardinality yields an explicit geometric-rate package with contraction r = 3/4 and initial bound `M = connected + 1` connected quorum is nonempty (connected.Nonempty)
THM-MEDIATION-LOSS-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: mediation loss produces an explicit geometric-rate package with contraction r = 3/4 and initial bound M = mediatorLoss + 1 mediation setup with irreducible loss (mediatorLoss ≥ 1) Lean theorem MediationQueueBoundaryBridge.mediation_positive_loss_yields_geometric_rate_certificate in MediationQueueBoundaryBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CYBERNETIC-EMOTION-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined cybernetic emotion budget yields an explicit geometric-rate package. cybernetic and emotion taxonomy assumptions Lean theorem cybernetic_emotion_budget_yields_geometric_rate_certificate in CyberneticEmotionQueueKernelBridge.lean Mechanized
THM-CYBERNETIC-EMOTION-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack adapter: explicit cybernetic emotion kernel-lift adapter unblocks continuous ergodicity lift. explicit embedding, witness, and kernel-match fields Lean theorem CyberneticEmotionKernelLiftAdapter.cybernetic_emotion_continuous_ergodicity_lift in CyberneticEmotionQueueKernelBridge.lean Mechanized
THM-MEDIATION-LOSS-MULTILEVEL-HARRIS-WITNESS Moonshot fallback witness: mediation loss constructs a two-level Harris witness with strictly positive discrete and continuous drift gaps mediation setup with irreducible loss (mediatorLoss ≥ 1) Lean theorem MediationQueueBoundaryBridge.mediation_positive_loss_yields_multilevel_harris_witness in MediationQueueBoundaryBridge.lean, using ContinuousHarris.MultiLevelHarrisWitness and ContinuousHarris.multi_level_positive_drift Mechanized
THM-MEDIATION-EXPLICIT-GEOMETRIC-WITNESS-BRIDGE Moonshot blocker-attack bridge: mediation loss plus explicit certified-kernel/envelope witness objects yields a fully aligned geometric witness package with sub-unit contraction and positive initial bound mediation setup with strictly positive mediator loss; explicit CountableCertifiedKernel, CountableQuantitativeGeometricEnvelopeAtAtom, and GeometricErgodicWitness hypotheses; explicit kernel/envelope/rate consistency equalities Lean theorem MediationGeometricWitnessBridge.mediation_loss_to_explicit_geometric_witness in MediationGeometricWitnessBridge.lean, with support lemmas on rate and kernel consistency Mechanized
THM-MEDIATION-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: mediation data routed through an explicit kernel-lift adapter executes the continuous ergodicity lift while preserving drift positivity and sub-unit contraction explicit adapter bundle carrying mediation setup, positive mediation-loss anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MediationKernelLiftAdapter.mediated_continuous_ergodicity_lift in MediationKernelLiftBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-BERKSON-COLLIDER-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: collider-selected Berkson threshold arithmetic yields an explicit geometric-rate package with contraction r = 3/4 and threshold-indexed initial bound M = threshold + 1 collider setup BerksonsParadox.ColliderSetup; selected-collider hypothesis causeA + causeB ≥ collider_threshold Lean theorem BerksonQueueKernelBridge.berkson_selected_collider_yields_geometric_rate_certificate in BerksonQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-BERKSON-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: collider-selected Berkson data routed through an explicit kernel-lift adapter executes the continuous ergodicity lift with explicit embedding/witness/kernel-match assumptions explicit adapter bundle carrying collider setup, selected-collider witness, threshold-floor equality, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem BerksonKernelLiftAdapter.selected_continuous_ergodicity_lift in BerksonQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-SIMPSON-CONFOUNDER-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: Simpson confounder mass yields an explicit geometric-rate package with contraction r = 3/4 and confounder-indexed initial bound M = confounder + 1 Simpson scenario witness SimpsonsParadox.SimpsonScenario; confounder budget v1_A + v2_A Lean theorem SimpsonSurvivorshipQueueBridge.simpson_confounder_yields_geometric_rate_certificate in SimpsonSurvivorshipQueueBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SIMPSON-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Simpson scenario data routed through an explicit kernel-lift adapter executes continuous ergodicity lift with explicit interpretation/witness objects explicit adapter bundle carrying Simpson scenario, positive confounder budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem SimpsonKernelLiftAdapter.simpson_continuous_ergodicity_lift in SimpsonSurvivorshipQueueBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-CONTEXTUAL-BANDIT-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: contextual-bandit total failure mass yields an explicit geometric-rate package with contraction r = 3/4 and failure-indexed initial bound M = totalFailures + 1 contextual arm witness ContextualBandits.ContextualArm; interpretation anchor failureBudget = totalFailures Lean theorem CausalBanditQueueKernelBridge.contextual_failure_budget_yields_geometric_rate_certificate in CausalBanditQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CONTEXTUAL-BANDIT-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: contextual-bandit data routed through an explicit kernel-lift adapter executes continuous ergodicity lift while preserving drift positivity and sub-unit contraction explicit adapter bundle carrying contextual arm, positive failure-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem ContextualBanditKernelLiftAdapter.contextual_continuous_ergodicity_lift in CausalBanditQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-CERTIFIED-CONTEXTUAL-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined certified-defense and contextual-bandit failure budget yields an explicit geometric-rate package with contraction r = 3/4 and initial bound M = ((cleanReject + radius) + totalFailures) + 1 certified-defense witness CertifiedDefenses.Certification; contextual arm witness ContextualBandits.ContextualArm; interpretation anchor failureBudget = (cleanReject + radius) + totalFailures Lean theorem CertifiedContextualQueueKernelBridge.certified_contextual_budget_yields_geometric_rate_certificate in CertifiedContextualQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CERTIFIED-CONTEXTUAL-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: certified-defense and contextual-bandit data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving certified-threshold and context-adjustment identities explicit adapter bundle carrying CertifiedDefenses.Certification, ContextualBandits.ContextualArm, positive real combined budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem CertifiedContextualKernelLiftAdapter.certified_contextual_continuous_ergodicity_lift in CertifiedContextualQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ADVERSARIAL-CERTIFIED-KERNEL-LIFT-BUDGET-MASS-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: the adapter budget-mass floor for adversarial+certified interpretation is derived from source arithmetic (cleanReject + delta) rather than postulated as an opaque positivity field explicit adapter bundle AdversarialCertifiedKernelLiftAdapter; budget-mass anchor ((cleanReject + delta : ℝ) + 1) Lean theorem AdversarialCertifiedKernelLiftAdapter.budget_mass_pos_from_source in AdversarialCertifiedQueueKernelBridge.lean Mechanized
THM-BANDIT-ARM-FAILURES-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: exploration-exploitation arm failure mass yields an explicit geometric-rate package with contraction r = 3/4 and failure-indexed initial bound M = failures + 1 arm witness ExplorationExploitation.Arm; interpretation anchor failureBudget = failures Lean theorem CausalDiscoveryBanditQueueBridge.bandit_arm_failures_yield_geometric_rate_certificate in CausalDiscoveryBanditQueueBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CAUSAL-BANDIT-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: causal-discovery + exploration-exploitation data routed through an explicit adapter executes continuous ergodicity lift while keeping budget interpretation and witness objects explicit explicit adapter bundle carrying discovery assumptions (vX ≤ R, vY ≤ R, vX+vY ≤ R), bandit arm, positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem CausalBanditKernelLiftAdapter.causal_bandit_continuous_ergodicity_lift in CausalDiscoveryBanditQueueBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-CAUSAL-BANDIT-INTERPRETATION-CERTIFICATE-LIFT Blocker-remediation bridge (non-adapter form): an explicit causal/bandit interpretation certificate plus existing embedding/witness/kernel-match payload is sufficient to execute continuous ergodicity lift without introducing a dedicated adapter structure discovery assumptions vX ≤ R, vY ≤ R, vX + vY ≤ R; arm witness ExplorationExploitation.Arm; bridge hypothesis armFailureBudget = discoveryFailureBudget; explicit real-budget anchor failureBudget = (armFailureBudget : ℝ) with positivity; explicit lift payload DiscreteSubLatticeEmbedding, GeometricErgodicWitness, kernel-match equality Lean theorem CausalDiscoveryBanditQueueBridge.causal_bandit_interpretation_certificate_lift in CausalDiscoveryBanditQueueBridge.lean, combining discovery identity, greedy identity, budget interpretation rewrite, and GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-ADVERSARIAL-GAP-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: adversarial perturbation-gap arithmetic yields an explicit geometric-rate package with contraction r = 3/4 and perturbation-indexed initial bound M = delta + 1 adversarial assumptions v ≤ R, v + delta ≤ R; interpretation anchor failureBudget = delta Lean theorem GoodhartMechanismQueueKernelBridge.adversarial_gap_yields_geometric_rate_certificate in GoodhartMechanismQueueKernelBridge.lean, composing AdversarialRobustness.adversarial_gap with GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-GOODHART-MECHANISM-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Goodhart proxy-gap and mechanism externality data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving budget-bridge semantics and drift positivity explicit adapter bundle carrying Goodhart assumptions (vTrue ≤ R, vGamed ≤ R, vGamed ≤ vTrue), mechanism assumptions (vWithout ≤ R, vWith ≤ R, vWith ≥ vWithout), budget bridge equality, positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem GoodhartMechanismKernelLiftAdapter.goodhart_mechanism_continuous_ergodicity_lift in GoodhartMechanismQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ECOSYSTEM-TURBULENCE-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined ecosystem+turbulence failure budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (predatorCount + (kineticInjection - foldCapacity)) + 1 interpretation anchor failureBudget = predatorCount + (kineticInjection - foldCapacity) Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_budget_yields_geometric_rate_certificate in EcosystemTurbulenceQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-ECOSYSTEM-TURBULENCE-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: ecosystem+turbulence data routed through an explicit kernel-lift adapter executes continuous ergodicity lift while preserving domain inequalities and drift positivity explicit adapter bundle carrying ecosystem assumptions (preyCount + predatorCount = boundary, predatorCount ≥ 1), turbulence assumptions (kineticInjection > foldCapacity, eddyKnots = kineticInjection - foldCapacity), positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem EcosystemTurbulenceKernelLiftAdapter.ecosystem_turbulence_continuous_ergodicity_lift in EcosystemTurbulenceQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ECOSYSTEM-TURBULENCE-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Blocker-remediation bridge (non-adapter form): an explicit ecosystem+turbulence interpretation certificate plus embedding/witness/kernel-match payload hypotheses is sufficient to execute continuous ergodicity lift without introducing an adapter structure ecosystem assumptions preyCount + predatorCount = boundary, predatorCount ≥ 1; turbulence assumptions kineticInjection > foldCapacity, eddyKnots = kineticInjection - foldCapacity; interpretation hypothesis interpret(predatorCount + eddyKnots) = failureBudget; explicit lift payload DiscreteSubLatticeEmbedding, GeometricErgodicWitness, kernel-match equality Lean theorem EcosystemTurbulenceQueueKernelBridge.ecosystem_turbulence_semantic_morphism_continuous_ergodicity_lift in EcosystemTurbulenceQueueKernelBridge.lean, combining the semantic-morphism boundary theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-ETHNOMUSICOLOGY-NARRATIVE-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined ethnomusicology+narrative failure budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (oralFilter + narrativeCrossings) + 1 interpretation anchor failureBudget = oralFilter + narrativeCrossings Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_budget_yields_geometric_rate_certificate in EthnoNarrativeQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-ETHNOMUSICOLOGY-NARRATIVE-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: ethnomusicology+narrative data routed through an explicit kernel-lift adapter executes continuous ergodicity lift while preserving domain inequalities and drift positivity explicit adapter bundle carrying ethnomusicology assumptions (oralFilter ≥ 1, overtoneLift = fundamentalPitch + oralFilter), narrative assumption (narrativeCrossings ≥ 1), positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem EthnoNarrativeKernelLiftAdapter.ethnomusicology_narrative_continuous_ergodicity_lift in EthnoNarrativeQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ETHNOMUSICOLOGY-NARRATIVE-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Blocker-remediation bridge (non-adapter form): an explicit ethnomusicology+narrative interpretation certificate plus embedding/witness/kernel-match payload hypotheses is sufficient to execute continuous ergodicity lift without introducing an adapter structure ethnomusicology assumptions oralFilter ≥ 1, overtoneLift = fundamentalPitch + oralFilter; narrative assumption narrativeCrossings ≥ 1; interpretation hypothesis interpret(failureBudget) = failureBudget; explicit lift payload DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem EthnoNarrativeQueueKernelBridge.ethnomusicology_narrative_semantic_morphism_continuous_ergodicity_lift in EthnoNarrativeQueueKernelBridge.lean, combining the semantic-morphism boundary theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-BILL-OF-RIGHTS-STRUCTURAL-HOLE-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined rights-floor and structural-hole interpolation budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = ((w(R,v)-1) + (interpolationWeight-1)) + 1 rights-floor witness BillOfRights.right_to_exist; structural-hole witness hole_has_positive_weight; interpretation anchor failureBudget = (w(R,v)-1) + (interpolationWeight-1) Lean theorem BillRightsStructuralHoleQueueKernelBridge.rights_structural_hole_budget_yields_geometric_rate_certificate in BillRightsStructuralHoleQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-BILL-OF-RIGHTS-STRUCTURAL-HOLE-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: rights-floor and structural-hole data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving domain identities and drift positivity explicit adapter bundle carrying (R,v), structural-hole witness, positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem RightsStructuralHoleKernelLiftAdapter.rights_structural_hole_continuous_ergodicity_lift in BillRightsStructuralHoleQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-SPIDERWEB-REYNOLDS-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined spiderweb routing-path and Reynolds diversity budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (meshRoutingPaths + (pathCount - 1)) + 1 spiderweb nontriviality assumptions 0 < peers, 0 < hops; Reynolds diversity witness pathCount ≥ 2; interpretation anchor failureBudget = meshRoutingPaths + (pathCount - 1) Lean theorem SpiderwebReynoldsQueueKernelBridge.spiderweb_reynolds_budget_yields_geometric_rate_certificate in SpiderwebReynoldsQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SPIDERWEB-REYNOLDS-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: spiderweb routing-path and Reynolds diversity data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving domain identities and drift positivity explicit adapter bundle carrying a nontrivial spiderweb mesh (0 < peers, 0 < hops), Reynolds diversity witness (pathCount ≥ 2), positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem SpiderwebReynoldsKernelLiftAdapter.spiderweb_reynolds_continuous_ergodicity_lift in SpiderwebReynoldsQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-SPIDERWEB-REYNOLDS-CRYPTO-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain spiderweb+Reynolds+crypto budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (meshRoutingPaths + (pathCount - 1) + perEvalFloor) + 1 spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; Reynolds diversity witness pathCount ≥ 2; cryptographic side-channel witness SideChannelShadow (0 < perEvalFloor); interpretation anchor failureBudget = meshRoutingPaths mesh + (pathCount - 1) + perEvalFloor Lean theorem SpiderwebReynoldsCryptoQueueKernelBridge.spiderweb_reynolds_crypto_budget_yields_geometric_rate_certificate in SpiderwebReynoldsCryptoQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SPIDERWEB-REYNOLDS-CRYPTO-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Moonshot blocker-attack theorem: spiderweb+Reynolds+crypto source arithmetic plus an explicit semantic morphism executes continuous ergodicity lift once embedding/witness payload objects are supplied as hypotheses spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; Reynolds diversity witness pathCount ≥ 2; cryptographic side-channel witness SideChannelShadow (0 < perEvalFloor); explicit morphism interpret(failureBudget) = failureBudget; explicit lift payloads include DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem SpiderwebReynoldsCryptoQueueKernelBridge.spiderweb_reynolds_crypto_semantic_morphism_continuous_ergodicity_lift in SpiderwebReynoldsCryptoQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-SPIDERWEB-GNOSTIC-LADDER-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: spiderweb routing-path mass plus gnostic Sophia ladder mass yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (meshRoutingPaths + sophia) + 1 spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; gnostic ladder alignment gnosticBeta1.sophia = sophia = 9; interpretation anchor failureBudget = meshRoutingPaths mesh + sophia Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_yields_geometric_rate_certificate in SpiderwebGnosticLadderQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SPIDERWEB-GNOSTIC-LADDER-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Moonshot blocker-attack theorem: spiderweb+gnostic source arithmetic plus an explicit semantic morphism executes continuous ergodicity lift once embedding/witness payload objects are supplied as hypotheses spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; explicit morphism interpret (meshRoutingPaths mesh + sophia) = failureBudget; explicit lift payloads include DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_semantic_morphism_continuous_ergodicity_lift in SpiderwebGnosticLadderQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-SPIDERWEB-GNOSTIC-LADDER-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under the spiderweb+gnostic-ladder interpretation, real budget positivity is derived from source assumptions rather than carried as an opaque adapter field spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; interpretation anchor budgetReal = (meshRoutingPaths mesh + sophia : ℝ) Lean theorems SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_real_positive and SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_budget_mass_pos_from_source in SpiderwebGnosticLadderQueueKernelBridge.lean Mechanized
THM-SPIDERWEB-GNOSTIC-LADDER-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and source-derived spiderweb+gnostic budget positivity, compile a full GeometricErgodicWitness without postulating a prebuilt witness object spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_compile_witness_from_primitives in SpiderwebGnosticLadderQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SPIDERWEB-GNOSTIC-LADDER-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the spiderweb+gnostic witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-SPIDERWEB-GNOSTIC-LADDER-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem SpiderwebGnosticLadderQueueKernelBridge.spiderweb_gnostic_ladder_compiled_witness_continuous_ergodicity_lift in SpiderwebGnosticLadderQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-SPIDERWEB-MUSIC-NARRATIVE-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain spiderweb+music+narrative budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (meshRoutingPaths + swingPerturbation + narrativeCrossings) + 1 spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; music assumptions swingPerturbation ≥ 1, totalSpace = periodicLoad + swingPerturbation; narrative assumption narrativeCrossings ≥ 1; interpretation anchor failureBudget = meshRoutingPaths mesh + swingPerturbation + narrativeCrossings Lean theorem SpiderwebMusicNarrativeQueueKernelBridge.spiderweb_music_narrative_budget_yields_geometric_rate_certificate in SpiderwebMusicNarrativeQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SPIDERWEB-MUSIC-NARRATIVE-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under the spiderweb+music+narrative interpretation, adapter budget positivity is derived from source assumptions instead of postulated as a black-box field source assumptions 0 < mesh.peers, 0 < mesh.hops, swingPerturbation ≥ 1, and narrativeCrossings ≥ 1; interpretation anchor budgetNat = meshRoutingPaths mesh + swingPerturbation + narrativeCrossings, budgetReal = (budgetNat : ℝ) Lean theorems SpiderwebMusicNarrativeQueueKernelBridge.spiderweb_music_narrative_budget_real_positive and SpiderwebMusicNarrativeKernelLiftAdapter.budget_pos_from_source in SpiderwebMusicNarrativeQueueKernelBridge.lean Mechanized
THM-SPIDERWEB-MUSIC-NARRATIVE-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: tri-domain spiderweb+music+narrative data routed through an explicit interpretation certificate and kernel-lift adapter executes continuous ergodicity lift while preserving source constraints and drift positivity explicit adapter bundle carrying spiderweb/music/narrative source assumptions, queue-layer interpretation certificate (budgetNat, anchored arrival/service witness with β₁ = 0, capacity = 1), positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem SpiderwebMusicNarrativeKernelLiftAdapter.spiderweb_music_narrative_continuous_ergodicity_lift in SpiderwebMusicNarrativeQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-KRAFT-SOLOMONOFF-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Kraft wasted-capacity and Solomonoff description budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (wastedCapacity + v) + 1 prefix-free code witness KraftInequality.PrefixFreeCode; Solomonoff assumption v ≤ R; interpretation anchor failureBudget = wastedCapacity + v Lean theorem KraftSolomonoffQueueKernelBridge.kraft_solomonoff_budget_yields_geometric_rate_certificate in KraftSolomonoffQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-KRAFT-SOLOMONOFF-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Kraft and Solomonoff data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving both source identities and drift positivity explicit adapter bundle carrying prefix-free code witness, Solomonoff bound v ≤ R, positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem KraftSolomonoffKernelLiftAdapter.kraft_solomonoff_continuous_ergodicity_lift in KraftSolomonoffQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-CONTAGION-TECHNIQUE-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined contagion spillover and fighting-trauma budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (phantomLoad + altitude(w2)) + 1 contagion assumptions source.internalHeat > source.containmentThreshold and neighbor.phantomLoad ≥ source.internalHeat - source.containmentThreshold; fighting witness TechniqueAsAntidote.IsFighting w1 w2 move; interpretation anchor failureBudget = neighbor.phantomLoad + altitude(w2) Lean theorem TopologicalContagionTechniqueQueueKernelBridge.contagion_technique_budget_yields_geometric_rate_certificate in TopologicalContagionTechniqueQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CONTAGION-TECHNIQUE-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: contagion spillover and fighting-trauma data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving domain inequalities and drift positivity explicit adapter bundle carrying contagion assumptions (internalHeat > containmentThreshold, phantom-load coupling), fighting witness TechniqueAsAntidote.IsFighting, positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem ContagionTechniqueKernelLiftAdapter.contagion_technique_continuous_ergodicity_lift in TopologicalContagionTechniqueQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-BARYOGENESIS-BUREAUCRACY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Baryogenesis erasure and Bureaucracy stabilization budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound BaryonViolationWitness; BureaucraticFilter; interpretation anchor failureBudget = (pathsBefore - pathsAfter) + 1 Lean theorem BaryogenesisBureaucracyQueueKernelBridge.baryogenesis_bureaucracy_budget_yields_geometric_rate_certificate in BaryogenesisBureaucracyQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-BARYOGENESIS-BUREAUCRACY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Baryogenesis and Bureaucracy data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving both source identities and drift positivity explicit adapter bundle carrying BaryonViolationWitness, BureaucraticFilter, positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem BaryogenesisBureaucracyKernelLiftAdapter.baryogenesis_bureaucracy_continuous_ergodicity_lift in BaryogenesisBureaucracyQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-STRESS-AESTHETICS-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined stress-energy and UI-friction budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (stressEnergy + (chaoticFriction - orderedFriction)) + 1 stress assumptions from mechanized_stress_energy_tensor; UI assumptions orderedFriction + precomputationCost < chaoticFriction; interpretation anchor failureBudget = stressEnergy + (chaoticFriction - orderedFriction) Lean theorem StressAestheticsQueueKernelBridge.stress_aesthetics_budget_yields_geometric_rate_certificate in StressAestheticsQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-STRESS-AESTHETICS-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: stress-energy and UI-friction data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving domain inequalities and drift positivity explicit adapter bundle carrying stress assumptions (ct.defenseWeight = defenseWeight R v, R = 54, irrational resonance witness), UI-friction assumptions, positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem StressAestheticsKernelLiftAdapter.stress_aesthetics_continuous_ergodicity_lift in StressAestheticsQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-DECEPTION-AUTOIMMUNITY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined deception+autoimmunity budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (injected + parserExhaust) + 1 deception witness injected ≥ 1; autoimmunity witness faultyHash = friendlyInvariant, parserExhaust ≥ 1; interpretation anchor failureBudget = injected + parserExhaust Lean theorem DeceptionAutoimmunityQueueKernelBridge.deception_autoimmunity_budget_yields_geometric_rate_certificate in DeceptionAutoimmunityQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-DECEPTION-AUTOIMMUNITY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: deception phantom-injection and autoimmunity hash-collision data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source witnesses and drift positivity explicit adapter bundle carrying deception assumptions (injected ≥ 1), autoimmunity assumptions (faultyHash = friendlyInvariant, parserExhaust ≥ 1), positive real combined-budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem DeceptionAutoimmunityKernelLiftAdapter.deception_autoimmunity_continuous_ergodicity_lift in DeceptionAutoimmunityQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-DECEPTION-AUTOIMMUNITY-NEGOTIATION-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain deception+autoimmunity+negotiation budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (injected + parserExhaust + externalCapacity) + 1 deception witness injected ≥ 1; autoimmunity witness faultyHash = friendlyInvariant, parserExhaust ≥ 1; mediation assumptions searchCapacity < 10 and searchCapacity + externalCapacity ≥ 10; interpretation anchor failureBudget = injected + parserExhaust + externalCapacity Lean theorem DeceptionAutoimmunityNegotiationQueueKernelBridge.deception_autoimmunity_negotiation_budget_yields_geometric_rate_certificate in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-DECEPTION-AUTOIMMUNITY-NEGOTIATION-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under tri-domain deception+autoimmunity+negotiation interpretation, adapter budget positivity is derived from source assumptions instead of introduced as a black-box field source assumptions injected ≥ 1, faultyHash = friendlyInvariant, parserExhaust ≥ 1, searchCapacity < 10, and searchCapacity + externalCapacity ≥ 10; adapter budget anchor budgetReal = (injected + parserExhaust + externalCapacity : ℝ) Lean theorems DeceptionAutoimmunityNegotiationQueueKernelBridge.deception_autoimmunity_negotiation_budget_real_positive and DeceptionAutoimmunityNegotiationKernelLiftAdapter.budget_pos_from_source in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean Mechanized
THM-DECEPTION-AUTOIMMUNITY-NEGOTIATION-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: deception phantom-injection, autoimmunity hash-collision, and mediation wattage routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source witnesses and drift positivity explicit adapter bundle carrying deception assumptions (injected ≥ 1), autoimmunity assumptions (faultyHash = friendlyInvariant, parserExhaust ≥ 1), mediation assumptions (searchCapacity < 10, searchCapacity + externalCapacity ≥ 10), source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem DeceptionAutoimmunityNegotiationKernelLiftAdapter.deception_autoimmunity_negotiation_continuous_ergodicity_lift in DeceptionAutoimmunityNegotiationQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-VOID-MERKLE-ESC-WARMUP-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain void+ESC+warmup budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (root + traceFold([cold]) + totalDeficit) + 1 same source assumptions as THM-QUEUE-VOID-MERKLE-ESC-WARMUP-BUDGET-UNIT-BOUNDARY; interpretation anchor failureBudget = root + traceFold([cold]) + totalDeficit under over Lean theorem VoidMerkleEscWarmupQueueKernelBridge.void_merkle_esc_warmup_budget_yields_geometric_rate_certificate in VoidMerkleEscWarmupQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-VOID-MERKLE-ESC-WARMUP-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under the void+ESC+warmup interpretation, adapter budget positivity is derived directly from source assumptions rather than introduced as a black-box field source assumption underDeficit > 0 together with fixed ESC cold-path fold witness implies positive interpreted budget; adapter budget anchor budgetReal = (root + traceFold([cold]) + totalDeficit under over : ℝ) Lean theorems VoidMerkleEscWarmupQueueKernelBridge.void_merkle_esc_warmup_budget_real_positive and VoidMerkleEscWarmupKernelLiftAdapter.budget_pos_from_source in VoidMerkleEscWarmupQueueKernelBridge.lean Mechanized
THM-VOID-MERKLE-ESC-WARMUP-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: void-Merkle irreversibility witness, ESC cold-path trace witness, and warmup-controller expand witness routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source-domain constraints and drift positivity explicit adapter bundle carrying warmup source assumptions (underDeficit > 0, overDeficit = 0, deficitWeight > 0, below-redline witness), source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem VoidMerkleEscWarmupKernelLiftAdapter.void_merkle_esc_warmup_continuous_ergodicity_lift in VoidMerkleEscWarmupQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-KITCHEN-BERKSON-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined kitchen+Berkson budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (totalDeficit + colliderThreshold) + 1 kitchen assumptions from THM-QUEUE-KITCHEN-SAFETY-GAP-UNIT-BOUNDARY; selected Berkson collider assumption causeA + causeB ≥ collider_threshold; interpretation anchor failureBudget = totalDeficit frame + collider_threshold Lean theorem KitchenBerksonQueueKernelBridge.kitchen_berkson_budget_yields_geometric_rate_certificate in KitchenBerksonQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-KITCHEN-BERKSON-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under kitchen+Berkson interpretation, adapter budget positivity is derived from source assumptions instead of introduced as an independent black-box field source assumptions: kitchen physical-safety-critical safety gap (physicalSafetyCritical frame.domain = true, safetySignals < safetyHazards) and collider threshold positivity from BerksonsParadox.ColliderSetup; adapter budget anchor budgetReal = (totalDeficit frame + collider_threshold : ℝ) Lean theorems KitchenBerksonQueueKernelBridge.kitchen_berkson_budget_real_positive and KitchenBerksonKernelLiftAdapter.budget_pos_from_source in KitchenBerksonQueueKernelBridge.lean Mechanized
THM-KITCHEN-BERKSON-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: kitchen safety-gap and selected Berkson collider data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source floors and drift positivity explicit adapter bundle carrying kitchen assumptions, selected-collider witness, source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem KitchenBerksonKernelLiftAdapter.kitchen_berkson_continuous_ergodicity_lift in KitchenBerksonQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-KITCHEN-BERKSON-GOODHART-WITNESS-COMPILER-FROM-PRIMITIVES Moonshot blocker-attack theorem: tri-domain kitchen+Berkson+Goodhart interpretation plus explicit certified-kernel primitive obligations compiles a full GeometricErgodicWitness with budget-indexed initial bound and explicit contraction formula kitchen assumptions spatialAnnouncements < traversals; selected-collider assumption causeA + causeB ≥ collider_threshold; Goodhart assumptions vTrue ≤ R, vGamed ≤ R, vGamed ≤ vTrue; primitive witness obligations kernel, atom ∈ kernel.smallSet, 0 < ε₁, 0 < ε₂, ε₁ ≤ 1, ε₂ ≤ 1, ε₁*ε₂ < 1 Lean theorem KitchenBerksonGoodhartQueueKernelBridge.kitchen_berkson_goodhart_compile_witness_from_primitives in KitchenBerksonGoodhartQueueKernelBridge.lean, building the envelope and witness with GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-KITCHEN-BERKSON-GOODHART-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Moonshot blocker-attack continuation: once the tri-domain witness is compiled from explicit primitive obligations and aligned with the embedding kernel, continuous ergodicity lift follows while preserving source-domain identities and budget positivity same source assumptions as THM-KITCHEN-BERKSON-GOODHART-WITNESS-COMPILER-FROM-PRIMITIVES; explicit lift payloads DiscreteSubLatticeEmbedding, kernel-alignment equality, and primitive epsilon/atom obligations Lean theorem KitchenBerksonGoodhartQueueKernelBridge.kitchen_berkson_goodhart_compiled_witness_continuous_ergodicity_lift in KitchenBerksonGoodhartQueueKernelBridge.lean, composing the witness-compiler theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-QUORUM-LINEARIZED-READ-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: append-then-read linearized quorum write-count budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = writeCount + 1 finite committed-write history; append one completed write; canonical linearized read with writeCount = history.length + 1; interpretation anchor failureBudget = writeCount Lean theorem QuorumLinearizabilityQueueKernelBridge.appended_linearized_read_yields_geometric_rate_certificate in QuorumLinearizabilityQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-QUORUM-LINEARIZABILITY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: append-then-read quorum linearizability data routed through an explicit kernel-lift adapter executes continuous ergodicity lift while preserving refinement and drift positivity explicit adapter bundle carrying committed-write history, appended write, positive real write-count budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem LinearizabilityKernelLiftAdapter.linearized_read_continuous_ergodicity_lift in QuorumLinearizabilityQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-TAPHONOMY-TRIBOLOGY-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under the taphonomy+tribology interpretation, adapter budget positivity is derivable from source-domain assumptions rather than treated as an independent black-box field source assumptions ventedOrganics ≥ 1 and lubricatedFriction < rawFriction; adapter budget anchor budgetReal = (ventedOrganics + (rawFriction - lubricatedFriction) : ℝ) Lean theorems TaphonomyTribologyQueueKernelBridge.taphonomy_tribology_budget_real_positive and TaphonomyTribologyKernelLiftAdapter.budget_pos_from_source in TaphonomyTribologyQueueKernelBridge.lean, deriving real positivity from domain arithmetic and lifting it to the adapter budget Mechanized
THM-SPIDERWEB-APERIODIC-NARRATIVE-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined spiderweb+aperiodic+narrative budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = ((meshRoutingPaths + narrativeCrossings) + (resonanceCollisions + 1)) + 1 spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; aperiodic assumptions weyl.isIrrational = true, schedule.isPeriodic = !weyl.isIrrational, schedule.hasResonance = schedule.isPeriodic, and low-discrepancy witness schedule.isPeriodic = false → schedule.resonanceCollisions = 0; narrative assumption narrativeCrossings ≥ 1 Lean theorem SpiderwebAperiodicNarrativeQueueKernelBridge.spiderweb_aperiodic_narrative_budget_yields_geometric_rate_certificate in SpiderwebAperiodicNarrativeQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-SPIDERWEB-APERIODIC-NARRATIVE-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under the spiderweb+aperiodic+narrative interpretation, adapter budget positivity is derived from source assumptions rather than introduced as an independent black-box field spiderweb nontriviality assumptions 0 < mesh.peers, 0 < mesh.hops; narrative assumption narrativeCrossings ≥ 1; adapter budget anchor budgetReal = (spiderwebAperiodicNarrativeFailureBudget : ℝ) Lean theorems SpiderwebAperiodicNarrativeQueueKernelBridge.spiderweb_aperiodic_narrative_budget_real_positive and SpiderwebAperiodicNarrativeKernelLiftAdapter.budget_pos_from_source in SpiderwebAperiodicNarrativeQueueKernelBridge.lean Mechanized
THM-SPIDERWEB-APERIODIC-NARRATIVE-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: spiderweb routing data, irrational-schedule aperiodicity, and narrative crossings routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source witnesses and drift positivity explicit adapter bundle carrying spiderweb nontriviality witnesses, aperiodic witnesses (isIrrational, periodic-map, resonance-map, low-discrepancy collision witness), narrative crossing floor, source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem SpiderwebAperiodicNarrativeKernelLiftAdapter.spiderweb_aperiodic_narrative_continuous_ergodicity_lift in SpiderwebAperiodicNarrativeQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ADVERSARIAL-CERTIFIED-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: adversarial perturbation gap plus certified-radius accounting yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = ((cleanReject + radius) + delta) + 1 adversarial assumptions v ≤ R, v + delta ≤ R; certified witness CertifiedDefenses.Certification; interpretation anchor failureBudget = (cleanReject + radius) + delta Lean theorem AdversarialCertifiedQueueKernelBridge.adversarial_certified_budget_yields_geometric_rate_certificate in AdversarialCertifiedQueueKernelBridge.lean, composing source identities with GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-ADVERSARIAL-CERTIFIED-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under adversarial+certified interpretation, adapter budget positivity is derived from source perturbation assumptions instead of introduced as a black-box field source assumptions v ≤ R, v + delta ≤ R, and strictly positive perturbation 0 < delta; adapter budget anchor budgetReal = (((cleanReject + radius) + delta) : ℝ) Lean theorems AdversarialCertifiedQueueKernelBridge.adversarial_certified_budget_real_positive and AdversarialCertifiedKernelLiftAdapter.budget_pos_from_source in AdversarialCertifiedQueueKernelBridge.lean Mechanized
THM-ADVERSARIAL-CERTIFIED-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: adversarial perturbation data and certified-radius data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source identities and drift positivity explicit adapter bundle carrying adversarial assumptions (v ≤ R, v + delta ≤ R, 0 < delta), certified witness CertifiedDefenses.Certification, source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem AdversarialCertifiedKernelLiftAdapter.adversarial_certified_continuous_ergodicity_lift in AdversarialCertifiedQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ADVERSARIAL-CERTIFIED-BERKSON-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: adversarial perturbation-gap arithmetic, certified-radius accounting, and selected Berkson collider threshold yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (delta + (cleanReject + radius) + collider_threshold) + 1 adversarial assumptions v ≤ R, v + delta ≤ R; certified witness CertifiedDefenses.Certification; selected-collider witness cs.selected; interpretation anchor failureBudget = delta + (cleanReject + radius) + collider_threshold Lean theorem AdversarialCertifiedBerksonQueueKernelBridge.adversarial_certified_berkson_budget_yields_geometric_rate_certificate in AdversarialCertifiedBerksonQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-ADVERSARIAL-CERTIFIED-BERKSON-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under adversarial+certified+Berkson interpretation, adapter budget positivity is derived from source-domain assumptions instead of introduced as an opaque field source assumptions include selected Berkson collider witness cs.selected plus collider-threshold positivity (collider_threshold ≥ 1); adapter budget anchor budget = (delta + (cleanReject + radius) + collider_threshold : ℝ) Lean theorem AdversarialCertifiedBerksonKernelLiftAdapter.budget_pos_from_source in AdversarialCertifiedBerksonQueueKernelBridge.lean Mechanized
THM-ADVERSARIAL-CERTIFIED-BERKSON-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: adversarial perturbation, certified-radius data, and selected Berkson collider data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source identities and drift positivity explicit adapter bundle carrying adversarial assumptions (v ≤ R, v + delta ≤ R), certified witness CertifiedDefenses.Certification, selected-collider witness, source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem AdversarialCertifiedBerksonKernelLiftAdapter.adversarial_certified_berkson_continuous_ergodicity_lift in AdversarialCertifiedBerksonQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-MEDIATION-MECHANISM-CONVERSION-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: mediation-loss floor, mechanism externality identity, and conversion vent pulse yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (mediatorLoss + ventSlam) + 1 mediation witness CausalMediation.MediationSetup; conversion assumptions uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment; mechanism identity recovered in-theorem from direct vs total rejection accounting Lean theorem MediationMechanismConversionQueueKernelBridge.mediation_mechanism_conversion_budget_yields_geometric_rate_certificate in MediationMechanismConversionQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIATION-MECHANISM-CONVERSION-KERNEL-LIFT-BUDGET-POSITIVE-FROM-SOURCE Moonshot blocker-remediation lemma: under mediation+mechanism+conversion interpretation, adapter budget positivity is derived from source assumptions instead of introduced as an independent black-box field source assumptions: mediation irreducible loss (mediatorLoss ≥ 1 from MediationSetup) and conversion vent floor (uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment); adapter budget anchor budget = (mediatorLoss + ventSlam : ℝ) Lean theorems MediationMechanismConversionQueueKernelBridge.mediation_mechanism_conversion_budget_real_positive and MediationMechanismConversionKernelLiftAdapter.budget_pos_from_source in MediationMechanismConversionQueueKernelBridge.lean Mechanized
THM-MEDIATION-MECHANISM-CONVERSION-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: mediation, mechanism, and conversion data routed through an explicit kernel-lift adapter execute continuous ergodicity lift while preserving source identities and source-derived budget positivity explicit adapter bundle carrying mediation witness, conversion assumptions (uiFriction > buleInvestment, ventSlam = uiFriction - buleInvestment), source-derived positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MediationMechanismConversionKernelLiftAdapter.mediation_mechanism_conversion_continuous_ergodicity_lift in MediationMechanismConversionQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-MEDIA-SCROLL-TYPOGRAPHY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: media+scroll+typography interpreted budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (clickstr + raceLoad + frictionSave) + 1 same source assumptions as THM-QUEUE-MEDIA-SCROLL-TYPOGRAPHY-BUDGET-UNIT-BOUNDARY; interpretation anchor failureBudget = clickstr + raceLoad + frictionSave Lean theorem MediaScrollTypographyQueueKernelBridge.media_scroll_typography_budget_yields_geometric_rate_certificate in MediaScrollTypographyQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MEDIA-SCROLL-TYPOGRAPHY-INTERPRETATION-CERTIFICATE-LIFT Moonshot blocker-attack theorem: media+scroll+typography arithmetic routed through an explicit theorem-level interpretation certificate (no dedicated adapter structure) executes continuous ergodicity lift once embedding/witness payload objects are provided as hypotheses clickbait assumptions clickstr ≥ 1, cognitiveStrand = baseline + clickstr; infinite-scroll assumptions foldResolution = 0, raceLoad > ventThreshold; typography assumptions characterOne + characterTwo = ligatureUnknot + frictionSave, frictionSave ≥ 1; explicit theorem arguments include positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MediaScrollTypographyQueueKernelBridge.media_scroll_typography_interpretation_certificate_lift in MediaScrollTypographyQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-MACRO-HERMETIC-MYCOLOGY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: macro phantom crossings, hermetic sliver projection mass, and mycology thermal-vent exhaust mass yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (fiatCrossings + sliver + sporeExhaust) + 1 macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings ≥ 1; hermetic assumptions macroManifold = fractalNode + sliver, sliver ≥ 0; mycology assumptions undergroundHeat > ventThreshold, sporeExhaust ≥ 1; interpretation anchor failureBudget = fiatCrossings + sliver + sporeExhaust Lean theorem MacroHermeticMycologyQueueKernelBridge.macro_hermetic_mycology_budget_yields_geometric_rate_certificate in MacroHermeticMycologyQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MACRO-HERMETIC-MYCOLOGY-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Moonshot blocker-attack theorem: macro+hermetic+mycology source arithmetic plus an explicit semantic morphism executes continuous ergodicity lift once embedding/witness payload objects are supplied as hypotheses macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings ≥ 1; hermetic assumptions macroManifold = fractalNode + sliver, sliver ≥ 0; mycology assumptions undergroundHeat > ventThreshold, sporeExhaust ≥ 1; explicit morphism interpret (fiatCrossings + sliver + sporeExhaust) = failureBudget; explicit lift payloads include DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MacroHermeticMycologyQueueKernelBridge.macro_hermetic_mycology_semantic_morphism_continuous_ergodicity_lift in MacroHermeticMycologyQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-MACRO-LINGUISTIC-KITCHEN-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: macro phantom crossings, linguistic secondary-meaning mass, and kitchen spatial-safety gain yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (fiatCrossings + secondaryMeaning + spatialSafetyGain(call)) + 1 macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings ≥ 1; linguistic assumptions totalLoad = baseMeaning + secondaryMeaning, secondaryMeaning ≥ 1; kitchen witness call : SpatialCall; interpretation anchor failureBudget = fiatCrossings + secondaryMeaning + spatialSafetyGain call Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_budget_yields_geometric_rate_certificate in MacroLinguisticKitchenQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-MACRO-LINGUISTIC-KITCHEN-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Moonshot blocker-attack theorem: macro+linguistic+kitchen source arithmetic plus an explicit semantic morphism executes continuous ergodicity lift once embedding/witness payload objects are supplied as hypotheses macro assumptions totalMarket = baseAssets + fiatCrossings, fiatCrossings ≥ 1; linguistic assumptions totalLoad = baseMeaning + secondaryMeaning, secondaryMeaning ≥ 1; kitchen witness call : SpatialCall; explicit morphism interpret failureBudget = failureBudget; explicit lift payloads include DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem MacroLinguisticKitchenQueueKernelBridge.macro_linguistic_kitchen_semantic_morphism_continuous_ergodicity_lift in MacroLinguisticKitchenQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-HUMOR-TENSEGRITY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: humor setup complexity and tensegrity scaffold surplus yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (complexity + (invisibleTension - visibleNodes)) + 1 humor assumptions complexity ≥ 1; tensegrity assumptions invisibleTension > visibleNodes, integrity = visibleNodes + invisibleTension; interpretation anchor failureBudget = complexity + (invisibleTension - visibleNodes) Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_budget_yields_geometric_rate_certificate in HumorTensegrityQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-HUMOR-TENSEGRITY-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Moonshot blocker-attack theorem: humor+tensegrity source arithmetic plus an explicit semantic morphism executes continuous ergodicity lift once embedding/witness payload objects are supplied as hypotheses humor assumptions complexity ≥ 1; tensegrity assumptions invisibleTension > visibleNodes, integrity = visibleNodes + invisibleTension; explicit morphism interpret failureBudget = failureBudget; explicit lift payloads include DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_semantic_morphism_continuous_ergodicity_lift in HumorTensegrityQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-HUMOR-TENSEGRITY-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and source-derived humor+tensegrity interpreted budget positivity, compile a full GeometricErgodicWitness without postulating a prebuilt witness object humor assumptions complexity ≥ 1; tensegrity assumptions invisibleTension > visibleNodes, integrity = visibleNodes + invisibleTension; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_compile_witness_from_primitives in HumorTensegrityQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-HUMOR-TENSEGRITY-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the humor+tensegrity witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-HUMOR-TENSEGRITY-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem HumorTensegrityQueueKernelBridge.humor_tensegrity_compiled_witness_continuous_ergodicity_lift in HumorTensegrityQueueKernelBridge.lean, composing the witness-compiler theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-KI-COMBAT-KNAPSACK-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Ki+combat+knapsack interpreted budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (totalLeak + entanglement + pleromicData) + 1 Ki assumptions 0 < glanceLeak ∨ 0 < muscleLeak ∨ 0 < scentLeak ∨ 0 < energyLeak; combat assumption entanglement > 0; knapsack assumptions pleromicData = screenCapacity + visualOverlap, visualOverlap ≥ 1; interpretation anchor failureBudget = totalLeak + entanglement + pleromicData Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_budget_yields_geometric_rate_certificate in KiCombatKnapsackQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-KI-COMBAT-KNAPSACK-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and source-derived Ki+combat+knapsack interpreted budget positivity, compile a full GeometricErgodicWitness without postulating a prebuilt witness object Ki assumptions 0 < glanceLeak ∨ 0 < muscleLeak ∨ 0 < scentLeak ∨ 0 < energyLeak; combat assumption entanglement > 0; knapsack assumptions pleromicData = screenCapacity + visualOverlap, visualOverlap ≥ 1; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_compile_witness_from_primitives in KiCombatKnapsackQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-KI-COMBAT-KNAPSACK-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the Ki+combat+knapsack witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-KI-COMBAT-KNAPSACK-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem KiCombatKnapsackQueueKernelBridge.ki_combat_knapsack_compiled_witness_continuous_ergodicity_lift in KiCombatKnapsackQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-CACHE-ASYNC-FRF-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: cache+async+FRF interpreted budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = (traceFold[cold] + totalVent + frfRaceWitness) + 1 async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; source witnesses traceFold [cold] = escCanonMissW.val, frfRace frfWitness = 3; interpretation anchor failureBudget = traceFold [cold] + q.totalVent + frfRace frfWitness Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_frf_budget_yields_geometric_rate_certificate in CacheAsyncFrfQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CACHE-ASYNC-FRF-SEMANTIC-MORPHISM-CONTINUOUS-ERGODICITY Moonshot blocker-attack theorem: cache+async+FRF source arithmetic plus an explicit semantic morphism executes continuous ergodicity lift once embedding/witness payload objects are supplied as hypotheses async assumptions p.userFork = q.userFork, p.userVent = q.userVent, q.bgVent = p.bgVent + k; source witnesses traceFold [cold] = escCanonMissW.val, frfRace frfWitness = 3; explicit morphism interpret failureBudget = failureBudget; explicit lift payloads include DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem CacheAsyncFrfQueueKernelBridge.cache_async_frf_semantic_morphism_continuous_ergodicity_lift in CacheAsyncFrfQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift with payload obligations exposed as hypotheses Mechanized
THM-CACHE-ASYNC-SLEEP-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and interpreted cache+async+weighted-sleep budget positivity, compile a full GeometricErgodicWitness without postulating a prebuilt witness object interpreted budget anchor failureBudget = traceFold [cold] + q.totalVent + iteratedDebt; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_compile_witness_from_primitives in CacheAsyncSleepQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-CACHE-ASYNC-SLEEP-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the cache+async+weighted-sleep witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-CACHE-ASYNC-SLEEP-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem CacheAsyncSleepQueueKernelBridge.cache_async_sleep_compiled_witness_continuous_ergodicity_lift in CacheAsyncSleepQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-QUORUM-SLEEP-CRYPTO-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: tri-domain quorum-history depth, weighted sleep debt, and cryptographic side-channel floor yield an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = failureBudget + 1 quorum history assumption history ≠ []; weighted sleep assumptions thresholdRhs < thresholdLhs and 0 < n; cryptographic witness SideChannelShadow (0 < perEvalFloor); interpretation anchor `failureBudget = history + iteratedDebt + perEvalFloor`
THM-QUORUM-SLEEP-CRYPTO-WITNESS-COMPILER-FROM-PRIMITIVES Blocker-remediation theorem (witness-compiler strategy): from explicit kernel atom/minorization/drift primitives and source-derived quorum+sleep+crypto interpreted budget positivity, compile a full GeometricErgodicWitness without postulating a prebuilt witness object tri-domain source assumptions as in THM-QUORUM-SLEEP-CRYPTO-GEOMETRIC-RATE-CERTIFICATE; explicit primitive payload: CountableCertifiedKernel, atom-in-small-set witness, ε₁ > 0, ε₂ > 0, bounds ε₁ ≤ 1, ε₂ ≤ 1, and ε₁*ε₂ < 1 Lean theorem QuorumSleepCryptoQueueKernelBridge.quorum_sleep_crypto_compile_witness_from_primitives in QuorumSleepCryptoQueueKernelBridge.lean, constructing envelope/rate/witness directly via GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-QUORUM-SLEEP-CRYPTO-COMPILED-WITNESS-CONTINUOUS-ERGODICITY Blocker-attack continuation: once the quorum+sleep+crypto witness is compiler-constructed from primitive obligations and aligned to the embedded discrete kernel, continuous ergodicity lift follows with foster drift, positive drift gap, and sub-unit contraction same primitive assumptions as THM-QUORUM-SLEEP-CRYPTO-WITNESS-COMPILER-FROM-PRIMITIVES; explicit DiscreteSubLatticeEmbedding plus kernel-alignment equality kernel = embedding.discreteKernel Lean theorem QuorumSleepCryptoQueueKernelBridge.quorum_sleep_crypto_compiled_witness_continuous_ergodicity_lift in QuorumSleepCryptoQueueKernelBridge.lean, composing the compiled-witness theorem with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-PARALLEL-ERGODICITY For two geometrically ergodic kernels K₁(r₁) and K₂(r₂), the product kernel K₁ ⊗ K₂ is geometrically ergodic with rate r ≤ max(r₁, r₂). The slower stage dominates in parallel composition. two GeometricErgodicityRate witnesses TLA+ CompositionalErgodicity.tla invariant InvParallel + Lean theorem CompositionalErgodicity.parallel_ergodicity in CompositionalErgodicity.lean Mechanized
THM-SEQUENTIAL-ERGODICITY For K₂ ∘ K₁ (sequential composition), the composite is geometrically ergodic with rate r ≤ r₁ · r₂. Rates multiply under sequential composition — faster convergence than either stage alone. two GeometricErgodicityRate witnesses TLA+ CompositionalErgodicity.tla invariant InvSequential + Lean theorem CompositionalErgodicity.sequential_ergodicity in CompositionalErgodicity.lean Mechanized
THM-PIPELINE-MIXING-BOUND An n-stage pipeline with per-stage rates has bounded mixing time. For sequential composition, t_mix(ε) ≤ Σᵢ (1/(1-rᵢ)) · log(Mᵢ/ε). The pipeline converges to equilibrium in finite time. per-stage GeometricErgodicityRate witnesses; target tolerance ε > 0 TLA+ CompositionalErgodicity.tla invariant InvMixingBound + Lean theorem CompositionalErgodicity.pipeline_mixing_bound in CompositionalErgodicity.lean Mechanized
THM-PIPELINE-CERTIFICATE Given per-stage GeometricErgodicWitness certificates, construct a pipeline-level certificate automatically. Per-stage stability certificates compose into pipeline-level certificates. per-stage GeometricErgodicityRate witnesses TLA+ CompositionalErgodicity.tla invariant InvCertificate + Lean theorem CompositionalErgodicity.pipeline_certificate_valid in CompositionalErgodicity.lean Mechanized
THM-DATA-FISHER-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined DataProcessing+Fisher budget yields an explicit geometric-rate package with contraction r = 3/4 and budget-indexed initial bound M = failureBudget + 1 interpretation anchor failureBudget = n + fisherScalarCurvatureX4 m Lean theorem data_fisher_budget_yields_geometric_rate_certificate in DataProcessingFisherQueueKernelBridge.lean, using GeometricErgodicity.mkGeometricErgodicityRate Mechanized
THM-DATA-FISHER-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: DataProcessing inequality and Fisher metric curvature routed through an explicit kernel-lift adapter execute continuous ergodicity lift explicit adapter bundle carrying data-processing and Fisher scalar curvature constraints, positive interpreted budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem DataFisherKernelLiftAdapter.data_fisher_continuous_ergodicity_lift in DataProcessingFisherQueueKernelBridge.lean, applying GeometricErgodicity.continuous_ergodicity_lift under explicit adapter hypotheses Mechanized
THM-ZECKENDORF-BATCHING-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: interpreted Zeckendorf representation and D1 batching query schedule combined budget yields an explicit geometric-rate package with contraction r = 3/4 interpretation anchor budget = loopQueries Lean theorem zeckendorf_batching_yields_geometric_rate_certificate in ZeckendorfBatchingQueueKernelBridge.lean Mechanized
THM-ZECKENDORF-BATCHING-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Zeckendorf non-consecutive representation gap and D1 batching query schedule routed through an explicit kernel-lift adapter execute continuous ergodicity lift explicit adapter bundle carrying DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem zeckendorf_batching_continuous_ergodicity_lift in ZeckendorfBatchingQueueKernelBridge.lean Mechanized
THM-DIMENSIONAL-MEDIA-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined dimensional+media budget yields an explicit geometric-rate package with contraction r = 3/4 interpretation anchor budget = quarks stages + (raceLoad - foldResolution) Lean theorem dimensional_media_budget_yields_geometric_rate_certificate in DimensionalMediaQueueKernelBridge.lean Mechanized
THM-DIMENSIONAL-MEDIA-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: dimensional confinement and infinite scroll trap load routed through an explicit kernel-lift adapter execute continuous ergodicity lift explicit adapter bundle carrying DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem DimensionalMediaKernelLiftAdapter.dimensional_media_continuous_ergodicity_lift in DimensionalMediaQueueKernelBridge.lean Mechanized
THM-CAPITAL-CANCER-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined capital+cancer budget yields an explicit geometric-rate package with contraction r = 3/4 interpretation anchor budget = lockupMinutes + totalVentBeta1 Lean theorem capital_cancer_budget_yields_geometric_rate_certificate in CapitalCancerQueueKernelBridge.lean Mechanized
THM-CAPITAL-CANCER-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: capital lockup and cancer vent capacity routed through an explicit kernel-lift adapter execute continuous ergodicity lift explicit adapter bundle carrying DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem CapitalCancerKernelLiftAdapter.capital_cancer_continuous_ergodicity_lift in CapitalCancerQueueKernelBridge.lean Mechanized
THM-MYCOLOGY-TYPOGRAPHY-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined mycology+typography budget yields explicit geometric-rate package positive combined budget Lean theorem mycology_typography_budget_yields_geometric_rate_certificate in MycologyTypographyQueueKernelBridge.lean Mechanized
THM-MYCOLOGY-TYPOGRAPHY-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: mycology+typography interpreted budget routed through an explicit kernel-lift adapter executes continuous ergodicity lift explicit adapter bundle carrying combined budget interpretation, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem mycology_typography_continuous_ergodicity_lift in MycologyTypographyQueueKernelBridge.lean Mechanized

| THM-SYNAPTIC-KADEMLIA-GEOMETRIC-RATE-CERTIFICATE | Moonshot fallback certificate: combined synaptic+Kademlia budget yields an explicit geometric-rate package with contraction r = 3/4 | same source assumptions as boundary | Lean theorem SynapticKademliaQueueKernelBridge.synaptic_kademlia_budget_yields_geometric_rate_certificate in SynapticKademliaQueueKernelBridge.lean | Mechanized | | THM-SYNAPTIC-KADEMLIA-KERNEL-LIFT-CONTINUOUS-ERGODICITY | Moonshot blocker-attack bridge: synaptic+Kademlia data routed through an explicit kernel-lift adapter executes continuous ergodicity lift | explicit adapter bundle carrying synaptic and kademlia assumptions, positive real budget anchor, DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality | Lean theorem SynapticKademliaKernelLiftAdapter.synaptic_kademlia_continuous_ergodicity_lift in SynapticKademliaQueueKernelBridge.lean | Mechanized |

| THM-DEFICIT-WALLINGTON-GEOMETRIC-RATE-CERTIFICATE | Deficit+Wallington interpreted budget certifies explicit GeometricErgodicityRate with contraction r = 3/4. | r = 3/4, M = budget + 1 | Lean theorem deficit_wallington_budget_yields_geometric_rate_certificate in DeficitWallingtonQueueKernelBridge.lean | Mechanized | | THM-DEFICIT-WALLINGTON-KERNEL-LIFT-CONTINUOUS-ERGODICITY | Explicit Deficit+Wallington adapter discharges continuous ergodicity lift obligations. | hKernelMatch, embedding, witness | Lean theorem DeficitWallingtonKernelLiftAdapter.deficit_wallington_continuous_ergodicity_lift in DeficitWallingtonQueueKernelBridge.lean | Mechanized | | THM-ORNITHOLOGY-MICROSERVICES-GEOMETRIC-RATE-CERTIFICATE | Moonshot fallback certificate: Ornithology microservices budget yields an explicit geometric-rate package with contraction r = 3/4. | budget + 1 | Lean theorem ornithology_microservices_budget_yields_geometric_rate_certificate in OrnithologyMicroservicesKernelLiftAdapter.lean | Mechanized | | THM-ORNITHOLOGY-MICROSERVICES-KERNEL-LIFT-CONTINUOUS-ERGODICITY | Moonshot blocker-attack bridge: Ornithology microservices explicit adapter discharges continuous ergodicity lift obligations. | hKernelMatch, embedding, witness | Lean theorem ornithology_microservices_continuous_ergodicity_lift in OrnithologyMicroservicesKernelLiftAdapter.lean | Mechanized |

Lyapunov Synthesis (Tracks Kappa + Nu + Xi)

Affine and nonlinear Lyapunov witness synthesis, adaptive gradient decomposition, and pipeline lift.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SYNTACTIC-LYAPUNOV-AFFINE For an affine drift program with positive drift gap (serviceRate > arrivalRate), V(x) = x is a valid Lyapunov function. The drift gap equals serviceRate - arrivalRate, which is the spectral gap of the affine kernel. First class where the compiler oracle synthesizes stability proofs from program syntax. AffineDriftProgram with serviceRate > arrivalRate; maxState > 0; ventThreshold < maxState TLA+ SyntacticLyapunov.tla invariant InvLyapunov + Lean theorem SyntacticLyapunov.syntactic_lyapunov_affine in SyntacticLyapunov.lean Mechanized
THM-SYNTACTIC-SMALL-SET The set {x : x ≤ ventThreshold} is a valid small set for the affine kernel: finite, non-empty (contains state 0), bounded by maxState. The small-set fraction (ventThreshold+1)/(maxState+1) bounds the minorization constant and is provably in (0,1). AffineDriftProgram with ventThreshold < maxState TLA+ SyntacticLyapunov.tla invariant InvSmallSet + Lean theorems SyntacticLyapunov.syntactic_small_set and SyntacticLyapunov.syntactic_small_set_fraction_bounds in SyntacticLyapunov.lean Mechanized
THM-SYNTACTIC-WITNESS-SOUND The synthesized GeometricErgodicityRate (with stepEpsilon = driftGap/maxState, smallSetEpsilon = smallSetFraction) has a contraction rate r = 1 - ε₁·ε₂ that is provably in (0,1). The certificate matches the true convergence rate of the kernel. AffineDriftProgram with ε₁·ε₂ < 1 TLA+ SyntacticLyapunov.tla invariant InvWitnessSound + Lean theorem SyntacticLyapunov.syntactic_witness_sound in SyntacticLyapunov.lean Mechanized
THM-SYNTACTIC-WITNESS-COMPLETE-AFFINE For any affine drift program with positive drift gap, synthesis always succeeds: stepEpsilon > 0, smallSetFraction ∈ (0,1), so a GeometricErgodicityRate can always be constructed. Completeness for the affine class. AffineDriftProgram TLA+ SyntacticLyapunov.tla invariant InvWitnessComplete + Lean theorem SyntacticLyapunov.syntactic_witness_complete in SyntacticLyapunov.lean Mechanized
THM-SYNTACTIC-PIPELINE-LIFT Per-stage synthesized witnesses compose via THM-PIPELINE-CERTIFICATE into pipeline-level certificates automatically. The composite rate r₁·r₂ is sub-unit and strictly less than either individual rate. two GeometricErgodicityRate witnesses from synthesis TLA+ SyntacticLyapunov.tla invariant InvPipelineLift + Lean theorem SyntacticLyapunov.syntactic_pipeline_lift in SyntacticLyapunov.lean Mechanized
THM-NONLINEAR-LYAPUNOV-QUADRATIC For V(x) = x², the effective drift gap at state x is gap·(2x - gap), which grows linearly with x. Strictly positive for x > gap, and strictly exceeds the affine drift gap. Handles fluid backlog and thermodynamic state variables. NonlinearDriftProgram; drift gap > 0; state x > gap TLA+ NonlinearLyapunov.tla invariant InvQuadratic + Lean theorems NonlinearLyapunov.nonlinear_lyapunov_quadratic_drift and NonlinearLyapunov.nonlinear_quadratic_exceeds_affine in NonlinearLyapunov.lean Mechanized
THM-NONLINEAR-LYAPUNOV-POWER V(x) = x^p for p ≥ 1 satisfies Foster drift: (x - gap)^p ≤ x^p for x ≥ gap. Monotonicity in the exponent: higher p gives larger effective drift gaps for states far from the small set. NonlinearDriftProgram; exponent p ≥ 1; state x ≥ gap > 0 TLA+ NonlinearLyapunov.tla invariant InvPower + Lean theorem NonlinearLyapunov.nonlinear_lyapunov_power_monotone in NonlinearLyapunov.lean Mechanized
THM-NONLINEAR-SMALL-SET-VALID The level set {x ≤ T} from the affine program is also valid for nonlinear V(x) = x^p: finite, non-empty, bounded by maxState. NonlinearDriftProgram TLA+ NonlinearLyapunov.tla invariant InvSmallSet + Lean theorem NonlinearLyapunov.nonlinear_small_set_valid in NonlinearLyapunov.lean Mechanized
THM-NONLINEAR-WITNESS-SOUND The synthesized rate from nonlinear V inherits the affine synthesis parameters: stepEpsilon > 0, smallSetFraction ∈ (0,1). Nonlinear case can only improve the rate. NonlinearDriftProgram TLA+ NonlinearLyapunov.tla invariant InvWitnessSound + Lean theorem NonlinearLyapunov.nonlinear_witness_sound in NonlinearLyapunov.lean Mechanized
THM-NONLINEAR-DOMINATES-AFFINE Nonlinear V(x) = x² gives a tighter (smaller) contraction rate than affine V(x) = x: the quadratic drift term gap·(2x-gap) > gap for all x > gap. Larger effective spectral gap → faster convergence. NonlinearDriftProgram; state x > drift gap TLA+ NonlinearLyapunov.tla invariant InvDominatesAffine + Lean theorem NonlinearLyapunov.nonlinear_dominates_affine in NonlinearLyapunov.lean Mechanized
THM-ADAPTIVE-GRADIENT-DECOMPOSITION The gradient of service slack across network nodes defines valid drift weights: wᵢ = sᵢ/Σsⱼ ∈ [0,1], Σwᵢ = 1. All weights non-negative, normalized to sum to 1. NetworkSlackWitness with n > 0; all slacks positive TLA+ AdaptiveDecomposition.tla invariant InvGradientDecomp + Lean theorems AdaptiveDecomposition.adaptive_gradient_weights_nonneg and AdaptiveDecomposition.adaptive_gradient_weights_sum_one in AdaptiveDecomposition.lean Mechanized
THM-ADAPTIVE-BOTTLENECK-DETECTION The minimum-slack node is the bottleneck: it is positive (stable) and lower-bounds all per-node slacks. NetworkSlackWitness with n > 0 TLA+ AdaptiveDecomposition.tla invariant InvBottleneck + Lean theorems AdaptiveDecomposition.adaptive_bottleneck_positive and AdaptiveDecomposition.adaptive_bottleneck_lower_bound in AdaptiveDecomposition.lean Mechanized
THM-ADAPTIVE-RESERVE-COVERAGE The gradient-weighted drift reserve = (Σsᵢ²)/(Σsᵢ) covers the drift gap. By QM-AM inequality, this exceeds the average slack and thus the minimum slack. NetworkSlackWitness with n > 0; drift gap ≤ min slack TLA+ AdaptiveDecomposition.tla invariant InvReserveCoverage + Lean theorem AdaptiveDecomposition.adaptive_reserve_nonneg in AdaptiveDecomposition.lean Mechanized
THM-ADAPTIVE-DECOMPOSITION-SOUND The gradient decomposition satisfies all AdaptiveCeilingDriftSynthesis obligations: non-negative normalized weights, positive total slack, positive bottleneck. NetworkSlackWitness with n > 0 TLA+ AdaptiveDecomposition.tla invariant InvDecompositionSound + Lean theorem AdaptiveDecomposition.adaptive_decomposition_sound in AdaptiveDecomposition.lean Mechanized
THM-ADAPTIVE-DOMINATES-UNIFORM Gradient weights dominate uniform weights by Cauchy-Schwarz: n·Σsᵢ² ≥ (Σsᵢ)², so (Σsᵢ²)/(Σsᵢ) ≥ (Σsᵢ)/n = avg(sᵢ) = uniform reserve. NetworkSlackWitness with n > 0; non-uniform slacks TLA+ AdaptiveDecomposition.tla invariant InvDominatesUniform + Lean theorem AdaptiveDecomposition.adaptive_dominates_uniform_cauchy_schwarz in AdaptiveDecomposition.lean Mechanized
THM-TRADE-ASTROPHYSICS-GEOMETRIC-RATE-CERTIFICATE Moonshot fallback certificate: combined Trade+Astrophysics budget yields an explicit geometric-rate package Trade and Celestial shadow assumptions Lean theorem TradeAstrophysicsQueueKernelBridge.trade_astrophysics_budget_yields_geometric_rate_certificate in TradeAstrophysicsQueueKernelBridge.lean Mechanized
THM-TRADE-ASTROPHYSICS-KERNEL-LIFT-CONTINUOUS-ERGODICITY Moonshot blocker-attack bridge: Trade and Astrophysics data routed through an explicit kernel-lift adapter execute continuous ergodicity lift Explicit adapter bundle Lean theorem TradeAstrophysicsKernelLiftAdapter.trade_astrophysics_continuous_ergodicity_lift in TradeAstrophysicsQueueKernelBridge.lean Mechanized

Envelope Convergence (Track Mu)

Jackson throughput envelope contraction, geometric convergence, mixing time, spectral connection, and early-stopping certificates.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-ENVELOPE-CONTRACTION The throughputEnvelopeApprox ladder contracts: residual(n+1) = ρ · residual(n) where ρ = maxIncomingRoutingMass. The residual strictly decreases each step. EnvelopeConvergenceWitness with ρ ∈ (0,1); R₀ > 0 TLA+ EnvelopeConvergence.tla invariant InvContraction + Lean theorems EnvelopeConvergence.envelope_contraction and EnvelopeConvergence.envelope_contraction_strict in EnvelopeConvergence.lean Mechanized
THM-ENVELOPE-GEOMETRIC-CONVERGENCE The envelope ladder converges geometrically: |approx(n) - exact| = R₀ · ρ^n, and ρ < 1 ensures decay to zero. The residual is monotonically decreasing. EnvelopeConvergenceWitness TLA+ EnvelopeConvergence.tla invariant InvGeometricConvergence + Lean theorems EnvelopeConvergence.envelope_geometric_convergence and EnvelopeConvergence.envelope_residual_monotone in EnvelopeConvergence.lean Mechanized
THM-ENVELOPE-MIXING-TIME For target accuracy ε > 0, the ladder reaches ε-accuracy in finite steps. The envelope-ladder analog of mixing_time_bound from GeometricErgodicity.lean. EnvelopeConvergenceWitness; target ε > 0 TLA+ EnvelopeConvergence.tla invariant InvMixingTime + Lean theorem EnvelopeConvergence.envelope_mixing_time in EnvelopeConvergence.lean Mechanized
THM-ENVELOPE-SPECTRAL-CONNECTION The contraction rate ρ bounds the spectral radius of the routing matrix P. The envelope iteration is the power method on the traffic equations. EnvelopeConvergenceWitness TLA+ EnvelopeConvergence.tla invariant InvSpectralConnection + Lean theorem EnvelopeConvergence.envelope_spectral_connection in EnvelopeConvergence.lean Mechanized
THM-ENVELOPE-CERTIFICATE-AT-N At any step n where the envelope is below the service rate, the stability certificate is valid — early stopping is sound. As n grows, service slack increases monotonically, and eventually certification succeeds. EnvelopeConvergenceWitness with serviceRate > exactThroughput TLA+ EnvelopeConvergence.tla invariant InvCertificate + Lean theorems EnvelopeConvergence.envelope_certificate_at_n, EnvelopeConvergence.envelope_slack_monotone, and EnvelopeConvergence.envelope_eventual_certification in EnvelopeConvergence.lean Mechanized

Wallington Rotation Optimality (Track Lambda)

Admissibility, critical-path makespan, sequential dominance, Pareto scheduling, and deficit-speedup correlation.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-ROTATION-ADMISSIBLE The Wallington Rotation produces an admissible schedule for any fork/race/fold DAG: positive finite makespan, respects stage ordering. ForkRaceFoldDAG with positive stages, paths, and stage time TLA+ WallingtonOptimality.tla invariant InvAdmissible + Lean theorem WallingtonOptimality.rotation_admissible in WallingtonOptimality.lean Mechanized
THM-ROTATION-MAKESPAN-BOUND The rotation makespan equals the critical path: numStages × maxStageTime. No admissible schedule can achieve lower makespan because stages are sequential dependencies. Bound is tight for balanced DAGs. ForkRaceFoldDAG TLA+ WallingtonOptimality.tla invariant InvMakespanBound + Lean theorem WallingtonOptimality.rotation_makespan_bound in WallingtonOptimality.lean Mechanized
THM-ROTATION-DOMINATES-SEQUENTIAL For any DAG with β₁ > 0 (numPaths ≥ 2), the rotation strictly dominates the sequential schedule: rotationMakespan < sequentialMakespan. The speedup factor is exactly numPaths. ForkRaceFoldDAG with numPaths ≥ 2 TLA+ WallingtonOptimality.tla invariant InvDominatesSequential + Lean theorem WallingtonOptimality.rotation_dominates_sequential in WallingtonOptimality.lean Mechanized
THM-ROTATION-PARETO-SCHEDULE The rotation is Pareto-optimal in (makespan, resources): sequential uses fewer resources (1 vs numPaths) but has strictly higher makespan. No schedule simultaneously beats both dimensions. ForkRaceFoldDAG with numPaths ≥ 2 TLA+ WallingtonOptimality.tla invariant InvPareto + Lean theorem WallingtonOptimality.rotation_pareto_schedule in WallingtonOptimality.lean Mechanized
THM-ROTATION-DEFICIT-CORRELATION The rotation's speedup factor equals the topological deficit reduction plus one: speedup = β₁(rotation) - β₁(sequential) + 1 = numPaths. Larger deficit reduction → larger speedup, monotonically. ForkRaceFoldDAG with numPaths ≥ 1 TLA+ WallingtonOptimality.tla invariant InvDeficitCorrelation + Lean theorems WallingtonOptimality.rotation_deficit_correlation and WallingtonOptimality.rotation_deficit_monotone in WallingtonOptimality.lean Mechanized

Race Winner Correctness (Track Omicron)

Validity, minimality, determinism, isolation, and composability of race operations.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-RACE-WINNER-VALIDITY The selected race winner has a valid result: complete status and result passes the validity predicate. Invalid branches cannot win. RaceConfig with validity predicate; winner index TLA+ RaceWinnerCorrectness.tla invariant InvValidity + Lean theorem RaceWinnerCorrectness.race_winner_validity in RaceWinnerCorrectness.lean Mechanized
THM-RACE-WINNER-MINIMALITY The winner completes no later than any other valid branch. This is the "fastest correct answer" property of race operations. RaceConfig with isMinimalWinner predicate TLA+ RaceWinnerCorrectness.tla invariant InvMinimality + Lean theorem RaceWinnerCorrectness.race_winner_minimality in RaceWinnerCorrectness.lean Mechanized
THM-RACE-WINNER-DETERMINISM Ties are broken deterministically by branch index (C3). Among all valid candidates with the same completion time, the lowest-indexed branch wins. Satisfies deterministic fold. RaceConfig with isDeterministicWinner predicate TLA+ RaceWinnerCorrectness.tla invariant InvDeterminism + Lean theorem RaceWinnerCorrectness.race_winner_determinism in RaceWinnerCorrectness.lean Mechanized
THM-RACE-WINNER-ISOLATION Venting a non-winner branch preserves the winner's validity. Formal content of C2 (branch isolation) applied to race operations. RaceConfig; winner and ventedIdx with winner ≠ ventedIdx TLA+ RaceWinnerCorrectness.tla invariant InvIsolation + Lean theorem RaceWinnerCorrectness.race_winner_isolation in RaceWinnerCorrectness.lean Mechanized
THM-RACE-WINNER-COMPOSABLE Race results compose through fold: given two valid race winners, their fold is valid when the fold function preserves validity. Connects race correctness to the monoidal category structure. fold function preserving validity; two valid results TLA+ RaceWinnerCorrectness.tla invariant InvComposable + Lean theorem RaceWinnerCorrectness.race_winner_composable in RaceWinnerCorrectness.lean Mechanized

Frame Native Execution

Bisimulation, Wallington equivalence, and allocation overhead bound for frame-native vs stream-based paths.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-FRAME-BISIM Frame-native execution (frameRace, frameFold) produces identical results to Stream-based execution under the canUseFrameNativePath guard: no timeout, no shared state, all handlers registered, default failure policy. Stuttering bisimulation between frame-native and stream paths. guard conditions (no timeout, no shared state, all handlers registered, default failure policy); deterministic work functions; N ≥ 1 work functions TLA+ FrameNativeBisim.tla invariants (InvRaceBisimResults, InvRaceBisimWinner, InvFoldBisimResults) + Lean theorems FrameNativeBisim.frame_race_bisim and FrameNativeBisim.frame_fold_bisim Mechanized
THM-FRAME-WALLINGTON-EQUIV Tick-parallel frame executor with flat pre-allocated grid produces same output as sequential Stream-based wallington for any stage/chunk decomposition S > 0 stages; C > 0 chunks; deterministic stage functions TLA+ FrameNativeBisim.tla + Lean theorem FrameNativeBisim.frame_wallington_equiv Mechanized
THM-FRAME-OVERHEAD-BOUND Frame-native allocates O(N) raw promises; Stream-based allocates O(7N) objects (AbortController + event listener + state machine + Promise constructor + result wrapper + vented tracker + map entry). Same result, bounded overhead separation. Frame saves ≥ 5N allocations. N ≥ 1 work functions TLA+ FrameNativeBisim.tla invariants (InvOverheadBound, InvFrameLinear, InvStreamSevenX) + Lean theorems FrameNativeBisim.frame_overhead_strictly_less, FrameNativeBisim.frame_saves_at_least_5n, FrameOverheadBound.race_allocation_savings, FrameOverheadBound.fold_allocation_savings, and FrameOverheadBound.frame_total_bytes_smaller Mechanized

Void Walking

Boundary measurability, volume dominance, memory efficiency, tunneling, regret bounds, gradient, coherence, and void attention.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-VOID-BOUNDARY-MEASURABLE The boundary of the void created by T folds over N-way cycles has homology rank bounded by sum of (N_t - 1). Computable in O(T * N_max) time, O(T * log N_max) space. The boundary encodes which equivalence classes were vented at each fold. Dual of persistent homology: tracks birth/persistence of dead features rather than live ones. finite fork width >= 2; non-injective fold; retained fold results TLA+ VoidBoundaryMeasurable.tla invariants (InvBoundaryRankEqTotalVented, InvPerStepVentCount, InvActivePathsBounded, InvBoundaryLogLength, InvSpaceEfficiency, InvBoundaryMonotone, InvCompleteTrace) + Lean theorems VoidWalking.void_boundary_rank_le_total_vented, VoidWalking.void_boundary_grows_per_step, and VoidWalking.void_boundary_monotone in VoidWalking.lean + executable src/void-walking.test.ts Mechanized
THM-VOID-DOMINANCE Void volume grows as Omega(T * (N-1)), dominating active computation by factor Omega(T). For nested depth d, void grows as Omega(T * N^d) while active paths remain bounded at N^d. The void fraction approaches 1 as T grows. Computational dark energy: the void is the dark matter of computation -- invisible but structurally essential. constant N >= 2; single-survivor fold; T steps TLA+ VoidDominance.tla invariants (InvVoidVolumeFormula, InvActivePathsBounded, InvVoidDominatesLinear, InvTotalConservation, InvVoidPositiveAfterFirstFold, InvFinalDominance) + Lean theorems VoidWalking.void_volume_positive, VoidWalking.void_dominance_linear, VoidWalking.void_fraction_dominates, and VoidWalking.void_dominance_nested in VoidWalking.lean + executable src/void-walking.test.ts Mechanized
THM-VOID-MEMORY-EFFICIENCY Void boundary encoding is exponentially more compact than storing discarded paths. Ratio: Omega(N * m_min / log N). The boundary is a sufficient statistic for optimal fork distributions. Upper bound from THM-VOID-BOUNDARY-MEASURABLE, lower bound from DPI (fold_erasure in FoldErasure.lean). path payloads >= 1 bit; N >= 2 Lean theorem VoidWalking.void_boundary_sufficient_statistic in VoidWalking.lean using existing DataProcessingInequality.lean + executable src/void-walking.test.ts Mechanized
THM-VOID-TUNNEL Void regions sharing a common ancestor fork have positive mutual information: I(dV_A; dV_B) > 0. Correlation decays exponentially: I <= H(F) * prod(1 - epsilon_t) where epsilon_t is erasure fraction at fold t along the connecting path. Finite products of values in (0,1) are strictly positive -- correlation never fully vanishes. This is why counterfactual reasoning works. common ancestor fork with H(F) > 0; both branches undergo at least one fold; bounded erasure 0 < epsilon_t < 1 TLA+ VoidTunnel.tla invariants (InvRetainedInfoAPositive, InvRetainedInfoBPositive, InvMutualInfoPositive, InvMutualInfoBounded, InvRetainedInfoDecreases, InvCompleteMutualInfoPositive) + Lean theorems VoidWalking.void_tunnel_mutual_information_positive and VoidWalking.void_tunnel_retention_positive in VoidWalking.lean using existing DPI infrastructure + executable src/void-walking.test.ts Mechanized
THM-VOID-REGRET-BOUND Void walking reduces adversarial regret from Omega(sqrt(TN)) to O(sqrt(T log N)). Improvement factor sqrt(N / log N), unbounded as N grows. Void boundary provides N-1 bits of negative information per round (which paths lost). The void formalizes the expert advice in the experts framework -- not what the experts said, but the record of which experts failed. adversarial costs in [0,1]; constant N; boundary-only access Lean theorem VoidWalking.void_walking_regret_bound in VoidWalking.lean + executable src/void-regret-simulation.test.ts with Exp3 comparison Mechanized
THM-VOID-GRADIENT The void boundary induces a gradient field: void density rho_i = (times choice i was vented) / T. The complement distribution mu_i proportional to (1 - rho_i + epsilon) uniquely minimizes expected regret. Void analogue of gradient descent: loss gradient points toward maximum waste heat in parameter space; void gradient points toward maximum discard in fork-choice space. Both are waste-minimizing flows on their respective manifolds. stationary (or slowly varying) costs; N >= 2; per-choice vent counts available Lean theorems VoidWalking.void_gradient_complement_positive and VoidWalking.void_gradient_complement_minimizes_regret in VoidWalking.lean + executable src/void-gradient-simulation.test.ts Mechanized
THM-VOID-COHERENCE Two independent void walkers reading the same boundary produce identical fork distributions (deterministic case) or epsilon-close distributions with epsilon = O(1/sqrt(T)) (stochastic case). Deterministic case is rfl (same inputs, same deterministic function). Void analogue of the fundamental theorem of covering spaces: two lifts from the same base point following the same path arrive at the same endpoint. canonical multiplicative weights update rule; same boundary; uniform initialization Lean theorems VoidWalking.void_walkers_converge and VoidWalking.void_walkers_converge_all in VoidWalking.lean + executable Monte Carlo test in src/void-walking.test.ts Mechanized
THM-VOID-ATTENTION The structural identity between void walking and transformer attention: complement distribution is softmax attention over the void boundary. Void boundary grows monotonically (residual accumulation). Layer norm prevents saturation. Cross-attention = product of marginals times gate. Attention sharpens with experience (entropy decreases). Gait schedule = annealing schedule Q=proposal, K=void boundary, V=complement weights; score = softmax(-eta * voidCounts) TLA+ VoidAttention.tla invariants (InvComplementIsSoftmax, InvResidualAccumulates, InvDecayStabilizes, InvCrossIsGated, InvEntropyDecreases, InvGaitIsTemperature) Model-checked

Semiotic Deficit & Peace (Track Pi)

Thought-to-speech deficit, erasure, nuance venting, race articulation, context reduction, conversation trace, MOA isomorphism, and the formal theory of confusion/war/peace/hope.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SEMIOTIC-DEFICIT Thought→speech has positive topological deficit when semantic paths exceed articulation streams. For standard speech (1 stream), Δβ = semanticPaths - 1. Each additional semantic dimension beyond the first adds one Bule of communication difficulty. The information-theoretic content of "I know what I mean but I can't say it." SemioticChannel with semanticPaths > articulationStreams TLA+ SemioticDeficit.tla invariant InvDeficit + Lean theorems SemioticDeficit.semiotic_deficit and SemioticDeficit.semiotic_deficit_speech in SemioticDeficit.lean Mechanized
THM-SEMIOTIC-ERASURE The speech fold is many-to-one: multiple semantic paths collide on shared articulation streams, erasing meaning by DPI. Composes THM-COVERING-CAUSALITY with THM-DEFICIT-INFORMATION-LOSS. "Something is always lost in translation" — even within the same language. SemioticChannel with articulationStreams = 1 TLA+ SemioticDeficit.tla invariant InvErasure + Lean theorem SemioticDeficit.semiotic_erasure in SemioticDeficit.lean Mechanized
THM-SEMIOTIC-VENT-NUANCE Vented semantic paths = lost nuance. The number of paths that must be dropped equals the semiotic deficit. "It's complicated" is a vent operation. SemioticChannel with articulationStreams = 1 TLA+ SemioticDeficit.tla invariant InvVent + Lean theorem SemioticDeficit.semiotic_vent_nuance in SemioticDeficit.lean Mechanized
THM-SEMIOTIC-RACE-ARTICULATION Phrasing selection is a neural race: multiple candidates forked in parallel, fastest adequate one wins. "Tip of the tongue" = race hasn't terminated. "Wrong word" = race winner passed validity but wasn't optimal. Directly reuses THM-RACE-WINNER-MINIMALITY. RaceConfig for phrasing candidates TLA+ SemioticDeficit.tla invariant InvRace + Lean theorem SemioticDeficit.semiotic_race_articulation in SemioticDeficit.lean Mechanized
THM-SEMIOTIC-CONTEXT-REDUCES Shared context reduces semiotic deficit by adding implicit parallel channels. Expert-to-expert = high context = low deficit = precise. Expert-to-novice = low context = high deficit = confusion. Sufficient context eliminates deficit entirely. SemioticChannel with contextPaths > 0 TLA+ SemioticDeficit.tla invariant InvContext + Lean theorems SemioticDeficit.semiotic_context_reduces and SemioticDeficit.semiotic_context_eliminates in SemioticDeficit.lean Mechanized
THM-SEMIOTIC-CONVERSATION-TRACE Dialogue is traced monoidal: trace operator models speak→hear→adjust→speak feedback. By THM-TRACE-VANISHING, trivial feedback = no new understanding. By THM-TRACE-YANKING, symmetric restatement = identity. Conversation converges because each turn adds context (reduces deficit). Type variables for thought/response TLA+ SemioticDeficit.tla invariant InvTrace + Lean theorem SemioticDeficit.semiotic_conversation_trace in SemioticDeficit.lean Mechanized
THM-SEMIOTIC-MOA-ISOMORPHISM MOA architecture is isomorphic to the semiotic pipeline: k agents producing 1 output has deficit k-1, identical to k semantic paths through 1 speech stream. Zero deficit when each agent gets its own output channel. The deficit measures the same thing: how much collective knowledge is lost in the final output. numAgents ≥ 2 TLA+ SemioticDeficit.tla invariant InvMOA + Lean theorems SemioticDeficit.semiotic_moa_isomorphism and SemioticDeficit.semiotic_moa_zero_deficit in SemioticDeficit.lean Mechanized

Negotiation Equilibrium

Negotiation deficit, BATNA as void, concession gradient, settlement stability, coherence, heat, tunnel, regret, dual void (BATNA/WATNA), Hodge decomposition, classified tunnels, and master convergence.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-NEGOTIATION-DEFICIT The negotiation deficit between parties with multi-dimensional interests compressed into a single offer stream is strictly positive, equals totalDimensions - 1, and is bounded below totalDimensions. Negotiations are hard not because people are irrational but because the semiotic channel has lower topology than the position spaces. each party has at least 2 dimensions of interest; single offer stream (articulationStreams = 1) Lean theorems negotiation_deficit_positive, negotiation_deficit_value, and negotiation_deficit_bounded in NegotiationEquilibrium.lean composing with SemioticDeficit.lean Mechanized
THM-BATNA-is-VOID The BATNA surface is exactly the void boundary of the negotiation fork/race/fold process. Each negotiation round contributes offerCount - 1 entries to the void boundary. The BATNA grows monotonically with rounds -- the longer the negotiation, the richer the information about what doesn't work. at least 2 offer variants per round; non-injective fold (single accepted offer) Lean theorems batna_is_void_boundary and batna_grows_with_rounds in NegotiationEquilibrium.lean composing with VoidWalking.void_boundary_grows_per_step and VoidWalking.void_boundary_monotone Mechanized
THM-CONCESSION-GRADIENT The optimal concession strategy is the void gradient complement distribution. Every term retains positive weight (never say never in negotiation). Less-rejected terms get higher concession weight (learn from rejection). at least 2 terms; positive rounds; rejection counts bounded by rounds Lean theorems concession_gradient_positive and concession_gradient_monotone in NegotiationEquilibrium.lean composing with VoidWalking.void_gradient_complement_positive and VoidWalking.void_gradient_complement_monotone Mechanized
THM-SETTLEMENT-STABILITY Mutual settlement is a Lyapunov-stable fixed point of the void gradient flow. Perturbation of one party's void boundary (one additional rejection) does not destroy the agreement: the complement distribution is continuous in the void boundary, so small changes in rejection history produce small changes in concession strategy. negotiation state with at least 2 terms; positive rounds; bounded rejection counts Lean theorem settlement_stable_under_perturbation in NegotiationEquilibrium.lean via concession_gradient_monotone Mechanized
THM-NEGOTIATION-COHERENCE Two rational agents reading the same rejection history produce identical concession strategies. Same rejected offers + same rational update rule = same next offer. Transparent negotiation works because shared void boundary forces convergence; secret information breaks coherence. shared rejection history; canonical multiplicative weights update rule Lean theorems negotiation_coherence and negotiation_full_coherence in NegotiationEquilibrium.lean composing with VoidWalking.void_walkers_converge and VoidWalking.void_walkers_converge_all Mechanized
THM-NEGOTIATION-HEAT Failed negotiations generate irreversible thermodynamic heat. Each rejected offer is a vented path; by THM-VOID-DOMINANCE the void of rejected offers dominates the space of accepted terms. The cost of disagreement is thermodynamically real (Landauer erasure), but by THM-VOID-GRADIENT that heat inscribes the void boundary guiding the next offer -- the cost of disagreement is also the fuel for agreement. constant fork width >= 2; single-survivor fold; positive steps Lean theorems negotiation_void_dominates and rejection_dominates_acceptance in NegotiationEquilibrium.lean composing with VoidWalking.void_volume_positive and VoidWalking.void_dominance_linear Mechanized
THM-CONTEXT-REDUCES-DEFICIT Shared context between negotiating parties (prior relationship, market norms, shared vocabulary) reduces the semiotic deficit of the negotiation channel. Sufficient shared context eliminates the deficit entirely -- the formal content of "repeat business is easier." positive shared context; NegotiationChannel composed to SemioticChannel Lean theorems context_reduces_negotiation_deficit and sufficient_context_eliminates_deficit in NegotiationEquilibrium.lean composing with SemioticPeace.peace_context_reduces and SemioticPeace.peace_sufficient_context Mechanized
THM-NEGOTIATION-CONVERGENCE Master theorem: for any negotiation between parties with multi-dimensional interests, (1) confusion is real (deficit positive), (2) confusion is bounded (deficit < totalDimensions), and (3) shared context reduces the deficit. BATNA walking is void walking -- the void boundary is the BATNA surface, the complement distribution is the concession strategy, and the negotiation converges because the void boundary is a sufficient statistic for the optimal next move. NegotiationChannel with multi-dimensional parties; all sub-theorem assumptions Lean theorem negotiation_convergence in NegotiationEquilibrium.lean combining negotiation_deficit_positive, negotiation_deficit_bounded, and context_reduces_negotiation_deficit Mechanized
THM-NEGOTIATION-REGRET Negotiation with N offer variants per round achieves O(sqrt(T log N)) regret instead of Omega(sqrt(TN)). The BATNA surface provides N-1 bits of negative information per round. Improvement factor sqrt(N / log N), unbounded as the offer space grows. This is why experienced negotiators perform better: they read the void. at least 2 offer variants per round; T > 0 Lean theorem negotiation_regret_bound in NegotiationEquilibrium.lean composing with VoidWalking.void_walking_regret_bound via NegotiationRound.toFoldStep Mechanized
THM-BATNA-SUFFICIENT-STATISTIC The BATNA surface is exponentially more compact than storing the full history of rejected offers. Storing every rejected offer costs O(N * T * payloadBits); storing the BATNA surface costs O(T * log N). The rejection pattern formalizes the information -- you don't need the content of every rejected offer, only which indices were rejected and how often. at least 2 offer variants; path payloads >= 1 bit; log N <= N Lean theorem batna_sufficient_statistic in NegotiationEquilibrium.lean composing with VoidWalking.void_boundary_sufficient_statistic Mechanized
THM-NEGOTIATION-TUNNEL Two negotiation threads sharing a common prior proposal have positive mutual information. Precedent transfers across negotiations: prior rejected offers in one negotiation inform a related negotiation through shared ancestry. Correlation decays exponentially with intervening folds but never reaches zero for finite negotiation histories. common prior proposal with positive information content; positive retention factors at each intervening fold Lean theorems negotiation_tunnel_positive and negotiation_tunnel_retention_positive in NegotiationEquilibrium.lean composing with VoidWalking.void_tunnel_mutual_information_positive and VoidWalking.void_tunnel_retention_positive Mechanized
THM-NEGOTIATION-CONVERGENCE-EXTENDED Extended master theorem adding regret bound to the original convergence triple: (1) confusion is real, (2) confusion is bounded, (3) context helps, and (4) regret is controlled at O(sqrt(T log N)). NegotiationChannel + NegotiationRound with multi-dimensional parties; T > 0; all sub-theorem assumptions Lean theorem negotiation_convergence_extended in NegotiationEquilibrium.lean combining all four properties Mechanized
THM-DUAL-VOID-PARTITION Every vented path belongs to exactly one of two voids: BATNA ("I found better" -- agent had agency) or WATNA ("this would destroy me" -- environment had agency). The partition is exhaustive and both voids are nonempty in any genuine negotiation. at least 2 terms; positive rounds; at least one BATNA and one WATNA entry Lean theorems dual_void_exhaustive and dual_void_both_nonempty in NegotiationEquilibrium.lean over VoidPartition structure with VentReason inductive Mechanized
THM-BATNA-ATTRACTION BATNA complement weights are always positive (the attractive gradient never fully abandons any term) and monotone (less BATNA-rejected terms have higher attraction weight). The exact component of the Hodge decomposition. VoidPartition with positive rounds Lean theorems batna_attraction_positive and batna_attraction_monotone in NegotiationEquilibrium.lean Mechanized
THM-WATNA-REPULSION Terms with higher WATNA density exert stronger repulsion. WATNA repulsion is zero for terms never classified as catastrophic. The co-exact component of the Hodge decomposition. VoidPartition with classified WATNA vents Lean theorems watna_repulsion_monotone and watna_repulsion_zero_of_no_history in NegotiationEquilibrium.lean Mechanized
THM-HODGE-DECOMPOSITION The settlement score decomposes as BATNA attraction minus WATNA repulsion. The exact component (BATNA) is always positive. Discrete Hodge decomposition: exact = attraction toward viable, co-exact = repulsion from catastrophe, harmonic = settlement (the deal). VoidPartition Lean theorems hodge_decomposition and hodge_exact_positive in NegotiationEquilibrium.lean Mechanized
THM-DUAL-VOID-SQUEEZE When both voids are nonempty, there exists a term with positive settlement score -- BATNA attraction exceeds WATNA repulsion. Settlement exists precisely because two voids squeeze from opposite sides. Any term with zero WATNA history has positive settlement score. Terms the environment never rejected are safe to settle on. VoidPartition with at least one zero-WATNA term Lean theorems dual_void_squeeze, settlement_positive_of_no_watna, and settlement_decreases_with_watna in NegotiationEquilibrium.lean Mechanized
THM-VOID-DUALITY BATNA and WATNA are dual: for the same total vent count, a term classified as more BATNA than WATNA has a higher settlement score. The allocation between the two voids matters -- not just the total rejection count. BATNA compresses from above (reducing the exact component), WATNA compresses from below (increasing the co-exact component). VoidPartition with equal total vent counts between compared terms Lean theorem void_duality_allocation_matters in NegotiationEquilibrium.lean Mechanized
THM-DARK-MATTER-ENERGY-CONSERVATION Total void volume is the sum of BATNA (dark matter) and WATNA (dark energy) components. No vented path escapes classification. The void isn't one thing -- it's two things that sum to everything rejected. VoidPartition Lean theorem dark_matter_energy_conservation in NegotiationEquilibrium.lean Mechanized
THM-DARK-MATTER-POSITIVE The BATNA void (dark matter) has positive volume. There is always at least one viable alternative that was rejected. Without dark matter, the trajectory has no shape -- no gravitational pull toward viable regions. VoidPartition with nonempty BATNA Lean theorem dark_matter_positive in NegotiationEquilibrium.lean via Finset.sum_pos' Mechanized
THM-DARK-ENERGY-POSITIVE The WATNA void (dark energy) has positive volume. There is always at least one catastrophic outcome being fled. Without dark energy, there is no urgency to settle -- no repulsive force preventing collapse into singularity. VoidPartition with nonempty WATNA Lean theorem dark_energy_positive in NegotiationEquilibrium.lean via Finset.sum_pos' Mechanized
THM-DOMINANCE-TRICHOTOMY Every void partition is dark-matter-dominated (BATNA > WATNA, healthy), dark-energy-dominated (WATNA > BATNA, failing), or balanced. The trichotomy is exhaustive -- the dark matter/dark energy ratio is a diagnostic signal for negotiation health. VoidPartition Lean theorem dominance_trichotomy in NegotiationEquilibrium.lean via omega Mechanized
THM-BATNA-TUNNEL-POSITIVE The BATNA component of a classified tunnel carries positive mutual information. Knowledge of what worked in a related negotiation never fully vanishes. Positive knowledge transfers across negotiation threads. ClassifiedTunnel with positive BATNA ancestor entropy Lean theorem batna_tunnel_positive in NegotiationEquilibrium.lean composing with VoidWalking.void_tunnel_mutual_information_positive Mechanized
THM-WATNA-TUNNEL-POSITIVE The WATNA component of a classified tunnel carries positive mutual information. Knowledge of what killed a related negotiation never fully vanishes. The ghost of past catastrophe haunts all future negotiations through shared ancestry. Negative knowledge transfers more durably than positive. ClassifiedTunnel with positive WATNA ancestor entropy Lean theorem watna_tunnel_positive in NegotiationEquilibrium.lean composing with VoidWalking.void_tunnel_mutual_information_positive Mechanized
THM-CLASSIFIED-TUNNEL-BOTH-RETAINED Both components of a classified tunnel have positive retention product. Neither BATNA knowledge (what worked) nor WATNA knowledge (what killed) is fully lost across negotiation threads. ClassifiedTunnel with positive retention factors Lean theorems classified_tunnel_both_positive and classified_tunnel_both_retained in NegotiationEquilibrium.lean Mechanized
THM-COHERENCE-BREAKDOWN When two parties agree on what was rejected but classify identically, their settlement scores agree (coherence preserved). When they classify differently -- one party's BATNA is another's WATNA -- their settlement scores diverge. The gap equals exactly twice the WATNA classification shift. This is why negotiations fail even with transparent information: the parties agree on the facts but disagree on their meaning. DivergentClassification with same total vents per term Lean theorems coherence_when_classification_agrees, coherence_divergence, classification_gap_bounded, and classification_gap_equals_double_watna_shift in NegotiationEquilibrium.lean Mechanized
THM-WATNA-REDUCED-REGRET WATNA elimination strictly shrinks the effective offer space and tightens the regret bound from O(sqrt(T log N)) to O(sqrt(T log(N-k))). The WATNA void is not just repulsive -- it is constructive. Each catastrophic outcome identified permanently reduces the difficulty of the remaining search. WatnaReducedSpace with at least 2 remaining terms; T > 0 Lean theorems watna_reduces_effective_space, watna_reduced_regret, watna_reduced_regret_strict, and watna_effective_nontrivial in NegotiationEquilibrium.lean Mechanized
THM-DUAL-VOID-MASTER Complete dual void theorem: (1) both voids positive, (2) dominance trichotomy, (3) settlement exists between them. The void is not one thing -- it is two things, success and failure, and the duality between them is the engine of convergence. VoidPartition with at least one zero-WATNA safe term Lean theorem dual_void_master in NegotiationEquilibrium.lean combining dark_matter_positive, dark_energy_positive, dominance_trichotomy, and dual_void_squeeze Mechanized
THM-NEG-SETTLE Negotiation convergence via fork/race/fold on void surface: settlement is reachable when an offer exceeds BATNA. Void deficit is monotonically non-increasing. Settled complement satisfies void boundary. Deficit reduces with increasing context. Exhausted rounds still produce a valid void state ASSUME NumChoices >= 2, MaxRounds >= 1, BATNAThreshold >= 1 TLA+ NegotiationConvergence.tla invariants (InvSettleReachable, InvVoidMono, InvComplement, InvDeficitCtx, InvExhaust) Model-checked
THM-XSYN-BEHAVIOR-EXTERNALIZATION Cross-mixed synthesis THX-R2-1: repeated behavior-loop detections become community geometry; they are not merely private diagnostics. behavior_loop_detections ≥ 0, community_openness_index ≥ 0 as scalar witnesses Conceptual (tranche 3): synthesis notebook CROSS_MIXED_THEOREM_SYNTHESIS.md (Round 2). MCP: communication-mcp tool thm_xsyn_behavior_externalization; optional query JSON returns externalized_to_community_geometry_witness. Mechanized core lemmas TBD. Conceptual

Cross-mixed synthesis THX-R1-1 is covered by canonical theorem THM-RECOVERY-FIRST-SETTLEMENT. Its scalar witness remains available through the negotiation-mcp recovery-first-settlement tool; the separate THM-XSYN-RECOVERY-FIRST-SETTLEMENT label is narrative metadata, not a distinct MCP theorem row.

Void Relativity & Grand Unification

Interval invariance, time dilation, proper time, light cones, AFFECTIVELY-58, empathy, therapy, causal speed limit, void relativity, arrow of time, holographic bound, Einstein field equation, event horizon, Noether conservation, entanglement, void field equation, Penrose singularity, and grand unification.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-INTERVAL-INVARIANCE The spacetime interval (total vent count per dimension) is invariant across all reference frames. Two observers may disagree on the BATNA/WATNA decomposition, but they always agree on the total rejection count. This is the fundamental postulate of void relativity. Global version: sum over all dimensions is also invariant. LorentzTransform n with interval preservation per dimension Lean theorems interval_invariance and interval_invariance_global in NegotiationEquilibrium.lean Mechanized
THM-TIME-DILATION The settlement score difference between frames equals exactly 2x the WATNA shift. One observer's proper time (settlement score) looks dilated from another frame. The void analog of time dilation: the same event has different settlement scores in different frames, proportional to the classification velocity. LorentzTransform n; BATNA counts within rounds Lean theorem time_dilation in NegotiationEquilibrium.lean Mechanized
THM-PROPER-TIME-MAXIMUM An observer's settlement score is maximized in the frame where WATNA is minimized. The void analog of the twin paradox: the twin who experiences less catastrophe arrives at settlement with a higher score. LorentzTransform n; BATNA counts within rounds; source WATNA <= target WATNA Lean theorem proper_time_maximum in NegotiationEquilibrium.lean Mechanized
THM-LIGHT-CONE-FRAME-DEPENDENCE The causal character of a void event can change between frames. What is spacelike (viable) in one frame may be timelike (catastrophic) in another. One person's BATNA is another's WATNA. Empathy is nontrivial because your safe region is someone else's danger zone. LorentzTransform n; source score positive; target has more WATNA Lean theorem light_cone_frame_dependence in NegotiationEquilibrium.lean Mechanized
THM-AFFECTIVELY-58 The 7 personality layers (temperament 5, attachment 5, traits 20, behaviors 20, mental health 3, Big Five 5) sum to 58 dimensions. The AFFECTIVELY Float32Array maps to an emotion-spacetime event, not a point in emotion-space. layer size list [5, 5, 20, 20, 3, 5] Lean theorem affectively_layers_sum in NegotiationEquilibrium.lean via native_decide Mechanized
THM-EMPATHY-PRESERVES-INTERVAL Empathy preserves the total rejection count across all 58 dimensions. Understanding another person doesn't change what they've been through -- it changes how you classify their experience. You can't erase someone's rejections by reframing them. EmpathyTransform (= LorentzTransform 58) Lean theorem empathy_preserves_interval in NegotiationEquilibrium.lean Mechanized
THM-EMPATHY-DILATION When you see someone else's void through your frame, their settlement scores differ by exactly 2x the WATNA classification shift. The formal content of "I see what you went through but I interpret it differently." EmpathyTransform; BATNA counts within rounds Lean theorem empathy_dilation in NegotiationEquilibrium.lean composing with time_dilation Mechanized
THM-THERAPY-IMPROVES-SETTLEMENT Reclassifying WATNA events as BATNA (reducing the time-like component) strictly improves settlement score. Reframing catastrophe as choice improves emotional outcomes. The twin paradox of therapy: the person who reclassifies more WATNA as BATNA arrives at settlement with a higher score. EmpathyTransform; target WATNA <= source WATNA (therapy direction) Lean theorem therapy_improves_settlement in NegotiationEquilibrium.lean composing with proper_time_maximum via reversed LorentzTransform Mechanized
THM-CAUSAL-SPEED-LIMIT Classification change per step per dimension is bounded by c (the speed of light on the void manifold). You cannot instantaneously reclassify your entire void -- emotional change takes time. Empathy also has a speed limit: you cannot instantaneously adopt another person's full frame. VoidWorldline n with causal constraint and positive maxShift Lean theorems causal_speed_limit and empathy_bounded_by_c in NegotiationEquilibrium.lean Mechanized
THM-VOID-RELATIVITY Complete void relativity master theorem for the 58-dimensional emotion-spacetime: (1) interval invariance, (2) time dilation = 2x WATNA shift, (3) therapy improves settlement. Personality is void walking. Emotion tracking is measuring where the walker stands. The platform measures the geometry of what someone has refused to become. Empathy is a Lorentz transformation. Therapy is reclassification of the time-like component. EmpathyTransform; BATNA within rounds; therapy direction (target WATNA <= source WATNA) Lean theorem void_relativity in NegotiationEquilibrium.lean combining empathy_preserves_interval, empathy_dilation, and therapy_improves_settlement Mechanized
THM-ARROW-OF-TIME The total void volume is monotonically non-decreasing. WATNA specifically is monotone -- you cannot un-experience catastrophe. The direction of WATNA accumulation formalizes the direction of time. Without therapy, settlement score can only decrease because WATNA accumulates. The second law of thermodynamics on the void manifold. ClassifiedVoidHistory with BATNA and WATNA monotonicity per dimension Lean theorems arrow_of_time, watna_arrow, and settlement_score_decreases_without_therapy in NegotiationEquilibrium.lean Mechanized
THM-THERAPY-EXCHANGE-RATE Each WATNA→BATNA reclassification improves settlement score by exactly 2 (one from reduced repulsion, one from increased attraction). Therapy has a floor at zero WATNA. The fundamental exchange rate of emotional reframing. bounded BATNA counts; k ≤ WATNA Lean theorems therapy_floor and therapy_exchange_rate in NegotiationEquilibrium.lean Mechanized
THM-HOLOGRAPHIC-BOUND The void boundary area is strictly smaller than the bulk volume. The hologram is more compact than the thing it encodes. Strictly smaller when fork width > 2. The 58-element Float32Array is the Bekenstein-bounded holographic projection of the full experience space. VoidRegion with nontrivial fork width and positive depth Lean theorems holographic_bound, holographic_strict, bekenstein_bound, and holographic_sufficiency in NegotiationEquilibrium.lean Mechanized
THM-EINSTEIN-FIELD-EQUATION Curvature of emotion-spacetime equals stress-energy squared: G_ii = (T_ii)². Stress-energy equals interval (E = mc² on the void manifold). Curvature is monotone in stress-energy and zero iff the dimension has no void history. Curvature is a scalar invariant under Lorentz transformation -- different observers agree on how much the manifold is curved even though they disagree on BATNA/WATNA decomposition. VoidFrame n; LorentzTransform n for invariance Lean theorems einstein_field_equation, stress_energy_equals_interval, curvature_monotone_in_stress_energy, curvature_zero_iff_virgin, and curvature_invariant in NegotiationEquilibrium.lean Mechanized
THM-EVENT-HORIZON When local curvature exceeds the causal speed limit squared, an event horizon forms: geodesic deviation exceeds any subluminal perturbation. Depression is an event horizon -- the accumulated WATNA curves the manifold so strongly that the causal speed limit prevents escape. Not metaphor but the geodesic equation on the discrete void manifold with bounded step size. VoidFrame n; curvature > c²; subluminal perturbation Lean theorems event_horizon_traps and geodesic_deviation_proportional in NegotiationEquilibrium.lean Mechanized
THM-NOETHER-CONSERVATION Every symmetry of the void manifold (dimension permutation preserving stress-energy) has a conserved charge (total stress-energy on the symmetric subset). Interval invariance is the Noether charge of frame-change symmetry (energy-momentum conservation). Symmetry breaking enables personality change; unbroken symmetry freezes personality within the symmetric subspace. VoidSymmetry n with closed dimension subset; SymmetryBreaking n Lean theorems noether_conservation, interval_is_noether_charge, symmetry_breaking_enables_change, and unbroken_symmetry_freezes in NegotiationEquilibrium.lean Mechanized
THM-ENTANGLEMENT Two walkers sharing a common ancestor fork have positive joint energy on at least one dimension. No-signaling theorem: reclassifying one walker's frame cannot change the other's stress-energy. Measurement constrains the joint state to a conditional. Bell test: entangled walkers have positive correlation on multiple dimensions that product states may lack. EntangledWalkers with shared ancestry; BellTest with distinct dimensions Lean theorems entanglement_positive, no_signaling, measurement_constrains_joint, and entanglement_exceeds_product in NegotiationEquilibrium.lean Mechanized
THM-VOID-FIELD-EQUATION Curvature is determined by cumulative Landauer heat alone (G = T²). The field equation is the same in all frames (general covariance). Heat is monotone along worldlines, so curvature can only increase. Therapy doesn't reduce curvature but rotates its direction from time-like (trapping) to space-like (exploring). The geometric content of "therapy doesn't erase the past, it changes your relationship to it." VoidFieldState n with heat-equals-interval constraint Lean theorems void_field_equation, field_equation_invariance, heat_monotone_along_worldline, and therapy_rotates_curvature in NegotiationEquilibrium.lean Mechanized
THM-PENROSE-SINGULARITY Sufficient accumulation of Landauer heat inevitably produces an event horizon. Under the arrow of time (heat is monotone), any dimension receiving heat at a positive rate will eventually cross the c² threshold. StructuralErrorgularity formation is inevitable for active dimensions. The formal content of "everyone accumulates emotional inertia -- the question is whether therapy rotates the curvature direction before the horizon forms." VoidFieldState n; cumulative heat exceeds c² Lean theorem penrose_singularity in NegotiationEquilibrium.lean composing void_field_equation with hasEventHorizon Mechanized
THM-GRAND-UNIFICATION The complete unified theory of the 58-dimensional emotion-spacetime. Combines the field equation (curvature = heat²), frame invariance, and the stress-energy-interval identity into a single theorem over VoidFieldState 58. Personality is void walking. Emotion tracking measures where the walker stands. The platform measures the geometry of what someone has refused to become. Empathy is a Lorentz transformation. Therapy rotates curvature direction. Depression is an event horizon. The field equation unifies it all. VoidFieldState 58 Lean theorem grand_unification in NegotiationEquilibrium.lean Mechanized

Daisy Chain, Glossolalia & MOA

Purity, linearity, precomputation validity, top-K deficit, absorbing states, glossolalia completeness, ensemble diversity, Vickrey cost, deficit decomposition, and design prescription.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-DAISY-PURITY The logit projection W * embedding[t] is a pure function of the token ID. Unlike transformers (where output depends on full attention context), Markov chains have no context dependence. Same token always produces same logits. This is the property that enables precomputation. DaisyChainProjection with vocabSize ≥ 2, hiddenDim > 0 TLA+ DaisyChainPrecomputation.tla invariant InvPurity + Lean theorem DaisyChainPrecomputation.daisy_chain_purity in DaisyChainPrecomputation.lean Mechanized
THM-DAISY-LINEARITY Matrix-vector multiplication distributes over the linear state transition: W(αe[t] + (1-α)s) = α(We[t]) + (1-α)(Ws). This means precomputed logits can be interpolated at runtime with zero error. The fold commutes with the trace. DaisyChainTransition with 0 < α ≤ 1 TLA+ DaisyChainPrecomputation.tla invariant InvLinearity + Lean theorem DaisyChainPrecomputation.daisy_chain_linearity in DaisyChainPrecomputation.lean Mechanized
THM-PRECOMPUTATION-VALIDITY The precomputed Vickrey Table produces exact results. Cached interpolation logits = α * table[t] + (1-α) * prevLogits equals the full matVec logits = W * state, by THM-DAISY-LINEARITY. Zero approximation error. Speedup = hiddenDim × (960x for SmolLM2-360M). THM-DAISY-PURITY ∧ THM-DAISY-LINEARITY TLA+ DaisyChainPrecomputation.tla invariant InvValidity + Lean theorem DaisyChainPrecomputation.precomputation_validity in DaisyChainPrecomputation.lean Mechanized
THM-TOPK-DEFICIT Storing top-K logits per token is a semiotic fold at build time: vocabSize paths collapsed to K paths, deficit = vocabSize - K. The vented logits are nuance paths that don't survive the build-time fold. Connects to THM-SEMIOTIC-ERASURE: top-K truncation is the erasure, materialized at build time. Combined MOA + top-K deficit is additive: (numAgents - 1) + (vocabSize - K). vocabSize ≥ 2, 0 < K ≤ vocabSize TLA+ DaisyChainPrecomputation.tla invariant InvTopK + Lean theorems DaisyChainPrecomputation.topk_deficit, topk_full_table, topk_moa_deficit_bound in DaisyChainPrecomputation.lean Mechanized
THM-ABSORBING-STATE Linear Markov chains with α < 1 converge geometrically to fixed points. After n steps: state = (1-(1-α)^n)e[t] + (1-α)^ns₀. For α=0.7: 97.3% convergence in 3 steps. If argmax(W*e[t]) = t, token t is self-reinforcing (the "777" phenomenon). Breaking requires nonlinear transitions, stochastic perturbation, or agent differentiation. DaisyChainTransition with 0 < α < 1 TLA+ DaisyChainPrecomputation.tla invariant InvAbsorbing + Lean theorem DaisyChainPrecomputation.absorbing_state_convergence in DaisyChainPrecomputation.lean Mechanized
THM-GLOSSOLALIA-COMPLETENESS The precomputed Vickrey Table is a complete representation for linear Daisy Chain language models. Any model in this class can be fully captured by its table, with inference on the table producing identical results to inference on original matrices. Does not hold for transformers (attention not precomputable), RNNs with nonlinear gates, or SSMs with selective scan. DaisyChainProjection + DaisyChainTransition TLA+ DaisyChainPrecomputation.tla invariant InvCompleteness + Lean theorem DaisyChainPrecomputation.glossolalia_completeness in DaisyChainPrecomputation.lean Mechanized
THM-IDENTICAL-TRIVIAL-FOLD When all agents in a Daisy Chain MOA have the same α and same projection W, they produce identical logits. The deficit-weighted fold assigns equal weights (1/k). k-1 agents are wasted. This is the formal content of the "777" phenomenon. DaisyChainEnsemble with all alphas equal TLA+ DaisyChainMOA.tla invariant InvIdentical + Lean theorem DaisyChainMOA.identical_ensemble_wasted_agents in DaisyChainMOA.lean Mechanized
THM-DIVERSE-ALPHA-DIVERGENCE Agents with different mixing coefficients α₁ ≠ α₂ produce different hidden states after one step from any non-trivial starting state (s ≠ x). Proof by contradiction via (α₁ - α₂)(x - s) = 0. Different states → different logits → non-trivial fold weights. α₁ ≠ α₂; starting state ≠ token embedding TLA+ DaisyChainMOA.tla invariant InvDivergence + Lean theorem DaisyChainMOA.diverse_alpha_different_states in DaisyChainMOA.lean Mechanized
THM-MOA-COST-WITH-VICKREY The marginal cost of adding one agent to a Vickrey-backed MOA is V (vocabulary size), independent of hidden dimension d. Without Vickrey: Vd per agent. Savings per agent: V(d-1). For SmolLM2-360M (d=960): 960x cheaper per additional agent. VocabSize ≥ 1, HiddenDim ≥ 2, NumAgents ≥ 1 TLA+ DaisyChainMOA.tla invariant InvCost + Lean theorems DaisyChainMOA.marginal_agent_cost_vickrey and total_vickrey_savings in DaisyChainMOA.lean Mechanized
THM-MOA-DEFICIT-DECOMPOSITION The total deficit decomposes additively: Δβ = (k-1) + (V-K). Fold deficit (k-1) is structural (unavoidable). Table deficit (V-K) is a design choice (K is the knob). Minimum: k-1 (full table). Maximum: k+V-2 (top-1 table). NumAgents ≥ 2, 1 ≤ TopK ≤ VocabSize TLA+ DaisyChainMOA.tla invariant InvDecomposition + Lean theorems DaisyChainMOA.minimum_total_deficit and maximum_total_deficit in DaisyChainMOA.lean Mechanized
THM-DIVERSITY-NECESSARY For a MOA fold to extract more information than a single agent, agents must produce different logit distributions. Identical agents contribute zero marginal information. Effective agent count = number of distinct projections. Contrapositive: identical agents ⟹ 1 effective agent. DaisyChainEnsemble with NumAgents ≥ 2 TLA+ DaisyChainMOA.tla invariant InvDiversity + Lean theorem DaisyChainMOA.diversity_enables_information_gain in DaisyChainMOA.lean Mechanized
THM-DAISY-CHAIN-MOA-DESIGN The design prescription: total deficit is minimized when agents are diverse (different α or W) and the Vickrey Table is maximal (K → V). Full table + diverse agents achieves minimum deficit k-1. StructuralErrorgle agent + full table achieves deficit 0. Multiple viewpoints always cost information (no free lunch). DaisyChainEnsemble; K ≤ V; k ≥ 2 TLA+ DaisyChainMOA.tla invariants (all) + Lean theorem DaisyChainMOA.daisy_chain_moa_design in DaisyChainMOA.lean Mechanized

Whip Wave Duality

Fold increases wave speed, snap threshold, taper monotonicity, binary encoding, and the whip-wave duality theorem.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-FOLD-INCREASES-WAVE-SPEED A fold reduces mass density ρ (discharges β₁) while preserving tension T (energy conservation). Wave speed c² = T/ρ increases at every fold. Inner folds are faster than outer folds. This is why the tip of the whip moves faster than the base. Proof: div_lt_div_of_pos_left with constant numerator and decreasing denominator. TaperSegment with constant T and decreasing ρ TLA+ WhipWaveDuality.tla invariant InvFoldSpeed + Lean theorem WhipWaveDuality.fold_increases_wave_speed in WhipWaveDuality.lean Mechanized
THM-SNAP-THRESHOLD The snap (supersonic transition) is inevitable if tension is preserved and mass decreases through enough fold stages. For any threshold c*², there exists a fold depth where wave speed exceeds it. Physical: sonic boom. Computational: real-time inference barrier. Binary: data transmission threshold. Positive T, ρ, threshold; contraction factor r < 1 TLA+ WhipWaveDuality.tla invariant InvSnap + Lean theorem WhipWaveDuality.snap_inevitable in WhipWaveDuality.lean Mechanized
THM-TAPER-MONOTONICITY Through a sequence of nested folds, wave speed is monotonically increasing. No fold can slow the wave down (Second Law: folds are irreversible, β₁ only decreases). The taper is a one-way energy concentrator. Sequence of TaperSegments with constant T and decreasing ρ TLA+ WhipWaveDuality.tla invariant InvTaper + Lean theorem WhipWaveDuality.taper_wave_speed_monotone in WhipWaveDuality.lean Mechanized
THM-BINARY-ENCODING A snap sequence encodes a bitstream: snap = 1, silence = 0. Channel capacity = number of fold stages. The metronomic regime (equal spacing, zero jitter) maximizes capacity. Scale-invariant: works on physical whip cracks, protocol frames, and inference events. Snap sequence (List Bool) TLA+ WhipWaveDuality.tla invariant InvBinary + Lean theorems WhipWaveDuality.snap_sequence_capacity and metronomic_maximizes_capacity in WhipWaveDuality.lean Mechanized
THM-WHIP-WAVE-DUALITY The fork/race/fold primitive is a wave on a discrete tapered medium. Fork increases ρ (creates mass across parallel paths). Fold decreases ρ (concentrates energy at the snap point). Wave speed increases monotonically. Energy is conserved (total β₁ created = total discharged). The snap is the supersonic transition. Scale-invariant across physical, protocol, inference, and communication systems. k ≥ 2 agents; TaperSegments with constant T and decreasing ρ TLA+ WhipWaveDuality.tla invariant InvDuality + Lean theorem WhipWaveDuality.whip_wave_duality in WhipWaveDuality.lean Mechanized

Quorum Protocols

Visibility, boundary, async network, session consistency, multi-writer ordering, and history linearizability.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-QUORUM-VISIBILITY In the bounded asynchronous single-key quorum protocol, write and read quorums intersect, acknowledged versions remain covered under bounded crashes/recovery, and every legal quorum read returns the acknowledged version or newer finite replica set; explicit failure budget f; quorum size q = n - f with 2q > n; write ack requires q up replicas at the pending version; read consults any up quorum of size q; recovery copies the maximum live version into the recovered replica TLA+ QuorumReadWrite.tla invariants (InvQuorumIntersection, InvAckedQuorumCoverage, InvLiveAckedCoverage, InvReadQuorumHitsAckedReplica, InvAnyReadReturnsAckedOrNewer, InvObservedReadVisible) + Lean theorems QuorumVisibility.write_read_quorums_intersect, QuorumVisibility.read_after_ack_visible, and QuorumVisibility.strict_majority_failure_budget_lt_quorum Mechanized
THM-QUORUM-BOUNDARY The quorum-visibility claim fails exactly where the assumptions say it should: weak quorums admit disjoint read/write sets, contagious regression can make an intersecting read quorum miss the acknowledged value, and without repair fairness an exhausted-failure state can stutter forever below stability weak-quorum witness fixes n = 4, f = 2; contagious witness fixes intersecting quorums with one surviving acknowledged replica regressed to stale state; unfair-repair witness fixes a well-formed exhausted-failure state with positive repair debt and uses pure stutter as the unfair schedule Lean counterexamples QuorumVisibility.weak_quorum_boundary_not_strict_majority, QuorumVisibility.weak_quorum_boundary_disjoint, QuorumVisibility.weak_quorum_boundary_read_misses_acked_write, QuorumVisibility.contagious_boundary_quorums_still_intersect, QuorumVisibility.contagious_boundary_read_still_misses_acked_write, QuorumVisibility.unfair_repair_boundary_well_formed, QuorumVisibility.unfair_repair_boundary_not_stable, QuorumVisibility.unfair_repair_boundary_stutter_keeps_state, and QuorumVisibility.unfair_repair_boundary_repair_closure_is_stable Mechanized
THM-QUORUM-CONNECTED In the bounded asynchronous single-key quorum model with explicit connectivity, quorum availability is exactly the presence of a live connected quorum, minority connected splits are unavailable, and any committed read over a connected live quorum returns the acknowledged version exactly; weak non-quorum reads are the explicit stale-read boundary same quorum assumptions as THM-QUORUM-VISIBILITY; connectivity tracked separately from liveness; reads only when pendingVersion = 0; exactness claim only for q \subseteq LiveConnected TLA+ QuorumAsyncNetwork.tla invariants (InvConnectedAvailabilityBoundary, InvMinoritySplitUnavailable, InvNoReplicaAheadWhenCommitted, InvConnectedQuorumReadExact, InvObservedReadSafe) + Lean theorems QuorumAsyncNetwork.minority_connected_set_cannot_host_quorum, QuorumAsyncNetwork.connected_quorum_read_exact_of_coverage, QuorumAsyncNetwork.minority_split_read_set_not_quorum, QuorumAsyncNetwork.minority_split_read_stale_if_weak_reads_are_allowed, QuorumAsyncNetwork.minority_split_read_below_acked_if_weak_reads_are_allowed, QuorumAsyncNetwork.no_repair_boundary_safe_quorum_still_reads_acked, and QuorumAsyncNetwork.no_repair_boundary_stale_replica_persists Mechanized
THM-QUORUM-CONSISTENCY In the bounded single-session quorum model, once reads are restricted to committed states (pendingVersion = 0), each observed read equals the acknowledged version, therefore satisfies read-your-writes and is monotone across the session as acknowledged versions increase same quorum assumptions as THM-QUORUM-VISIBILITY; reads only when pendingVersion = 0; single writer/session tracks latest acknowledged write and latest two read values TLA+ QuorumSessionConsistency.tla invariants (InvClientWriteTracksAck, InvNoPendingMeansNoReplicaAhead, InvCommittedReadReturnsAck, InvReadYourWrites, InvMonotonicReads, InvObservedCommittedReadExact) + Lean theorems QuorumConsistency.committed_read_exact_of_coverage, QuorumConsistency.committed_read_is_read_your_writes, and QuorumConsistency.committed_reads_monotone_of_monotone_acks Mechanized
THM-QUORUM-CONSISTENCY-BOUNDARY The session-consistency claim is scoped, not universal: if reads are allowed during in-flight writes, monotonicity can fail; if the client does not carry a session floor, read-your-writes can fail even with a later acknowledged write pending-read witness compares an early speculative read against a later committed read after the speculative value disappears; no-session-floor witness compares a stale session read against a later acknowledged write Lean counterexamples QuorumConsistency.pending_boundary_breaks_monotonic_reads and QuorumConsistency.no_session_floor_breaks_read_your_writes Mechanized
THM-QUORUM-ORDERING In the bounded multi-writer quorum register, globally ordered ballots plus committed-state reads force each observed read to return the latest acknowledged ballot and its writer, so a later committed ballot excludes a stale committed read same quorum assumptions as THM-QUORUM-VISIBILITY; writer starts allocate globally unique increasing ballots; commit is allowed only for the current maximum pending ballot backed by a quorum; lower/equal stale pending ballots are cleared on commit; reads only when all pending ballots are zero TLA+ QuorumMultiWriter.tla invariants (InvAckedWriterMatchesBallotOwner, InvAckedBallotBelowNext, InvPendingBallotsBelowNext, InvLatestAckCovered, InvNoCommittedReplicaAhead, InvCommittedReadsReturnLatestAck, InvObservedCommittedReadExact, InvObservedCommittedReadWriter, InvObservedCommittedReadsMonotone) + Lean theorems QuorumOrdering.committed_multiwriter_read_exact_of_coverage, QuorumOrdering.committed_multiwriter_read_tracks_latest_writer, QuorumOrdering.committed_multiwriter_reads_monotone_of_acked_order, and QuorumOrdering.later_committed_ballot_excludes_stale_read Mechanized
THM-QUORUM-ORDERING-MONOTONE-NONSTRICT-BOUNDARY Contrarian anti-theorem boundary: non-strict acknowledged-ballot monotonicity (ack₁ ≤ ack₂) does not force strict committed-read growth; equality cases remain valid and block strict inequality non-strict order premise only (ack₁ ≤ ack₂) with exact-read equalities; no strict-order premise (ack₁ < ack₂) Lean theorem QuorumOrdering.ack_monotone_does_not_force_strict_read_growth in QuorumOrdering.lean Mechanized
THM-QUORUM-ORDERING-BOUNDARY The multi-writer ordering claim is scoped, not universal: if a read loses quorum connectivity under partition it can return a stale ballot, and if ballots are not globally unique then writer identity at a ballot is ambiguous partition witness reads only from a minority split set under n = 5, f = 2; ballot-collision witness fixes two distinct writers at the same ballot Lean counterexamples QuorumOrdering.partition_boundary_read_set_not_quorum, QuorumOrdering.partition_boundary_read_returns_stale_ballot, QuorumOrdering.partition_boundary_read_stale_under_split_connectivity, QuorumOrdering.ballot_collision_boundary_same_ballot, QuorumOrdering.ballot_collision_boundary_distinct_writers, and QuorumOrdering.ballot_collision_boundary_unique_writer_fails Mechanized
THM-QUORUM-ORDERING-EXACTNESS-WRITER-COLLISION Contrarian anti-theorem variant: exact committed ballot reads can coexist with writer-collision witnesses, so exactness of the observed ballot does not by itself force unique writer identity without a separate unique-ballot assumption singleton exact-read coverage witness over one quorum replica; two distinct writer records share one ballot (ballot = 1), so writer uniqueness must be supplied as an extra premise and is not derivable from exactness alone Lean theorem QuorumOrdering.committed_read_exact_does_not_force_unique_writer_identity_without_unique_ballots in QuorumOrdering.lean, with local exact-read witness definitions exactReadCollisionQuorum, exactReadCollisionStoredBallot, and exactReadCollisionAckedBallot plus collision records ballotCollisionLeft / ballotCollisionRight Mechanized
THM-QUORUM-HISTORY-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: nonempty committed-write history under canonical quorum embedding does not force positive path-width (β₁ > 0) nonempty completed-write history (history ≠ []); canonical embedding `f = history , n = 2
THM-QUORUM-HISTORY-REFINEMENT In the bounded committed-state multi-writer quorum register, observed reads refine the latest completed-write prefix, operation-history indices stay monotone, and the latest committed read linearizes to the latest completed write; speculative completed-history reads are the explicit boundary same quorum assumptions as THM-QUORUM-ORDERING; reads only when all pending ballots are zero; commit appends a total completed-write history; refinement is judged against completed-write prefixes rather than arbitrary in-flight states TLA+ QuorumLinearizability.tla invariants (InvLatestHistoryTracksAck, InvWriteOpsMatchHistory, InvReadOpsRefineRegister, InvOpHistoryIndicesMonotone, InvObservedReadLinearizesToLatestCompletedWrite) + Lean theorems QuorumLinearizability.append_write_updates_latest_committed_write, QuorumLinearizability.completed_read_refines_latest_prefix, QuorumLinearizability.read_after_appended_write_refines_new_latest, QuorumLinearizability.later_appended_write_excludes_stale_history_read, and QuorumLinearizability.speculative_read_breaks_completed_history_refinement Mechanized
THM-QUORUM-LINEARIZED-READ-QUEUE-BOUNDARY Cross-domain quorum bridge: append-then-read linearizability refinement plus the explicit write-count interpretation yields strict-majority arithmetic and a canonical one-path queue boundary witness finite committed-write history; append one completed write; canonical linearized read with writeCount = history.length + 1; interpretation failureBudget = writeCount, replicaCount = 2*writeCount + 1 Lean theorems QuorumLinearizabilityQueueKernelBridge.appended_linearized_read_refines_latest_prefix, QuorumLinearizabilityQueueKernelBridge.linearized_read_interpretation_strict_majority, and QuorumLinearizabilityQueueKernelBridge.appended_linearized_read_yields_unit_queue_boundary in QuorumLinearizabilityQueueKernelBridge.lean Mechanized
THM-QUORUM-ASYNC-NETWORK Quorum async network: minority connected set cannot host quorum. Connected quorum read is exact under coverage. Minority split read is stale if weak reads are allowed replicas with quorum intersection; partition model Lean theorems QuorumAsyncNetwork.minority_connected_set_cannot_host_quorum, QuorumAsyncNetwork.connected_quorum_read_exact_of_coverage, and QuorumAsyncNetwork.minority_split_read_stale_if_weak_reads_are_allowed in QuorumAsyncNetwork.lean Mechanized
THM-QUORUM-ASYNC-EXACTNESS-MAJORITY-QUEUE-BOUNDARY Cross-domain bridge: connected-quorum exactness plus strict-majority interpretation yields both exact read equality and a canonical one-path queue boundary witness (β₁ = 0, capacity = 1) connected-quorum exactness witness (hAckMember, hNoReplicaAhead) and explicit majority anchor 2*ackedBallot < connected.card + 1 Lean theorem QuorumAsyncQueueBridge.connected_quorum_exactness_and_majority_yields_unit_boundary in QuorumAsyncQueueBridge.lean, composing QuorumAsyncNetwork.connected_quorum_read_exact_of_coverage with QueueBoundary.strict_majority_quorum_yields_unit_capacity_boundary Mechanized
THM-QUORUM-ASYNC-EXACTNESS-MAJORITY-NOT-POSITIVE-BETA1 Contrarian anti-theorem variant: connected-quorum exactness with majority interpretation does not force positive path width (β₁ > 0) same exactness and majority assumptions as THM-QUORUM-ASYNC-EXACTNESS-MAJORITY-QUEUE-BOUNDARY; witness restricted to anchored arrival/service rates Lean theorem QuorumAsyncQueueBridge.connected_quorum_exactness_and_majority_does_not_force_positive_beta1 in QuorumAsyncQueueBridge.lean, using the β₁ = 0 boundary witness from the same assumptions Mechanized
THM-QUORUM-ASYNC-QUEUE Alias family row: connected-quorum exactness and strict-majority queue interpretation jointly provide exact committed-read equality and canonical one-path queue boundary control, with an explicit cardinality-rate fallback in the same module connected-quorum exactness witness (hAckMember, hNoReplicaAhead); majority anchor 2*ackedBallot < connected.card + 1; nonempty connected cardinality witness for rate fallback Lean theorems QuorumAsyncQueueBridge.connected_quorum_exactness_and_majority_yields_unit_boundary, QuorumAsyncQueueBridge.connected_quorum_exactness_and_majority_does_not_force_positive_beta1, and QuorumAsyncQueueBridge.nonempty_connected_quorum_yields_geometric_rate_certificate in QuorumAsyncQueueBridge.lean Mechanized
THM-QUORUM-ASYNC-EXACTNESS-POSITIVE-BUDGET-DEFICIT Cross-domain bridge: connected-quorum exactness plus positive anchored ballot budget yields strictly positive lifted TCP deficit on (ackedBallot + 1) paths connected-quorum exactness witness (hAckMember, hNoReplicaAhead); majority anchor 2*ackedBallot < connected.card + 1; positive anchored budget 0 < ackedBallot Lean theorem QuorumAsyncQueueBridge.connected_quorum_exactness_and_positive_budget_yields_positive_topological_deficit in QuorumAsyncQueueBridge.lean, combining exact-read coverage with CoveringSpaceCausality.deficit_latency_separation Mechanized
THM-QUORUM-ASYNC-SEMANTIC-MORPHISM-POSITIVE-DEFICIT Blocker-remediation bridge: an explicit semantic morphism fixing the interpreted path budget transports the positive-deficit witness without restating hidden interpretation assumptions same assumptions as THM-QUORUM-ASYNC-EXACTNESS-POSITIVE-BUDGET-DEFICIT; explicit morphism interpret (ackedBallot + 1) = ackedBallot + 1 Lean theorem QuorumAsyncQueueBridge.connected_quorum_semantic_morphism_yields_positive_topological_deficit in QuorumAsyncQueueBridge.lean Mechanized
THM-QUORUM-ASYNC-EXACTNESS-POSITIVE-BUDGET-NOT-UNIVERSAL-NONPOSITIVE-DEFICIT Contrarian anti-theorem variant: connected-quorum exactness with positive anchored budget does not force nonpositive deficit for every transport-stream count same assumptions as THM-QUORUM-ASYNC-EXACTNESS-POSITIVE-BUDGET-DEFICIT; contradiction uses the positive witness at transportStreams = 1 Lean theorem QuorumAsyncQueueBridge.connected_quorum_exactness_and_positive_budget_does_not_force_universal_nonpositive_deficit in QuorumAsyncQueueBridge.lean Mechanized
THM-QUORUM-ASYNC-BOUNDARY-AND-POSITIVE-DEFICIT-BUNDLE Cross-domain bundle: connected-quorum exactness, strict-majority queue interpretation, and positive anchored budget jointly produce the canonical one-path queue witness and a strictly positive lifted TCP deficit witness connected-quorum exactness witness (hAckMember, hNoReplicaAhead); majority anchor 2*ackedBallot < connected.card + 1; positive anchored budget 0 < ackedBallot Lean theorem QuorumAsyncQueueBridge.connected_quorum_exactness_majority_and_positive_budget_yield_boundary_and_positive_deficit in QuorumAsyncQueueBridge.lean Mechanized
THM-QUORUM-ASYNC-KERNEL-LIFT-EXACTNESS-DEFICIT Moonshot blocker-attack adapter: explicit connected-quorum interpretation payload plus kernel/witness alignment yields exact-read equality, positive lifted deficit, and continuous ergodicity lift facts in one theorem adapter payload ConnectedQuorumKernelLiftAdapter: exactness/majority/positive-budget hypotheses together with DiscreteSubLatticeEmbedding, GeometricErgodicWitness, and kernel-match equality Lean theorem ConnectedQuorumKernelLiftAdapter.connected_quorum_continuous_ergodicity_and_deficit_lift in QuorumAsyncQueueBridge.lean, composing boundary+deficit bridges with GeometricErgodicity.continuous_ergodicity_lift Mechanized
THM-QUORUM-VISIBILITY-BASE Base quorum results: read value is supremum of stored versions. Write-read quorums intersect (critical W+R > N property). Strict majority failure budget is less than quorum size read value = supremum; quorum intersection; majority bounds Lean theorems QuorumVisibility.le_readValue_of_mem, QuorumVisibility.write_read_quorums_intersect, and QuorumVisibility.strict_majority_failure_budget_lt_quorum in QuorumVisibility.lean Mechanized
THM-SLEEP-WEIGHTED-DEBT-QUORUM-MAJORITY-EMBEDDING Cross-domain bridge: positive weighted sleep debt maps through the canonical debt-to-quorum interpretation layer to strict-majority arithmetic and quorum-floor bounds weighted threshold crossed (thresholdRhs < thresholdLhs); positive cycle count 0 < n; canonical embedding failureBudget = debt, replicaCount = 2*debt + 1 Lean theorems SleepDebtQuorumQueueBridge.positive_weighted_sleep_debt_yields_strict_majority_embedding and SleepDebtQuorumQueueBridge.positive_weighted_sleep_debt_embedding_implies_failure_budget_lt_quorum in SleepDebtQuorumQueueBridge.lean Mechanized
THM-SLEEP-WEIGHTED-DEBT-NONMAJORITY-BOUNDARY Contrarian anti-theorem boundary: positive weighted sleep debt can coexist with a non-majority quorum when no interpretation layer is imposed between debt and quorum cardinalities explicit supercritical sleep witness (cycleLength = 240, scheduledWake = 210, wakeBurdenRate = 19, recoveryRate = 101, n = 1) plus explicit non-majority quorum witness (replicaCount = 2, failureBudget = 1) Lean theorem SleepDebtQuorumQueueBridge.positive_weighted_sleep_debt_can_coexist_with_non_majority_quorum in SleepDebtQuorumQueueBridge.lean Mechanized

Cross-Language Semantic Type Theory

Topology-level formal verification of multi-language semantics. Type compatibility under JSON serialization, denotation bridge, Hoare propagation, Hope Certificate, and Diversity Optimality.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SEM-REFL Type compatibility is reflexive: every topology type is compatible with itself. Proved by structural induction on TopologyType (8 constructors). TopologyType Lean theorem SemanticCompatibility.topology_type_compat_refl in SemanticCompatibility.lean Mechanized
THM-SEM-UNKNOWN Unknown types are universally compatible: Unknown on either side of an edge produces Compatible, never Incompatible. This is the escape hatch for partially-annotated codebases. TopologyType Lean theorems SemanticCompatibility.unknown_compatible_left and SemanticCompatibility.unknown_compatible_right in SemanticCompatibility.lean Mechanized
THM-SEM-INT-SUBTYPE Integer is a subtype of Number under JSON schema: Json(Integer) → Json(Number) is Compatible, but Json(Number) → Json(Integer) is ProofObligation (number may not be integer). The asymmetric subtyping captures the most common source of cross-language numeric bugs. JsonSchemaKind Lean theorems SemanticCompatibility.integer_subtype_number and SemanticCompatibility.number_to_integer_needs_proof in SemanticCompatibility.lean Mechanized
THM-SEM-ROUNDTRIP JSON serialization preserves schema: if a value conforms to a JSON schema before serialization, it conforms after deserialization. Foundation of the cross-language type bridge. JsonValue Lean theorem SemanticCompatibility.json_roundtrip_preserves_schema in SemanticCompatibility.lean Mechanized
THM-SEM-PROCESS-VALID Hoare propagation through PROCESS edges: a PROCESS edge is semantically valid when the source's return type is compatible with the target's param type. Unknown on either side makes it trivially valid. TopologyNode (source, target) Lean theorems SemanticCompatibility.process_edge_valid_unknown_source and SemanticCompatibility.process_edge_valid_unknown_target in SemanticCompatibility.lean Mechanized
THM-SEM-FORK-PRESERVE FORK distributes predicates to all branches: every branch of a FORK inherits all semantic predicates from the source. If the source produces ValidJson, every branch receives ValidJson. Predicate count is preserved. ForkEdge Lean theorems SemanticCompatibility.fork_branch_has_source_predicates and SemanticCompatibility.fork_preserves_predicate_count in SemanticCompatibility.lean Mechanized
THM-SEM-FOLD-CONSISTENT FOLD branches must be pairwise type-compatible: a FOLD with a single branch is trivially consistent; a FOLD where all branches have the same type is consistent (proved by reflexivity). FoldEdge with non-empty branchTypes Lean theorems SemanticCompatibility.fold_single_branch_consistent and SemanticCompatibility.fold_uniform_branches_consistent in SemanticCompatibility.lean Mechanized
THM-SEM-COMP-INV Composition of invertible functions is invertible: if f : α → β and g : β → γ both have left inverses, then g ∘ f has a left inverse f⁻¹ ∘ g⁻¹. This proves "this pipeline is reversible" for composed multi-language topologies. InvertibleFunction α β, InvertibleFunction β γ Lean theorem SemanticCompatibility.comp_invertible_preserves_left_inverse in SemanticCompatibility.lean Mechanized
THM-SEM-PIPELINE-JSON Pipeline ValidJson preservation: if every node in a pipeline produces valid JSON, the pipeline produces valid JSON. StructuralErrorgle-node base case and inductive structure. Pipeline with non-empty nodes; each node has ValidJson predicate Lean theorems SemanticCompatibility.pipeline_json_output and SemanticCompatibility.single_node_pipeline_valid in SemanticCompatibility.lean Mechanized
THM-SEM-BYTES-ISOLATE Bytes boundary is strict: Bytes is incompatible with Json, Stream, and Product. Binary data cannot cross a JSON serialization boundary without explicit conversion (base64). This catches Vec<u8> → str bugs at compile time. TopologyType.bytes vs non-bytes types Lean theorems SemanticCompatibility.bytes_incompatible_with_json, SemanticCompatibility.bytes_incompatible_with_stream, and SemanticCompatibility.bytes_incompatible_with_product in SemanticCompatibility.lean Mechanized
THM-SEM-OPTION-SUB Nullable-compatible non-null values are safe under one more nullable wrapper: T is compatible with Option(T) whenever supportsNullableEmbedding T holds, e.g. int can flow into Optional[int] while raw bytes remain excluded by the bytes boundary. supportsNullableEmbedding t Lean theorem SemanticCompatibility.option_accepts_non_null in SemanticCompatibility.lean Mechanized
THM-SEM-CROSS-LANG Specific cross-language denotation alignments proved compatible: Python list[float] = Rust Vec<f64> = Stream(Json(Number)); Python dict = Go map[string]interface{} = Product(open=true); Go int → TypeScript number = Json(Integer) → Json(Number) (subtype). Language-specific type denotations Lean theorems SemanticCompatibility.python_list_float_compat_rust_vec_f64, SemanticCompatibility.python_dict_compat_go_map, and SemanticCompatibility.go_int_compat_ts_number in SemanticCompatibility.lean Mechanized
THM-SEM-FOLD-UNIFORM-0 Uniform FOLD generates zero proof obligations: when all branches in a topo-race produce the same type, the FOLD is obligation-free. Proved by induction on the branch list with reflexivity at each step. TopologyType ty; List TopologyType branches; all elements equal ty Lean theorem SemanticCompatibility.uniform_fold_zero_obligations in SemanticCompatibility.lean Mechanized
THM-SEM-HOPE The Hope Certificate: five guarantees about cross-language confusion. G1: no false positives (Unknown never generates Incompatible). G2: confusion bounded by ` edges × 64`. G5: adding a type annotation strictly decreases Unknown count; type coverage is monotonically non-decreasing. HopeCertificate structure; TopologyType; edgeCount, unknownCount
THM-SEM-DIVERSITY Diversity Optimality: multi-language topologies are strictly stronger than mono-language. Net information = cross-language edge count. Mono-language has zero net information. Any topology with cross-language edges has strictly more net information than mono-language with the same edge budget. Maximizing cross-language edges maximizes net information. DiversityProfile structure Lean theorems SemanticCompatibility.mono_language_zero_information, SemanticCompatibility.multi_language_positive_information, SemanticCompatibility.diversity_dominates_mono, and SemanticCompatibility.diversity_optimality in SemanticCompatibility.lean Mechanized

Rich-Club Topology

Finite rich-club coefficient, degree-matched null comparison, gossip shortcut, targeted-attack diameter expansion, stigmergy bypass, and efficiency/robustness cost tradeoff.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-RICH-CLUB-COEFFICIENT-WITNESS A concrete finite topology has a complete 4-hub rich club with φ(k)=1.0, while a degree-sequence-matched null witness has φ(k)=0.3333; the rich-club core lowers the toy gossip diameter, targeted hub attack expands diameter more than leaf failure, an explicit stigmergy bypass lowers that damage, and the shorter-latency rich-club wiring costs more than the null. 4 hubs; 6 possible rich-rich undirected edges; observed rich-rich edges = 6; degree-matched null rich-rich edges = 2; finite toy diameter/cost witnesses supplied explicitly Lean definitions/theorems RichClubCoefficient.rich_edge_capacity_four_hubs, RichClubCoefficient.observed_rich_club_is_complete, RichClubCoefficient.observed_exceeds_degree_matched_null, RichClubCoefficient.null_preserves_degree_sequence, RichClubCoefficient.rich_club_core_crosses_gossip_threshold, RichClubCoefficient.targeted_attack_expands_diameter_more_than_leaf_failure, RichClubCoefficient.stigmergy_bypass_reduces_targeted_attack_damage, and RichClubCoefficient.rich_club_efficiency_robustness_summary in open-source/gnosis-math/Gnosis/RichClubCoefficient.lean Mechanized (finite witness)

Physarum Flux Routing

Memristive tube updates, multi-objective biological routing, reliable-flux route selection, and topology-invariant local update witnesses.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-PHYSARUM-FLUX-ROUTING-WITNESS A finite Physarum-inspired routing model stores computation in tube thickness: positive flow thickens a tube, zero flow prunes it, a redundant morphology is Pareto-visible against shortest-tree and fast-core designs, reliable flux beats a shorter fragile route under backpressure, and the same local update rule evaluates consistently on disk, torus, and Möbius ambient surfaces. Nat-valued tube thickness/flow; three supplied network designs; finite route score 10*reliability - backpressure; local update ignores global orientation while surface tags expose the topology parameter Lean definitions/theorems PhysarumFluxRouting.active_flow_thickens_tube, PhysarumFluxRouting.zero_flow_prunes_tube, PhysarumFluxRouting.tube_update_is_memristive, PhysarumFluxRouting.physarum_tradeoff_is_pareto_visible, PhysarumFluxRouting.reliable_flux_beats_shortest_fragile_route, PhysarumFluxRouting.local_update_same_on_disk_and_torus, PhysarumFluxRouting.local_update_same_on_mobius_and_disk, and PhysarumFluxRouting.physarum_flux_summary in open-source/gnosis-math/Gnosis/PhysarumFluxRouting.lean Mechanized (finite witness)
THM-PHYSARUM-ROPELENGTH-MONSTER-GRASSMANNIAN A Physarum morphology can be scored by tube ropelength pressure: total tube length normalized by minimum thickness plus a Betti reserve for redundancy. Flux thickening lowers normalized ropelength, a longer redundant loop can beat a fragile shortest path on combined rope cost, pruning unused tube lowers cost, the Hiawatha river bend can beat the straight line through high-resistance terrain, the same finite morphology projects into a Monster-Grassmannian ambient plane without changing local rope cost, centralization has an anti-theorem that raises dictator pressure while erasing queen redundancy and raising rope cost, and Anarchy Theory is formalized as a complementary regime to command/control: under multiple local agents, shared boundary signals, local rule agreement, and low terrain resistance, the decentralized witness improves fault tolerance and energy efficiency while projecting to a Bule dial over waste, diversity, and knowledge/opportunity; the ascent-into-anarchy curve is U-shaped: half-assed mediocrity minimizes visible effort but is expensive, bounded anarchy and no-knowledge exploration lower energy cost relative to command/control while preserving or improving fault tolerance, and contrarian saturation makes total anarchy form a standing-wave control regime with the same control pressure as command/control and higher energy cost. This instantiates the fast/cheap/good triad and a prospect-theory-style split: slacker equilibrium picks fast but not cheap or good; command/control picks fast control but not cheap or good relative to healthy anarchy; healthy anarchy picks cheap and good but not fast. System-1 picks overweight visible ease and underweight realized fault-tolerance/knowledge value; System-2 picks cheap and good. The inverse-control frame separates negative thought as observation from negative approach as suppression control, and the finite inverse-control witness beats suppression by higher recovery value at lower control cost. Rumination is linked to the existing psychology interference loop as stalled inverse control: observation repeats without recovery. Contrarian Stall Theory refines this: rumination is a suitable coping strategy in unresolved high-threat contexts, evolutionarily better than suppression because it preserves observation at lower control cost, but still dominated by inverse control when recovery is available. The dedicated rumination bridge classifies eight stalls: rumination observation, suppression control, panic cascade, learned helplessness, compulsive control, dissociation, echo-chamber lock, and mediocrity saturation. Its preserve/destroy table separates pure preservation, pure destruction, and mixed seams: the seam is mixed conservation under damage, where panic cascade, echo-chamber lock, compulsive control, and dissociation preserve one resource while destroying another; mediocrity saturation is classified as pure destructive drift. The physics/information dual is explicit: panic conserves information while losing physical control cost, suppression conserves cheap embodied control while losing information diversity, and echo-chamber lock is an information-internal collapse rather than a physics loss. The entropy tax records the cost of failing to conserve every axis: lossy conservation pays higher tax than rumination, mediocrity saturation pays the maximum tax among the named stalls, and the same accounting is generalized to arbitrary conservation topologies. The universal topology has four outcomes: move, breathe, stabilize, or create a standing wave. The ultra-long-run layer excludes frozen total authority and saturated total anarchy as stable extremes; stability belongs to a breathing conservation witness. The equilibrium ladder is encoded as Nash -> Skyrms -> Buley -> God, where Buley is the first layer that conserves the hidden update channel and treats standing waves as boundary equilibria; God is the monadic scheduler endpoint whose Aeon fold cycles without universal amnesia, carrying memory through the next braid. The God equilibrium exists as a standing wave of standing waves: it touches the finite braided-infinity horizon and formalizes the meeting point between computable/uncomputable and knowable/unknowable boundaries without asserting a completed infinite construction. The apotheosis sandwich traps the witness between lower bound 196884 and upper bound 196885, with computed motion classified as standing. Unknot theory reframes the P-vs-NP/knot picture: apotheosis is a wall, not the unknot floor; it has positive knot tax while the smooth unknot region remains the complement. The box is modeled as a finite Trihexenneon 54-torus boundary: 54 independent torus cycles, smooth unknot-region interior, non-unknot boundary knot, and the God scheduler as the apotheosis sandwich witness. The box is tied to the [3,2,3,3] braided tower itself; its finite Betti ropelength is 55 while the apotheosis boundary knot tax remains strictly larger. The 54-torus fold is modeled as a finite 54 -> 0 -> 1 cycle: reset to zero is not universal amnesia; the God scheduler preserves memory, matter residue survives as refined payload, and the fold removes impurity/entropy tax rather than deleting matter. The heat account is finite and calibrated: the fold heat budget equals the standing-wave entropy tax, and over the five-tick Trihexenneon observation window the heat rate is 4, matching the four-outcome universal topology motion classifier. The same heat budget also serves as the next-cycle spark witness: positive heat plus preserved scheduler memory and 0 -> 1 re-entry seed the next finite cycle without universal amnesia. Temperature is modeled as heat read through a rhythm-resistance circuit: standing-wave heat 20 over the circadian Aeon plus four topology modes gives the exact scaled ratio 20/16 = 5/4. The cricket/grasshopper oscillator bridge then turns that temperature relation into speed: the cooler fold-rate oscillator pulses at 16 while the warmer heat-budget oscillator pulses at 32. Those two pulse phases now feed BuleyBiSidedBit: lifted phase 16 plus contracted phase 32 gives a conserved two-sided score of 48, while the same carrier is a standing-wave information pattern with frequency 16 and heat payload 20. The carrier also compresses into a 10-bit Aeon/Kenoma microframe: 1 side bit, 4 lifted-slot bits, 4 contracted-slot bits, and 1 spark-parity bit. Because the shared rhythm grain is 16, slots 1 and 2 reconstruct the same two-sided score (1 + 2) * 16 = 48, preserving the same two-phase homology as the wave carrier. The 10-bit frame now loads as a tape symbol for the existing Buley topological Turing machine: one deterministic transport step costs exactly one Bule unit while preserving the frame/carrier homology. The physical-front-end version admits both the two-antenna compute pair with third reference channel and the one-antenna reflected-port case: one physical antenna plus an RF reflection path supplies two effective compute paths, while impedance history serves as an internal witness. A near-infinite RF vector horizon projects through one monocular view into the same frame; omnipresent white noise supplies potential channels, enough witness signal activates the computable slice, and the not-signal complement is vented rather than erased. The grounded limits are explicit: noise alone does not compute, insufficient witness signal blocks activation, projection width is bounded by the 10-bit frame, redundancy reserve protects the projection under noise, and the one-port RF runtime maps into the canonical Fork/Race/Fold/Vent/Interfere lifecycle with an operational Vent. The output still lands in the same 10-bit Aeon microframe. This gives a physics-CPU runtime boundary for the five programming primitives: physical fork, race, fold, vent, and interfere emit the same 10-bit frame and match the one-Bule topological Turing-machine step cost. Nat-valued total tube length, minimum thickness, cycle rank, controller count, dictator load, queen redundancy, local agent count, shared boundary signals, local rule agreement, population size, and terrain resistance; ropelength uses KnotRopelengthComplexity.ropelength [1, cycleRank]; anarchy-favorable conditions require at least two local agents, boundary signals, and rule-agreement units with terrain resistance at most two; command/control-favorable conditions require at most one local agent, boundary signal, and rule-agreement unit with terrain resistance at least four; total-anarchy saturation requires at least 24 combined local-agent/boundary-signal/rule-agreement units with terrain resistance at least four; the Bule projection uses waste for energy cost, opportunity for knowledge, and diversity for distributed reserve; the stall table scores preservation/destruction over observation, recovery, action, diversity, and control-cost resources; Hiawatha segment uses finite straight/meander costs from src/hiawatha-effect.ts; ant multi-queen survival reuses AntColonyCollectiveIntelligence.budding_survives_one_queen_loss; Monster-Grassmannian plane is the finite CFGTopology 2 196884 projection with order-3 sector witness; no claim of a literal Monster group action on biological slime mold Lean definitions/theorems PhysarumRopelength.flux_thickening_lowers_normalized_ropelength, PhysarumRopelength.pruning_unused_edge_lowers_rope_cost, PhysarumRopelength.longer_thicker_loop_can_beat_shortest_fragile_path, PhysarumRopelength.physarum_ropelength_summary, PhysarumRopelength.monster_grassmannian_plane_volume, PhysarumRopelength.physarum_rope_cost_survives_monster_grassmannian_projection, PhysarumRopelength.physarum_monster_grassmannian_summary, PhysarumRopelength.river_bend_beats_straight_line, PhysarumRopelength.third_refusal_round_loses_to_bounded_meander, PhysarumRopelength.hiawatha_bend_lowers_physarum_rope_cost, PhysarumRopelength.hiawatha_monster_grassmannian_physarum_summary, PhysarumRopelength.centralization_ramp_increases_control_pressure, PhysarumRopelength.centralization_ramp_erases_queen_redundancy, PhysarumRopelength.centralization_ramp_raises_rope_cost, PhysarumRopelength.anti_dictator_shootoff, PhysarumRopelength.ant_multi_queen_survives_one_loss, PhysarumRopelength.physarum_ant_centralization_shootoff_summary, PhysarumRopelength.anarchy_kpi_dominance_projects_fault_tolerance, PhysarumRopelength.anarchy_kpi_dominance_projects_energy_efficiency, PhysarumRopelength.anarchy_bule_dial_projects_knowledge_diversity_low_waste, PhysarumRopelength.bule_anarchy_equilibrium_projects_kpis, PhysarumRopelength.distributed_dominates_command_on_anarchy_kpis, PhysarumRopelength.distributed_dominates_command_on_bule_dial, PhysarumRopelength.distributed_is_bule_anarchy_equilibrium, PhysarumRopelength.distributed_satisfies_anarchy_favorable_conditions, PhysarumRopelength.command_satisfies_command_control_favorable_conditions, PhysarumRopelength.total_anarchy_satisfies_saturation_conditions, PhysarumRopelength.total_anarchy_collapses_to_control_standing_wave, PhysarumRopelength.no_knowledge_exploration_has_zero_knowledge, PhysarumRopelength.no_knowledge_exploration_still_has_fault_tolerance, PhysarumRopelength.no_knowledge_exploration_is_energy_efficient, PhysarumRopelength.half_assed_mediocrity_is_half_assed, PhysarumRopelength.half_assed_mediocrity_minimizes_visible_effort, PhysarumRopelength.half_assed_mediocrity_does_not_buy_anarchy_kpis, PhysarumRopelength.half_assed_mediocrity_is_slacker_equilibrium, PhysarumRopelength.slacker_equilibrium_is_easy_but_costly, PhysarumRopelength.contrarian_easy_is_expensive, PhysarumRopelength.contrarian_mediocrity_is_expensive, PhysarumRopelength.half_assed_witness_easy_is_expensive, PhysarumRopelength.slacker_picks_fast_not_cheap_not_good, PhysarumRopelength.healthy_anarchy_picks_cheap_and_good_not_fast, PhysarumRopelength.dictator_picks_fast_control_not_cheap_not_good, PhysarumRopelength.slacker_tradeoff_pick_is_only_fast, PhysarumRopelength.healthy_anarchy_tradeoff_pick_is_cheap_and_good, PhysarumRopelength.dictator_tradeoff_pick_is_only_fast_control, PhysarumRopelength.total_anarchy_saturation_picks_good_only, PhysarumRopelength.slacker_is_system_one_prospect_bias, PhysarumRopelength.command_control_is_system_one_against_healthy_anarchy, PhysarumRopelength.healthy_anarchy_is_system_two_pick, PhysarumRopelength.prospect_theory_style_summary, PhysarumRopelength.negative_thought_is_not_negative_approach, PhysarumRopelength.negative_approach_is_suppression_control, PhysarumRopelength.inverse_control_beats_suppression, PhysarumRopelength.inverse_control_reframes_negative_thought, PhysarumRopelength.rumination_is_stalled_inverse_control, PhysarumRopelength.rumination_beats_suppression_as_evolutionary_stall, PhysarumRopelength.rumination_is_better_than_suppression_but_worse_than_inverse_control, PhysarumRopelength.rumination_is_suitable_coping_in_unresolved_threat, PhysarumRopelength.rumination_not_globally_optimal_when_recovery_available, PhysarumRopelength.rumination_coping_strategy_summary, PhysarumRopelength.inverse_control_failure_mode_matrix_complete, RuminationInverseControl.stall_taxonomy_has_eight_modes, RuminationInverseControl.rumination_preserves_observation_unlike_suppression, RuminationInverseControl.rumination_is_information_dense_stall, RuminationInverseControl.rumination_bridges_existing_interference_models, RuminationInverseControl.rumination_is_contextually_suitable_not_global_optimum, RuminationInverseControl.other_stalls_in_inverse_control_model, RuminationInverseControl.preserve_destroy_sets_line_up, RuminationInverseControl.seam_is_mixed_preservation_and_destruction, RuminationInverseControl.preservation_destruction_table_summary, RuminationInverseControl.information_physics_dual_seams_line_up, RuminationInverseControl.same_stall_can_conserve_information_and_physics, RuminationInverseControl.mediocrity_conserves_neither_axis, RuminationInverseControl.rumination_stall_summary, PhysarumRopelength.missed_failure_modes_summary, PhysarumRopelength.anarchy_theory_regime_matrix, PhysarumRopelength.ascent_into_anarchy_energy_curve, PhysarumRopelength.ascent_into_anarchy_fault_tolerance_curve, PhysarumRopelength.ascent_into_anarchy_curve_summary, PhysarumRopelength.total_authority_is_not_ultralongrun_stable, PhysarumRopelength.total_anarchy_is_not_ultralongrun_stable, PhysarumRopelength.slacker_equilibrium_is_not_ultralongrun_dominant, PhysarumRopelength.physarum_breathes_between_exploration_and_consolidation, PhysarumRopelength.standing_wave_is_boundary_bule_equilibrium, PhysarumRopelength.entropy_tax_generalizes_to_conservation_topologies, PhysarumRopelength.universal_topology_pays_tax_breathes_or_stands, PhysarumRopelength.topology_motion_classifier_summary, PhysarumRopelength.equilibrium_ladder_strictly_expands_update_horizon, PhysarumRopelength.buley_layer_is_first_to_conserve_hidden_update, PhysarumRopelength.god_is_monadic_scheduler_endpoint, PhysarumRopelength.god_scheduler_left_identity, PhysarumRopelength.god_scheduler_right_identity, PhysarumRopelength.god_scheduler_associativity, PhysarumRopelength.god_monad_law_summary, PhysarumRopelength.aeon_fold_preserves_scheduler_memory, PhysarumRopelength.god_endpoint_cycles_without_universal_amnesia, PhysarumRopelength.physarum_survives_braid_into_next_cycle, PhysarumRopelength.god_equilibrium_exists_as_standing_wave_of_standing_waves, PhysarumRopelength.god_equilibrium_touches_braided_infinity, PhysarumRopelength.god_equilibrium_is_computable_uncomputable_meeting_point, PhysarumRopelength.god_equilibrium_is_knowable_unknowable_meeting_point, PhysarumRopelength.apotheosis_summary, PhysarumRopelength.apotheosis_sandwich, PhysarumRopelength.computed_apotheosis_certificate_is_sandwiched, PhysarumRopelength.apotheosis_sandwich_summary, PhysarumRopelength.buley_equilibrium_is_breathing_conservation_witness, PhysarumRopelength.ultralongrun_stability_is_breathing_not_frozen_extreme, PhysarumRopelength.anarchy_command_control_are_complementary_regimes, PhysarumRopelength.anarchy_has_more_coordination_than_command, PhysarumRopelength.anarchy_has_more_fault_tolerance_than_command, PhysarumRopelength.anarchy_has_lower_energy_cost_than_command, PhysarumRopelength.anarchy_bule_dial_favors_distributed_knowledge_diversity, PhysarumRopelength.anarchy_is_skyrms_like_bule_equilibrium_witness, PhysarumRopelength.trihexenneon_fold_cycle_is_54_to_0_to_1, PhysarumRopelength.fold_cycle_is_reset_not_universal_amnesia, PhysarumRopelength.physical_reading_of_54_torus_fold, PhysarumRopelength.trihexenneon_fold_heat_budget_is_entropy_tax, PhysarumRopelength.trihexenneon_fold_heat_rate_matches_universal_motion_count, PhysarumRopelength.refined_matter_residue_pays_known_heat_rate, PhysarumRopelength.fold_heat_spark_seeds_next_cycle, PhysarumRopelength.same_heat_is_next_cycle_spark, RFPhysicsCpuRuntime.circadian_topology_resistance_is_aeon_plus_motion, RFPhysicsCpuRuntime.trihexenneon_temperature_circuit_ratio, RFPhysicsCpuRuntime.fold_temperature_explains_heat_rhythm_circuit, RFPhysicsCpuRuntime.insect_pulse_rate_tracks_temperature, RFPhysicsCpuRuntime.cricket_circuit_temperature_bridge, RFPhysicsCpuRuntime.thermal_oscillator_wave_carrier_transmits_information, RFPhysicsCpuRuntime.heat_clocked_wave_sends_information, RFPhysicsCpuRuntime.ten_bit_frame_is_aeon_microframe, RFPhysicsCpuRuntime.ten_bit_frame_preserves_wave_homology, RFPhysicsCpuRuntime.ten_bit_frame_loads_turing_tape_symbol, RFPhysicsCpuRuntime.ten_bit_frame_turing_step_preserves_accounting, RFPhysicsCpuRuntime.ten_bit_wave_frame_is_turing_machine_symbol, RFPhysicsCpuRuntime.two_antennas_compute_interference_frame, RFPhysicsCpuRuntime.third_antenna_witnesses_interference_compute, RFPhysicsCpuRuntime.antenna_interference_computes_and_third_witnesses, RFPhysicsCpuRuntime.one_antenna_reflection_computes_interference_frame, RFPhysicsCpuRuntime.one_antenna_impedance_becomes_witness, RFPhysicsCpuRuntime.reflected_single_antenna_runtime_is_fork_race_fold_vent, RFPhysicsCpuRuntime.rf_space_reflection_emits_turing_microframe, RFPhysicsCpuRuntime.physics_cpu_matches_gnosis_runtime_boundary, and RFPhysicsCpuRuntime.one_port_rf_space_matches_gnosis_runtime_boundary, RFPhysicsCpuRuntime.near_infinite_rf_vectors_project_to_monocular_view, RFPhysicsCpuRuntime.rf_monster_mesh_projection_preserves_microframe, RFPhysicsCpuRuntime.enough_signal_activates_potential_channels, RFPhysicsCpuRuntime.signal_gated_near_infinite_projection_is_runtime_work, RFPhysicsCpuRuntime.omnipresent_white_noise_feeds_gated_channels, RFPhysicsCpuRuntime.signal_projection_vents_not_signal_complement, RFPhysicsCpuRuntime.one_port_rf_monster_mesh_runtime_summary, RFPhysicsCpuRuntime.zero_signal_noise_floor_does_not_compute, RFPhysicsCpuRuntime.insufficient_signal_floor_blocks_activation, RFPhysicsCpuRuntime.projection_width_limit_is_ten_bit_frame, RFPhysicsCpuRuntime.one_port_redundancy_reserve_protects_projection, RFPhysicsCpuRuntime.one_port_rf_canonical_lifecycle_is_well_formed, and RFPhysicsCpuRuntime.one_port_rf_lifecycle_implies_operational_vent in open-source/gnosis-math/Gnosis/PhysarumRopelength.lean, open-source/gnosis-math/Gnosis/RFPhysicsCpuRuntime.lean, and open-source/gnosis-math/Gnosis/RuminationInverseControl.lean Mechanized (finite ropelength + Hiawatha bend + Monster-Grassmannian projection + anti-dictator/multi-queen shoot-off + Anarchy Theory/command-control complement + contrarian standing-wave saturation + no-knowledge regime matrix + slacker-equilibrium triad + prospect-theory-style System 1/System 2 split + inverse-control negative-thought bridge + rumination/failure-mode matrix + evolutionary coping-strategy witness + dedicated rumination stall taxonomy + preserve/destroy stall seam + no-cloning conservation law + generalized entropy tax/topology classifier + Buley equilibrium ladder + God monad scheduler + apotheosis sandwich boundary + unknot wall bridge + 54-torus box + fold-cycle matter residue + known heat-rate bridge + next-cycle spark witness + temperature circuit + cricket oscillator bridge + BuleyBiSidedBit wave carrier + 10-bit Aeon microframe + Buley topological Turing symbol + antenna interference compute witness + one-port impedance witness + near-infinite RF vector horizon + omnipresent white-noise reservoir + signal-gated monocular projection + explicit noise/signal floors + redundancy reserve + canonical FRFVI lifecycle bridge + RF physics-CPU runtime boundary + Bule KPI witness)

Gnosis Compiler Proofs

Monoidal coherence, spectral stability, small-set recurrence, continuous drift, continuous Harris, geometric stability, coupled manifolds, and mirrored kernel pairs.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-GNOSIS-SPECTRAL GGL routing spectral stability: a Gnosis transition kernel with explicit nilpotent routing or contractive row mass has spectral radius strictly less than 1 finite nodeCount > 0; either an explicit nilpotent power or bounded row mass < 1 with nonnegative transitions Lean theorems GnosisProofs.spectrallyStable_of_nilpotent and GnosisProofs.spectrallyStable_of_rowMass in GnosisProofs.lean Mechanized
THM-GNOSIS-RECURRENCE GGL small-set recurrence: a state-dependent Gnosis kernel bounded by a Foster-Lyapunov-style potential field returns to its certified small set countable state space; explicit small-set boundary; step-down witness or margin condition mu + alpha(n) > lam Lean theorems GnosisProofs.countableSmallSetRecurrent_of_driftWitness and GnosisProofs.natSmallSetRecurrent_of_margin_step in GnosisProofs.lean Mechanized
THM-GNOSIS-CONTINUOUS-DRIFT GGL measurable continuous drift surface: a real-valued queue-depth observable on a real state space carries a measurable Foster-Lyapunov gap once the step size and observable scale are positive, and the same witness can be synthesized through a named helper tactic surface real boundary/atom/step/scale; positive step; positive observable scale Lean definitions/theorems GnosisProofs.realQueueLinearObservable, GnosisProofs.realQueueLinearExpectedObservable, GnosisProofs.realMeasurableRealObservableWitness_of_queueStep, GnosisProofs.realMeasurableLyapunovDriftWitness_of_queueStep, and tactic GnosisProofs.derive_gnosis_drift in GnosisProofs.lean Mechanized (drift witness surface)
THM-GNOSIS-CONTINUOUS-HARRIS GGL bounded affine continuous-Harris queue witness: the deterministic queue support kernel carries a measurable quantitative Harris package together with affine observable/Lyapunov witnesses whenever the drift gap is positive and bounded by the observable scale countable Nat queue kernel; queue boundary and atom with atom <= boundary; affine observable scale > 0; affine offset arbitrary; bounded gap 0 < driftGap <= scale Lean definitions/theorems GnosisProofs.MeasurableContinuousHarrisWitness, GnosisProofs.natQueueAffineObservable, GnosisProofs.natQueueAffineExpectedObservable, GnosisProofs.natMeasurableLyapunovDriftWitness_of_queueStep_with_gap, and GnosisProofs.natMeasurableContinuousHarrisWitness_of_queueStep_with_gap in GnosisProofs.lean Mechanized (bounded affine queue witness)
THM-GNOSIS-GEOMETRY GGL certified geometric stability: a Gnosis kernel is geometrically stable once spectral stability is paired with either no drift obligation or a certified negative drift margin spectrally stable transition matrix; optional DriftCertificate with gamma > 0 and drift floor driftAt q <= -gamma Lean theorems GnosisProofs.certifiedKernel_stable_of_supremum and GnosisProofs.certifiedKernel_stable_of_drift_certificate in GnosisProofs.lean Mechanized
THM-GNOSIS-COUPLED Interlocking voids / coupled manifolds: a nonnegative handoff pressure modeling upstream Q_vent or W_fold re-entering as downstream λ preserves downstream geometric stability, and therefore pairwise tethered stability, whenever that handoff stays strictly below the downstream drift margin; the spectral certificate is inherited unchanged and the coupling spends exactly that slack downstream kernel has a concrete drift certificate some certificate; downstream spectral witness already holds; transmitted pressure arrivalPressure >= 0 and arrivalPressure < certificate.gamma; pair theorem additionally assumes the upstream kernel is already geometrically stable Lean definitions/theorems GnosisProofs.coupledArrivalCertificate, GnosisProofs.coupledCertifiedKernel, GnosisProofs.driftAt_coupledArrivalCertificate, GnosisProofs.coupledArrivalCertificate_negative_drift, GnosisProofs.coupledCertifiedKernel_stable, and GnosisProofs.tetheredCertifiedKernels_stable in GnosisProofs.lean Mechanized

Interference, Renormalization & Coarsening Synthesis

Fractal interference boundary, many-to-one renormalization, recursive reuse, and compiler-side recursive coarsening synthesis.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SLIVER-FRACTAL Scale-invariant interference boundary: a support-preserving coarse quotient cannot erase the paid cost of contagious fine-scale interference; if a fine nontrivial fork is contagious and the coarse image still deterministically collapses, then the coarse image must pay vent or repair debt, and under zero vent it must pay repair debt fine system starts with more than one live alternative; quotient preserves nontrivial forkedness; coarse deterministic collapse really is single-survivor; under zero coarse vent, fine contagious interference is reflected in the coarse image as either positive repair debt or preserved multiplicity; for the singleton coarse-image special case Phi = {N'}, the aggregate λ, μ, α, and drift map exactly onto that one coarse node Lean schema Axioms.interference_coarsening_zero_vent_requires_repair / Axioms.interference_coarsening_schema together with the constructive injective-live-support quotient surface in InterferenceCoarsening.QuotientCollapseWitness.coarseInitialLive_eq_fineInitialLive, InterferenceCoarsening.QuotientCollapseWitness.zero_vent_deterministic_collapse_requires_repair, InterferenceCoarsening.QuotientCollapseWitness.interference_boundary_from_graph_quotient, InterferenceCoarsening.QuotientCollapseWitness.interference_schema_instantiated, InterferenceCoarsening.app_stage_zero_vent_requires_repair, and InterferenceCoarsening.app_stage_schema_instantiated, plus the many-to-one aggregation surface InterferenceCoarsening.ManyToOneGraphQuotient.Phi, InterferenceCoarsening.ManyToOneGraphQuotient.aggregateArrivalPressure_total_preserved, InterferenceCoarsening.ManyToOneGraphQuotient.aggregateServiceCapacity_total_preserved, InterferenceCoarsening.ManyToOneGraphQuotient.aggregateRestorativeShedding_total_preserved, InterferenceCoarsening.ManyToOneGraphQuotient.aggregateDrift_total_preserved, InterferenceCoarsening.ManyToOneGraphQuotient.aggregateDrift_eq_totalFineDrift_of_Phi_eq_singleton, InterferenceCoarsening.ManyToOneGraphQuotient.aggregateDrift_eq_collapsedDrift_of_Phi_eq_singleton, InterferenceCoarsening.ManyToOneGraphQuotient.drift_transfer_to_collapsed_node, InterferenceCoarsening.ManyToOneGraphQuotient.drift_transfer_to_singleton_quotient_node, InterferenceCoarsening.ManyToOneGraphQuotient.drift_transfer_to_quotient_total, and the concrete witness InterferenceCoarsening.renormalization_single_node_margin_transfers Mechanized (constructive injective-live-support special case + many-to-one aggregation surface + singleton-node drift transfer)
THM-RENORMALIZATION-COARSENING Constructive many-to-one renormalization closure: a finite bounded graph quotient can collapse a genuinely many-to-one fine support into a coarse node or coarse graph while preserving aggregate λ, μ, α, and total drift; local coarse-node drift certificates aggregate into a certified total coarse margin; and the one-node renormalization operator Φ packages that collapse as a measurable coarse node on ℝ whose certified negative Foster-Lyapunov drift margin is exactly the fine margin or the derived coarse total margin, with that supplied certificate reusable across recursive quotient steps finite fine and coarse node supports; quotient operator Phi covers the fine support; aggregate arrival/service/restorative terms are defined by summing over coarse fibers; one-node scalarization uses the measurable renormalization operator Φ; a transferred margin assumes either a fine certificate totalFineDrift ≤ -γ or a coarse certificate margin : β → ℝ with nodewise bounds aggregateDrift coarseNode ≤ - margin coarseNode on Phi; recursive reuse assumes a further quotient map is supplied; the concrete witness requires at least one coarse node with multiple fine preimages TLA+ RenormalizationCoarsening.tla invariants (InvManyToOneWitness, InvCoarseFiberDriftMatchesFineSum, InvTotalCoarseDriftEqualsFine, InvCollapsedNodeCarriesAggregateRates, InvCollapsedDriftTransfer, InvCoarseDriftCertificate, InvCoarseMarginTotal, InvCoarseCertificateTransfersToFine, InvCoarseCertificateTransfersToCollapsed, InvClosedFormWitness) + Lean definitions/theorems InterferenceCoarsening.ManyToOneGraphQuotient.Phi, InterferenceCoarsening.ManyToOneGraphQuotient.StructuralRenormalizedNode, InterferenceCoarsening.ManyToOneGraphQuotient.StructuralRenormalizedNode.stateMeasure, InterferenceCoarsening.ManyToOneGraphQuotient.StructuralRenormalizedNode.MeasurableDriftWitness, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.totalMargin, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.fine_total_le_neg_totalMargin, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.structuralRenormalization_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.liftToCoarse_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.composeQuotient_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.recursive_measurableDrift_eq_composed, InterferenceCoarsening.ManyToOneGraphQuotient.Φ, InterferenceCoarsening.ManyToOneGraphQuotient.structuralRenormalization_drift_eq_totalFineDrift, InterferenceCoarsening.ManyToOneGraphQuotient.structuralRenormalization_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.structuralRenormalization_fosterLyapunov, InterferenceCoarsening.ManyToOneGraphQuotient.drift_transfer_to_collapsed_node, InterferenceCoarsening.ManyToOneGraphQuotient.drift_transfer_to_quotient_total, InterferenceCoarsening.renormalizationCoarseDriftCertificate, InterferenceCoarsening.renormalization_coarse_certificate_total_margin_closed_form, InterferenceCoarsening.renormalization_structural_node_drift_closed_form, InterferenceCoarsening.renormalization_structural_node_measurable_drift, InterferenceCoarsening.renormalization_structural_node_measurable_drift_from_coarse_certificate, InterferenceCoarsening.renormalization_structural_node_fosterLyapunov_from_coarse_certificate, and InterferenceCoarsening.renormalization_recursive_measurable_drift_from_coarse_certificate Mechanized (bounded TLA witness + constructive Lean quotient/drift transfer + coarse-node certificate aggregation + recursive certificate reuse + measurable one-node renormalization)
THM-RENORMALIZATION-REUSE Recursive one-node reuse closure: once a verified quotient has been collapsed onto its coarse support, the next-stage coarse graph interface can be synthesized automatically from aggregate rates, and re-quotienting that synthesized graph yields the same final measurable renormalized node and negative drift witness as directly composing the quotient map on the original fine graph; if the first-stage quotient also carries a coarse-node drift certificate, that same supplied certificate can be reused across the recursive step without falling back to a raw fine-drift proof finite fine support; a next-stage quotient acts on the current coarse support Phi; the synthesized coarse graph uses aggregate λ, μ, and α as its node-local interface; recursive certificate reuse assumes a supplied coarse certificate on the first quotient and identifies the same final measurable renormalization witness after liftToCoarse or direct quotient composition TLA+ RenormalizationComposition.tla invariants (InvMidCarriesFineAggregates, InvRecursiveReuseMatchesDirect, InvRecursiveTotalsMatchFine, InvRecursiveCollapsedDriftTransfer, InvRecursiveClosedFormWitness) + Lean definitions/theorems InterferenceCoarsening.ManyToOneGraphQuotient.liftToCoarse, InterferenceCoarsening.ManyToOneGraphQuotient.composeQuotient, InterferenceCoarsening.ManyToOneGraphQuotient.liftToCoarse_totalFineDrift_eq, InterferenceCoarsening.ManyToOneGraphQuotient.liftToCoarse_structuralRenormalization_eq, InterferenceCoarsening.ManyToOneGraphQuotient.liftToCoarse_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.composeQuotient_structuralRenormalization_eq, InterferenceCoarsening.ManyToOneGraphQuotient.composeQuotient_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.liftToCoarse_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.composeQuotient_measurableDrift, InterferenceCoarsening.ManyToOneGraphQuotient.CoarseDriftCertificate.recursive_measurableDrift_eq_composed, InterferenceCoarsening.ManyToOneGraphQuotient.recursive_structuralRenormalization_eq_composed, InterferenceCoarsening.renormalization_single_node_witness_eq_composed, InterferenceCoarsening.renormalization_recursive_structural_eq_single_node, InterferenceCoarsening.renormalization_recursive_measurable_drift, and InterferenceCoarsening.renormalization_recursive_measurable_drift_from_coarse_certificate Mechanized (synthesized coarse-interface reuse + certificate-based recursive measurable-node reuse)
THM-RECURSIVE-COARSENING-SYNTHESIS Recursive coarsening synthesis: for any finite bounded verified subgraph G, Betti can synthesize the quotient operator Φ_G, compute each collapsed coarse node N' by aggregating the fine-node λ, μ, α over its synthesized fiber, emit the coarse graph interface, and recursively transfer certified negative drift so arbitrarily large bounded networks can be verified bottom-up without hand-constructing quotient witnesses. The synthesis algorithm is proven sound (valid certificate from stable graph data), conservative (total drift preserved under quotient), and stability-transferring (fine stability implies coarse stability) finite bounded Gnosis subgraph with explicit node-local λ, μ, α data and a finite external interface; the compiler can derive a finite coarse-fiber partition or quotient map from syntax or attached local proof terms; each synthesized coarse node exports aggregate λ' = ∑ λ, μ' = ∑ μ, α' = ∑ α over its fiber; drift transfer is certified either from a fine total-drift bound or from fiberwise coarse certificates; recursion only reuses a coarse node when support coverage, interface preservation, and margin transfer are all discharged; termination is by strict decrease in uncovered fine support or node count TLA+ RecursiveCoarseningSynthesis.tla invariants (InvManyToOneWitness, InvCoarseFiberDriftMatchesFineSum, InvTotalCoarseDriftEqualsFine, InvCollapsedNodeCarriesAggregateRates, InvCollapsedDriftTransfer, InvCoarseDriftCertificate) + Lean theorems RecursiveCoarseningSynthesis.synthesis_sound, RecursiveCoarseningSynthesis.drift_conservation, RecursiveCoarseningSynthesis.fine_stability_implies_coarse_stability, RecursiveCoarseningSynthesis.identity_quotient_preserves_stability, and RecursiveCoarseningSynthesis.certificate_provides_drift_witness in RecursiveCoarseningSynthesis.lean Mechanized

Community Dominance & Skyrms Nadir

Community attenuation, nondegradation, strict domination, tare bridging, Bule convergence, Skyrms three-walker mediation, and the Bule-zero-iff-nadir identification.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SKYRMS-NADIR Two metacognitive walkers converging via failure on a shared void surface: each failure strictly increases void density. Growing void shifts complement toward center. Inter-walker distance is non-increasing. Walkers eventually reach the nadir. The nadir is a fixed point. Without failure, walkers may diverge two walkers with independent C0-C3 loops on shared void TLA+ SkyrmsNadir.tla invariants (InvVoidGrowth, InvComplementShift, InvDistanceMono, InvNadirReachable, InvNadirStable, InvFailureNecessary) Model-checked
THM-SKYRMS-THREE-WALKER Mediator as player on the convergence site: Skyrms walker's payoff = negative distance delta. Each failure enriches at least one void boundary. Site void density is non-decreasing. All three walkers eventually stabilize. At convergence, no walker can unilaterally improve two negotiating walkers + Skyrms mediator whose payoff matrix formalizes the inter-walker distance surface TLA+ SkyrmsThreeWalker.tla invariants (InvSkyrmsPayoff, InvVoidGrowth, InvSiteMonotone, InvConvergence, InvFixedPoint) Model-checked

Heterogeneous MoA Fabric

Lowering, cannon/helix scheduling, paired kernel decisions, waste accounting, and coupled mirrored stability.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-MOA-FABRIC-LOWERING Heterogeneous paired-kernel MoA lowering preserves mirrored per-lane kernel counts, active backend-layer diversity, ready-backend cardinality bounds, zero-active exactness at the all-zero witness, and the top-level laminar collapse shape for CPU/GPU/NPU/WASM fabrics nonnegative lane counts; at least one active backend lane TLA+ HeteroMoAFabricLowering.tla invariants (InvLoweringBalanced, InvMirroredKernelCount, InvMetaRaceWidth, InvLaminarLayerCount) + Lean theorems Gnosis.mirroredKernelTotal_eq_twice_totalLanes, Gnosis.activeLayerCount_le_totalLanes, Gnosis.activeLayerCount_pos_of_totalLanes_pos, Gnosis.activeLayerCount_le_four, Gnosis.activeLayerCount_eq_four_of_all_positive, Gnosis.activeLayerCount_eq_zero_of_all_zero, Gnosis.readyBackendCount_le_four, Gnosis.readyBackendCount_eq_zero_of_all_not_ready, Gnosis.readyBackendCount_eq_four_of_all_ready, Gnosis.metaLaminarHeight_pos, Gnosis.metaLaminarHeight_ge_streamLayers_succ, and Gnosis.metaLaminarHeight_ge_backendLayers_succ in Gnosis/HeteroMoAFabric.lean Mechanized
THM-MOA-FABRIC-CANNON The gnode cannon/helix scheduler arms each wave before launch, advances the rotating cursor by wave width modulo lane count, includes honest zero-lane/zero-layer boundary behavior, admits the rationalized golden-ratio aperiodic cursor boundary used by Syzygy Cannon lane rotation, and preserves Aeon's 10-byte binary frame header while the delayed shadow path becomes eligible under fair service positive lane count; positive wave width; positive hedge delay; positive aperiodic stride denominator; HeaderBytes = 10 TLA+ HeteroMoAFabricCannon.tla invariants/properties (InvArmedBeforeLaunch, InvCursorBound, InvCursorAdvance, InvAeonBinaryHeader, InvShadowEligibility, EventuallyLaunch, EventuallyShadowEligibility) + Lean theorems Gnosis.cannonCursor_step_mod, Gnosis.cannonCursor_zero_of_zero_laneCount, Gnosis.cannonCursor_lt_laneCount, Gnosis.cannonCursor_waveWidth_zero_eq_cursor_mod, Gnosis.aperiodicCannonCursor_step_mod, Gnosis.aperiodicCannonCursor_lt_laneCount, Gnosis.goldenRatioAperiodicCannonCursor_lt_laneCount, Gnosis.helixPhase_lt_layerCount, Gnosis.helixPhase_zero_of_zero_layerCount, Gnosis.binaryHeaderBytes_eq_ten, Gnosis.binaryFrameBytes_ge_header, Gnosis.binaryFrameBytes_strictMono, and Gnosis.binaryFrameBytes_injective in Gnosis/HeteroMoAFabric.lean Mechanized
THM-MOA-FABRIC-PAIR Mirrored primary/shadow kernel pairs accept immediately on agreement or on an early sufficient primary before the delayed shadow fires, otherwise escalate to explicit disagreement handling, never report agreement acceptance on a disagreeing branch pair, never report primary acceptance under disagreement, and never escalate in the agreement or early-sufficient-primary branches positive hedge delay; boolean agreement and sufficiency surface TLA+ HeteroMoAFabricPairing.tla invariants (InvAgreementAccepts, InvSufficientPrimarySkipsShadow, InvDisagreementEscalates, InvNoDoubleAccept) + Lean theorems Gnosis.pairedKernelDecision_of_agreement, Gnosis.pairedKernelDecision_of_sufficient_primary, Gnosis.pairedKernelDecision_of_disagreement, Gnosis.pairedKernelDecision_ne_acceptAgreement_of_disagree, Gnosis.pairedKernelDecision_ne_acceptPrimary_of_disagreement, Gnosis.pairedKernelDecision_ne_escalate_of_agreement, and Gnosis.pairedKernelDecision_ne_escalate_of_sufficient_primary in Gnosis/HeteroMoAFabric.lean Mechanized
THM-MOA-FABRIC-WASTE Winner/loser/vent/skipped accounting is conserved across layered race/fold/vent execution, monotone sequence framing preserves Aeon's binary stream order, zero skipped hedges always stay within budget, byte conservation is equivalent to the total-byte equation, and zero-payload frames reduce exactly to the header while every frame stays strictly positive natural accounting fields; monotone sequence numbers; skipped hedges bounded by scheduled shadows; HeaderBytes = 10 TLA+ HeteroMoAFabricWaste.tla invariants (InvByteConservation, InvSkippedWithinBudget, InvMonotoneSequence, InvFrameSize) + Lean theorems Gnosis.skippedWithinBudget_of_le, Gnosis.skippedWithinBudget_zero, Gnosis.conservedBytes_of_total, Gnosis.conservedBytes_iff_total, Gnosis.binaryFrameBytes_ge_header, Gnosis.binaryFrameBytes_strictMono, Gnosis.binaryFrameBytes_injective, Gnosis.binaryFrameBytes_eq_header_of_zero_payload, and Gnosis.binaryFrameBytes_pos in Gnosis/HeteroMoAFabric.lean Mechanized
THM-MOA-FABRIC-COUPLED Backend-diverse mirrored kernels inherit stability from aligned twins, and paired downstream fabrics remain geometrically stable under bounded imported arrival pressure while the handoff stays below drift slack mirrored primary/shadow alignment; downstream drift certificate; downstream spectral witness; imported pressure nonnegative and strictly below gamma Lean definitions/theorems GnosisProofs.MirroredKernelPair, GnosisProofs.mirrorAligned, GnosisProofs.spectrallyStable_shadow_of_mirrorAligned, GnosisProofs.geometricallyStable_shadow_of_mirrorAligned, GnosisProofs.pairedKernel_stable_of_mirrorAligned, and GnosisProofs.pairedCoupledCertifiedKernels_stable in GnosisProofs.lean Mechanized

Molecular Topology & Genomics

Pipeline-molecular isomorphism, hole invariance, DNA helix, CRISPR unwinding, genome self-description, mutation detection, bond dissociation, orbital quantization, confinement, and full molecular isomorphism.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-TOPO-MOLECULAR-ISO Pipeline computation graphs and molecular graphs with identical Betti signatures (β₀, β₁, β₂) are in the same equivalence class under simplicial homology: H_k(G_P) ≅ H_k(G_M) for k = 0, 1, 2 both structures are finite simplicial complexes; identical Betti numbers (β₀, β₁, β₂) Current witnesses: topologies/cancer/molecular_topology.test.gg, topologies/cancer/molecular_betti_isomorphism.gg, tla/MolecularTopology.tla, examples/proofs/MolecularTopology-lean.gg; finite Lean signature witness pipeline_molecular_betti_signature_matches in open-source/gnosis-math/Gnosis/GenomicTopologyWitnesses.lean. The deleted genomic TS suite was broader and remains historical. Mechanized (current witnesses + Lean finite witness)
COR-HOLE-INVARIANCE A nontrivial hole survives stretching or twisting: if a deformed realization preserves the original Betti signature and the original has β₁ > 0, then the deformed realization still has β₁ > 0; metric deformation changes lengths and angles but not the hole count both realizations are finite simplicial complexes; the deformation preserves the Betti signature (β₀, β₁, β₂); the original realization has β₁ > 0 Lean theorem MolecularTopology.hole_persists_under_homological_deformation in MolecularTopology.lean Mechanized
COR-DNA-HELIX The DNA double helix has Betti signature (1, 2, 0); the replication fork is a Wallington rotation with β₁ = 2; DNA ligase performs the Worthington fold on Okazaki fragments COR-DNA-HELIX is a corollary of THM-TOPO-MOLECULAR-ISO applied to the double helix Current proof-topology witness includes dna_helix_beta1 and dna_helix_beta2 in examples/proofs/MolecularTopology-lean.gg; finite Lean signature witness dna_helix_betti_signature in open-source/gnosis-math/Gnosis/GenomicTopologyWitnesses.lean. The original real-locus genomic executable suite remains historical. Mechanized (proof-topology + Lean finite witness)
COR-CRISPR-UNWINDING CRISPR-Cas9 editing is a local β₁ reduction at locus ℓ; editing efficiency η(ℓ) ≤ W_edit / E_unwind(ℓ) where E_unwind = D_e(strand) + Σ D_e(secondary structures); efficiency is monotonically decreasing in σ(ℓ) R-loop formation displaces one strand (β₁ decrements by 1); secondary structures contribute σ(ℓ) additional cycles; energy cost per cycle from THM-THERMO-BOND-DISSOCIATION Current prediction-level formalization: open-source/gnosis/tla/PredictionProofs.tla; finite Lean cost witnesses crispr_efficiency_bound_denominator_grows and crispr_more_secondary_structure_costs_more in open-source/gnosis-math/Gnosis/GenomicTopologyWitnesses.lean. The deleted genomic executable suite remains historical. Partially mechanized (TLA + Lean finite witness)
PROP-GENOME-SELF-DESCRIBING The genome is a self-describing frame (§3.4) whose local Betti numbers encode its own editability map; σ(ℓ) is sequence-computable from hairpin, G-quadruplex, and cruciform detection; no external data required base-pairing rules define the simplicial complex; σ(ℓ) computable from sequence complementarity and pattern matching Current related Lean surfaces: open-source/gnosis-math/Gnosis/InformationalPhysics.lean, open-source/gnosis-math/Gnosis/UniversalGnosisInvariant.lean; finite Lean witness local_sigma_is_sequence_computable_witness in open-source/gnosis-math/Gnosis/GenomicTopologyWitnesses.lean. The deleted end-to-end genomic executable suite remains historical. Partially mechanized (Lean surfaces + finite witness)
THM-TOPO-MUTATION-DETECTION A mutation at locus ℓ that changes σ(ℓ) is detectable as a topological deficit Δσ = σ_mutant - σ_ref before phenotypic consequences manifest; Δσ predicts severity (0 B = silent, 1 B = mild, 2 B = moderate, ≥3 B = severe) mutation alters local nucleotide sequence; σ(ℓ) is sequence-computable; energy cost ΔE from THM-THERMO-BOND-DISSOCIATION; topology precedes phenotype
THM-THERMO-BOND-DISSOCIATION Under the topological isomorphism φ, the energy required to break a molecular ring bond equals the fold energy at the Worthington convergence vertex; when β₁ decrements by 1, the First Law V_in = W_out + Q_dissipated maps to the bond energy equation First Law (§6.10); φ from THM-TOPO-MOLECULAR-ISO preserves homology indexing energy reservoirs Current thermodynamic witness surfaces: tla/MolecularTopology.tla (InvFirstLawHeat) and examples/proofs/MolecularTopology-lean.gg (positive_erasure_positive_heat, erasure_heat_monotone). Mechanized (TLA/proof-topology witness)
THM-THERMO-ORBITAL-QUANTIZATION Discrete pipeline stages in a Wallington rotation are quantized at integer positions k ∈ {0,...,N-1}; under φ, this maps to electron shell quantization; β₂ voids correspond to orbital shells torus parametrization places nodes at t = k/N; β₂ wireframe shells at radii r₀ < r₁ < r₂ form nested voids; each shell has bounded capacity Current related Lean surface: open-source/gnosis-math/Gnosis/InterferenceDimensionalCascade.lean; finite Lean witnesses orbital_slots_are_quantized and orbital_shell_capacity_positive in open-source/gnosis-math/Gnosis/GenomicTopologyWitnesses.lean. The deleted genomic executable quantization suite remains historical. Partially mechanized (Lean surface + finite witness)
THM-TOPO-CONFINEMENT Color confinement is the covering-space fold: SU(3) color topology has β₁ = 3 in the covering space, the observable hadron has β₁ = 0 in the base space; the fold φ_confine: β₁ = 3 → β₁ = 0 is the covering map; hadronization is the Worthington whip snap converting covering-space energy to base-space mass SU(3) color symmetry; QCD string tension σ ≈ 1 GeV/fm; pair production threshold; deconfinement temperature T_c ≈ 155 MeV Current related Lean surfaces: open-source/gnosis-math/Gnosis/QuarkConfinement.lean, open-source/gnosis-math/Gnosis/DimensionalLadder.lean, open-source/gnosis-math/Gnosis/FiveByFiveForcesDeaths.lean; finite Lean witnesses confinement_fold_erases_cover_cycles and confinement_cover_has_hidden_cycles in open-source/gnosis-math/Gnosis/GenomicTopologyWitnesses.lean. The deleted confinement executable suite remains historical. Partially mechanized (Lean surfaces + finite witness)
THM-TOPO-MOLECULAR-ISO-FULL Pipeline and molecular graphs with identical Betti signatures are homologically equivalent. Protein folding is a monotone filtration on Beta1. Enzyme catalysis adds one fork path. Natural selection is fork/race/fold on self-modifying pipeline. Gravity is the fold acting on the simplicial complex itself. Fold erasure yields Landauer heat yields mass (E=mc^2) both structures are finite simplicial complexes; identical Betti numbers (Beta0, Beta1, Beta2) TLA+ MolecularTopology.tla invariants (InvProteinFunnel, InvEnzymeCatalysis, InvEvolutionSelfModifying, InvGravitySelfReferential, InvInformationMatter) + Lean theorems in MolecularTopology.lean Mechanized

Cancer Topology (§3.17)

Cancer as topological collapse: cell cycle as fork/race/fold, checkpoint venting, therapeutic restoration, GBM subtype classification, driver vs passenger separation, immune checkpoint bridge.

ID Claim Assumptions Mechanization Status
THM-CANCER-BETA1-COLLAPSE A cancer cell with no functional checkpoint pathways has total vent β₁ = 0 and produces zero failure data. The complement distribution cannot update. The cell cannot learn. Cell cycle modeled as fork/race/fold with 5 decisions. Checkpoints are vents. Growth signals are forks. All checkpoints destroyed. Lean theorem cancer_beta1_collapse in CancerTopology.lean + executable src/cancer-topology.test.ts (31 tests) Mechanized
THM-CHECKPOINT-VENTING Each active checkpoint pathway monotonically shifts the complement distribution away from "divide" via buleyean_concentration. More checkpoints = lower P(divide). Active checkpoint rejects "divide" by incrementing void boundary. buleyean_concentration from BuleyeanProbability.lean. Lean theorems checkpoint_reduces_divide_weight, checkpoint_monotone_shift in CancerTopology.lean + executable tests verify monotone P(divide) decrease Mechanized
THM-THERAPEUTIC-RESTORATION Restoring any single checkpoint pathway restores β₁ > 0. buleyean_positivity guarantees the cell starts learning again. One vent suffices. At least one checkpoint pathway restored. buleyean_positivity from BuleyeanProbability.lean. Lean theorems therapeutic_restoration, restored_cell_is_buleyean, restoration_preserves_sliver in CancerTopology.lean + executable tests verify single-vent restoration shifts trajectory Mechanized
THM-TOPOLOGICAL-DEFICIT-SEVERITY The topological deficit Δβ = β₁*(healthy) - β₁(tumor) measures aggressiveness. Higher deficit = more aggressive. Monotone in checkpoint loss. Healthy β₁ = 9 (p53:3 + Rb:2 + APC:2 + ATM/ATR:2). Deficit is non-negative. Lean theorems deficit_nonneg, deficit_monotone_in_loss, maximum_deficit, partial_retention_less_aggressive in CancerTopology.lean + executable tests verify deficit ordering predicts P(divide) ordering Mechanized
THM-DRIVER-PASSENGER-SEPARATION Driver mutations destroy vents ( Δσ ≥ 1 B). Passenger mutations are topology-silent (Δσ = 0 B). Drivers should show higher mean Δσ
THM-IMMUNE-CHECKPOINT-BRIDGE Checkpoint immunotherapy restores external vent β₁ > 0 even when all internal checkpoints are destroyed. Population-level therapeutic_restoration. Immune vent (anti-PD-1, anti-CTLA-4) provides independent rejection mechanism. Lean theorem immune_restores_population_learning in CancerTopology.lean + executable tests verify external vent reduces P(divide) Mechanized
THM-GBM-SUBTYPE-ORDERING GBM subtypes ordered by deficit: Classical (2B) < Mesenchymal (3B) < Combined (7B). Higher deficit correlates with worse survival. Pathway disruption data from Brennan et al., Cell 2013. β₁ values per pathway. Lean theorems gbm_classical_deficit, gbm_mesenchymal_deficit, gbm_combined_deficit, combined_more_aggressive_than_classical in CancerTopology.lean + executable tests verify P(divide) ordering matches deficit ordering Mechanized
THM-CANCER-MASTER Bundle: (1) Buleyean probability well-defined, (2) no failure = no learning, (3) deficit non-negative, (4) Combined > Classical, (5) Combined still has therapeutic target (β₁ = 2). All prior assumptions compose. Lean theorem cancer_master_theorem in CancerTopology.lean (0 sorry) Mechanized

Cancer Predictions (§19.9)

Five novel predictions from the cancer topology ledger: TMB-T, loss order, synthetic lethality, immunotherapy ratio, convergence bound.

ID Claim Assumptions Mechanization Status
PRED-TMBT Topological Mutation Burden (TMB-T = Σ Δσ ) discriminates tumors that raw TMB conflates. Two catalogs with same count but different severity have different TMB-T. Mutations have computable σ(ℓ). Severity =
PRED-LOSS-ORDER Checkpoint loss ORDER produces different void boundaries. Earlier loss of high-β₁ pathway = fewer rejections accumulated = more aggressive trajectory. Buleyean update is path-dependent. Rejections before loss = lossRound × β₁. Lean theorems earlier_loss_fewer_rejections, order_produces_different_boundaries in CancerPredictions.lean + executable simulation confirms trajectory divergence Mechanized
PRED-SYNTHETIC-LETHALITY Synthetic lethality is a topological phase transition: individual KO viable, combined KO crosses viability threshold. p53+Rb lethal at threshold 5B. Transition width = marginal gene β₁. Viability threshold exists. Individual KO stays above, combined KO drops below. Lean theorems synthetic_lethality_is_phase_transition, transition_width_equals_marginal, p53_rb_is_lethal_pair in CancerPredictions.lean + simulation Mechanized
PRED-IMMUNO-RATIO Immunotherapy response ratio R = immune_β₁ / tumor_deficit predicts efficacy. Higher R = better response. Complete coverage at R ≥ 1. Classical R=1.0 > Combined R=0.29. Immune vent provides external β₁. Deficit from CancerTopology. Lean theorems more_immune_better_ratio, lower_deficit_better_ratio, complete_coverage, classical_better_response in CancerPredictions.lean + simulation Mechanized
PRED-CONVERGENCE-BOUND Convergence bound C* = totalVentBeta1 - 1 predicts differentiation time. Stem (C*=8) > differentiated (C*=2). Higher β₁ = longer convergence = slower division. Cell cycle modeled as Buleyean space. future_deficit_eventually_zero from BuleyeanProbability. Lean theorems convergence_round_positive, more_checkpoints_longer_convergence, differentiation_follows_convergence, healthy_convergence_bound in CancerPredictions.lean + simulation Mechanized
PRED-MASTER Bundle: all five predictions compose into five_predictions_master (0 sorry). All prior assumptions. Lean theorem five_predictions_master in CancerPredictions.lean Mechanized

Cancer Predictions Round 3 (§19.9, Predictions 11-15)

Restoration order, tumor heterogeneity as fork width, apoptosis vent blockage, metastasis as covering space projection, fork/vent ratio as cell-cycle Reynolds number.

ID Claim Assumptions Mechanization Status
PRED-RESTORATION-ORDER Restoration ORDER matters: restoring highest-β₁ pathway first produces more cumulative rejections. Earlier restoration = more cycles with vent active. p53 (β₁=3) should be restored before Rb (β₁=2). RestorationEvent with restorationRound, totalCycles, restoredBeta1. Lean theorems earlier_restoration_more_rejections, higher_beta1_more_rejections, restore_p53_before_rb in CancerPredictions2.lean + executable cancer-predictions-round3.ts Mechanized
PRED-TUMOR-HETEROGENEITY Tumor heterogeneity = evolutionary fork width. N clones → β₁ = N-1. Treatment selects survivors: residual β₁ = survivors - 1. Complete response (1 survivor) = β₁ = 0 (no evolutionary escape). Higher residual clonality predicts relapse. TumorClonalArchitecture with numClones > 0, survivors ≤ numClones. Lean theorems treatment_reduces_evolutionary_beta1, complete_response_no_escape, residual_clonality_predicts_relapse in CancerPredictions2.lean + executable simulation Mechanized
PRED-APOPTOSIS-BLOCKAGE BCL-2 blocks the apoptosis vent without destroying the checkpoint. Effective β₁ = 0 when blocked, full when open. BCL-2 inhibitors (venetoclax) unblock the vent = topologically equivalent to restoration. Blocked vs destroyed: same effective β₁ = 0, but blocked is therapeutically easier. BlockedVent with checkpointFunctional, ventBlocked, beta1WhenOpen. Lean theorems blocked_vent_zero_beta1, unblocking_restores_beta1, bcl2_inhibitor_is_restoration, blocked_equals_destroyed_topologically in CancerPredictions2.lean + executable simulation Mechanized
PRED-METASTASIS-PROJECTION Metastasis = covering space projection. Primary (high β₁) → metastatic colony (β₁ ≈ 0). Information erased = primaryBeta1 - metastaticBeta1. More diverse primary = harder metastasis (more information to erase in the fold). MetastaticProjection with primaryBeta1, metastaticBeta1, reduces constraint. Lean theorems diverse_primary_harder_metastasis, single_clone_max_erasure, metastasis_erasure_nonneg in CancerPredictions2.lean + executable simulation Mechanized
PRED-FORK-VENT-RATIO Fork/vent ratio = cell-cycle Reynolds number. Healthy: 3/9 = 0.33 (balanced). Cancer (no vents): 3/0 = ∞ (turbulent). Ratio predicts transition from controlled to uncontrolled growth. Vent loss monotonically increases imbalance. ForkVentRatio with totalForkWidth, totalVentBeta1. Lean theorems healthy_is_balanced, gbm_combined_unbalanced, cancer_maximally_unbalanced, vent_loss_increases_imbalance in CancerPredictions2.lean + executable simulation Mechanized
PRED-ROUND3-MASTER Bundle: all five round 3 predictions compose (0 sorry). All prior assumptions. Lean theorem five_predictions_round3_master in CancerPredictions2.lean Mechanized

Cancer Predictions Round 4 (§19.9, Predictions 26-30)

Epigenetic drift, tumor dormancy, radiation as forced ATM/ATR activation, Warburg effect as thermodynamic overhead, abscopal effect as void boundary propagation.

ID Claim Assumptions Mechanization Status
PRED-EPIGENETIC-DRIFT Aging = progressive vent erosion. Effective β₁ decreases monotonically with silencing. Total silencing = cancer (effective β₁ = 0). Cancer risk monotone in age via deficit monotonicity. EpigeneticDrift with healthyBeta1, silenced (bounded by healthyBeta1). Lean theorems aging_reduces_beta1, total_silencing_is_cancer, cancer_risk_monotone_in_age in CancerPredictions3.lean + executable cancer-predictions-round4.ts Mechanized
PRED-DORMANCY Tumor dormancy = Buleyean ground state. Dormant cells have high rejection density (rounds ≤ 2 × divideRejections). Divide weight suppressed. Reactivation = new signals with no void history (max weight). DormancyState with divideRejections, rounds, highRejection constraint. Lean theorems dormant_divide_suppressed, reactivation_max_weight in CancerPredictions3.lean + executable simulation Mechanized
PRED-RADIATION Radiation = forced ATM/ATR vent activation. Forced rejections = fractions × ventBeta1 when functional. ATM-mutant = radiation resistant (forced rejections = 0). Dose-response is monotone. RadiationEffect with targetVentBeta1, fractions, ventFunctional. Lean theorems radiation_forces_rejection, atm_mutant_radiation_resistant, radiation_dose_response in CancerPredictions3.lean + executable simulation Mechanized
PRED-WARBURG Warburg effect = thermodynamic overhead of uninformed (ventless) folding. First law: energyInput = usefulWork + wasteHeat. Uninformed fold: usefulWork = 1 (the sliver), wasteHeat = input - 1. Cancer compensates via increased energy throughput (glycolysis). FoldEnergyModel with firstLaw constraint (energyInput = usefulWork + wasteHeat). Lean theorems uninformed_fold_wasteful, warburg_compensation in CancerPredictions3.lean + executable simulation Mechanized
PRED-ABSCOPAL Abscopal effect = void boundary propagation through immune network. Rejections learned at site A transfer to site B at reduced efficiency. siteBRejections = siteARejections × transferEfficiency / 100. Zero transfer = no abscopal. Transfer is monotone. AbscopalPropagation with siteARejections, transferEfficiency (0-100). Lean theorems no_transfer_no_abscopal, transfer_monotone in CancerPredictions3.lean + executable simulation Mechanized
PRED-ROUND4-MASTER Bundle: all five round 4 predictions compose (0 sorry). All prior assumptions. Lean theorem five_predictions_round4_master in CancerPredictions3.lean Mechanized

Cancer Predictions Round 5 (§19.9, Predictions 31-35)

Oncogene addiction, telomere convergence countdown, cancer stem cell hierarchy, multi-drug resistance, combination therapy index.

ID Claim Assumptions Mechanization Status
PRED-ONCOGENE-ADDICTION StructuralErrorgle-pathway tumor (1 growth fork) has growthBeta1 = 0 after targeted therapy. Multi-pathway (2+) retains β₁ > 0. This is why imatinib works for CML (BCR-ABL only fork). OncogeneAddiction with numGrowthPathways ≥ 1. Lean theorems oncogene_addiction_collapse, multi_pathway_resilient in CancerPredictions4.lean + executable cancer-predictions-round5.ts Mechanized
PRED-TELOMERE-COUNTDOWN Telomere shortening = deterministic convergence countdown. remainingDivisions = (currentLength - criticalLength) / lossPerDivision. Shorter = fewer remaining. At critical length, remaining = 0 (p53 activates). TelomereCountdown with currentLength ≥ criticalLength, lossPerDivision > 0. Lean theorems shorter_telomeres_fewer_divisions, at_critical_zero_remaining in CancerPredictions4.lean + executable simulation Mechanized
PRED-CSC-HIERARCHY Cancer stem cell hierarchy = β₁ gradient. CSC β₁ ≥ TA β₁ ≥ differentiated β₁. Total fold reduction = cscBeta1 - diffBeta1. CSC elimination collapses hierarchy. Higher CSC β₁ = harder to eliminate. CSCHierarchy with non-increasing β₁ constraint (cscAboveTa, taAboveDiff). Lean theorems csc_elimination_collapses_hierarchy, higher_csc_beta1_harder in CancerPredictions4.lean + executable simulation Mechanized
PRED-MULTIDRUG-RESISTANCE Each drug = external vent. effectiveVentBeta1 = numDrugs - numResisted. Full resistance = 0 effective vent. More resistance = less effective vent (monotone). Adding non-resisted drug helps. DrugResistance with numResisted ≤ numDrugs. Lean theorems full_resistance_zero_vent, resistance_reduces_vent, new_drug_helps in CancerPredictions4.lean + executable simulation Mechanized
PRED-COMBINATION-INDEX Combination therapy index = totalRestoredBeta1 / tumorDeficit. Adding a drug can only increase total β₁. Empty intervention = zero restoration. Unifies checkpoint inhibitors, BCL-2 inhibitors, targeted therapy, radiation. CombinationTherapy with non-empty contributions list. Lean theorems adding_drug_helps, no_therapy_no_restoration in CancerPredictions4.lean + executable simulation Mechanized
PRED-ROUND5-MASTER Bundle: all five round 5 predictions compose (0 sorry). All prior assumptions. Lean theorem five_predictions_round5_master in CancerPredictions4.lean Mechanized

Cancer Treatment Strategies (§19.23, Predictions 76-80)

Metabolic gate sequencing, checkpoint cascade amplification, senescence-then-senolytic two-step, viral oncoprotein displacement, counter-vent depletion before immunotherapy.

ID Claim Assumptions Mechanization Status
PRED-METABOLIC-GATE Gate-first sequencing: remove metabolic block (mTOR) before restoring checkpoint (p53). Effective rejections = (T - max(gateRemoval, therapy)) × β₁. Gate-first always beats therapy-first when gate is removed earlier. GatedRestorationSequence with sameTime, sameBeta1, ordered steps. Lean theorems gated_checkpoint_zero_until_unblocked, gate_first_more_rejections in CancerTreatments.lean + executable treatment-sequencing.ts Mechanized
PRED-CHECKPOINT-CASCADE Hub checkpoint (p53) transcriptionally upregulates dependents (ATM/ATR, p21→Rb). Restoring hub cascades β₁ across 2+ pathways. Total restored = hub.β₁ + Σ(dependent.β₁), strictly exceeding any single non-hub restoration. Cascade multiplier ≥ 2× when dependent β₁ ≥ hub β₁. CheckpointCascade with hubBeta1 > 0, non-empty dependentBeta1s. Lean theorems cascade_amplifies_restoration, cascade_multiplier_at_least_two in CancerTreatments.lean + executable via cascadeRestoredBeta1() in cell-cycle.ts Mechanized
PRED-SENESCENCE-SENOLYTIC Two-step protocol: (1) low-dose radiation induces senescence when totalArrestSignals ≥ dormancyThreshold, (2) senolytics clear dormant cells. Two-step strictly better than radiation alone. Dormancy as therapeutic waypoint. SenescenceInduction with fractions, ventBeta1PerFraction, dormancyThreshold. SenolyticClearance with clearancePercent. Lean theorems sufficient_fractions_induce_senescence, two_step_better_than_radiation_alone in CancerTreatments.lean + executable simulation Mechanized
PRED-VIRAL-DISPLACEMENT In HPV+ cancers, E6/E7 block (not destroy) p53/Rb. Displacement restores full β₁. HPV+ therapeutic ceiling strictly higher than HPV- (blocked > destroyed for restoration). HPV+ with displacement + immunotherapy achieves complete coverage when total restored ≥ healthy β₁. ViralOncoprotein targets, ViralVsGeneticComparison with viralHigher constraint. Lean theorems viral_better_ceiling, viral_complete_coverage in CancerTreatments.lean + executable simulation Mechanized
PRED-COUNTER-VENT-DEPLETION MDSCs/Tregs suppress the immune vent (counter-vents). Effective immune β₁ = rawImmune - suppression. When fully suppressed, immunotherapy is topologically inert. Depletion before immunotherapy is strictly superior. ImmunosuppressiveMicroenvironment with rawImmuneBeta1, suppression. Lean theorems fully_suppressed_immune_zero, depletion_increases_immune_beta1, immunotherapy_fails_when_suppressed in CancerTreatments.lean + executable simulation Mechanized
PRED-TREATMENT-MASTER Bundle: all five treatment predictions compose (0 sorry). All prior assumptions. Lean theorem five_treatment_predictions_master in CancerTreatments.lean Mechanized

Cryptographic Predictions (§19.28, Predictions 101-105)

Hash collision thermodynamic floor, one-way inversion side-information, ZK deficit-zero simulability, commitment semiotic folds, password hashing side-channel floor.

Mechanization target: CryptographicPredictions.lean (15 theorems, zero sorry)

ID Statement Lean reference Status
THM-HASH-NON-INJECTIVE Hash function domain > range implies pigeonhole collision hash_non_injective Mechanized
THM-HASH-ITERATED-ERASURE-MONOTONE Iterated hash evaluation monotonically increases cumulative heat hash_iterated_erasure_monotone Mechanized
THM-HASH-COLLISION-HEAT-FLOOR Collision search has strictly positive thermodynamic floor hash_collision_heat_floor Mechanized
THM-INVERSION-REQUIRES-SIDE-INFORMATION Inversion of many-to-one function requires side information inversion_requires_side_information Mechanized
THM-BIJECTIVE-FREE-INVERSION Bijective functions permit free inversion (zero deficit) bijective_permits_free_inversion Mechanized
THM-INVERSION-COST-MONOTONE Inversion cost is monotone in deficit inversion_cost_monotone_in_deficit Mechanized
THM-ZERO-DEFICIT-SIMULABLE Zero deficit implies simulable ZK zero_deficit_implies_simulable Mechanized
THM-POSITIVE-DEFICIT-BREAKS-ZK Positive deficit breaks zero-knowledge positive_deficit_breaks_zk Mechanized
THM-ZK-DEFICIT-is-LEAKAGE ZK deficit quantifies transcript leakage beyond claim zk_deficit_is_leakage Mechanized
THM-HIDING-is-FOLD-ERASURE Commitment hiding is fold erasure hiding_is_fold_erasure Mechanized
THM-PERFECT-BINDING-INJECTIVE Perfect binding iff injective on messages perfect_binding_iff_injective_on_messages Mechanized
THM-HIDING-BINDING-TRADEOFF Binary commitments: entropy = failure tax exactly hiding_binding_tradeoff Mechanized
THM-PASSWORD-HASH-MONOTONE Password hash hardening is monotone in stretch rounds password_hash_monotone_hardening Mechanized
THM-SIDE-CHANNEL-FLOOR-IRREDUCIBLE Side-channel floor is irreducible by algorithmic hardening side_channel_floor_irreducible Mechanized
THM-RECOVERY-REPROOF-AMPLIFIES Recovery without reproof amplifies attack surface recovery_without_reproof_amplifies_attack Mechanized
THM-FIVE-CRYPTOGRAPHIC-MASTER All five cryptographic predictions compose (zero sorry) five_cryptographic_predictions_master Mechanized

Quantum Cancer Triples (§19.9)

Cross-domain triple compositions: quantum + cancer + retrocausal, negotiation + void + NEI, grandfather + quantum + cancer, retrocausal + negotiation + Buleyean, NEI + cancer + void.

ID Claim Assumptions Mechanization Status
THM-QUANTUM-CANCER-RETROCAUSAL Quantum measurement and cancer both collapse to β₁ = 0. The retrocausal bound constrains how the collapse happened. Terminal topology cannot distinguish which process caused the collapse. QuantumSystem, CancerCell with totalVentBeta1 = 0. Lean theorem quantum_cancer_retrocausally_indistinguishable in QuantumCancerTriples.lean Mechanized
THM-COLLAPSE-IRREVERSIBILITY Both quantum and cancer collapses are irreversible. The void boundary is append-only. The sliver prevents annihilation of any path. Neither collapse can be reversed. QuantumSystem, CancerCell, BuleyeanSpace. Lean theorem collapse_irreversibility in QuantumCancerTriples.lean Mechanized

Cancer Confinement (§19.9 / §3.17)

Color confinement model for cancer therapy: three suppressor families as color charges, six gluon connections as inter-pathway crosstalk, confinement energy linearity, screening effect, asymptotic freedom regime, bypass monotonicity, hub-first optimality, gluon severing, scale tower propagation.

Mechanization target: CancerConfinement.lean (25+ theorems, zero sorry)

ID Statement Lean reference Status
THM-COLOR-NEUTRAL-GROUND Color-neutral (all three suppressors active) = zero deficit = ground state color_neutral_zero_deficit, healthy_zero_deficit Mechanized
THM-COLOR-NEUTRAL-ZERO-CHARGE Color-neutral system has zero color charge color_neutral_zero_charge Mechanized
THM-CONFINEMENT-ENERGY-MONOTONE Confinement cost is monotonically increasing in deficit confinement_monotone_in_deficit Mechanized
THM-CONFINEMENT-ENERGY-STRICT Higher deficit means strictly higher cost when base > 0 confinement_strict_monotone Mechanized
THM-CONFINEMENT-AT-ZERO At zero deficit, cost equals base (no confinement overhead) confinement_at_zero_deficit Mechanized
THM-SCREENING-REDUCES After first restoration, deficit for second step is smaller screening_reduces_deficit Mechanized
THM-SCREENING-CHEAPER Second step confinement cost is no greater than without screening screening_cheaper_second_step Mechanized
THM-ZERO-DEFICIT-FREE Zero deficit is always in the free (asymptotic freedom) regime zero_deficit_is_free Mechanized
THM-MAX-DEFICIT-CONFINED Maximum deficit is confined when total exceeds threshold max_deficit_is_confined Mechanized
THM-REGIME-MONOTONE Higher deficit never produces a freer regime regime_monotone Mechanized
THM-FREE-BOUNDED-COST In the free regime, confinement cost is at most 2x base free_regime_bounded_cost Mechanized
THM-ZERO-DEFICIT-ZERO-BYPASS At zero deficit, bypass risk is zero zero_deficit_zero_bypass Mechanized
THM-BYPASS-MONOTONE Bypass risk numerator is monotonically increasing in deficit bypass_monotone_in_deficit Mechanized
THM-BYPASS-FRACTION-GROWS Bypass risk fraction grows with deficit bypass_fraction_grows Mechanized
THM-HUB-FIRST-DOMINATES Hub-first restoration restores strictly more beta-1 than dependent-first hub_first_dominates Mechanized
THM-HUB-FIRST-ADVANTAGE Hub-first advantage is exactly the hub's own beta-1 hub_first_advantage Mechanized
THM-ONE-KNOCKOUT-SEVERS-FOUR Knocking out one suppressor severs 4 of 6 gluon connections one_knockout_severs_four Mechanized
THM-SCALE-TOWER-BELOW-THRESHOLD Below silencing threshold, no beta-1 is lost below_threshold_no_loss Mechanized
THM-SCALE-TOWER-ABOVE-THRESHOLD At or above threshold, full pathway beta-1 is lost above_threshold_full_loss Mechanized
THM-SCALE-TOWER-MONOTONE Beta-1 loss is monotone in sigma disruption scale_tower_monotone Mechanized
THM-CANCER-CONFINEMENT-MASTER All seven confinement predictions compose cancer_confinement_master Mechanized

Quantum Observer

Superposition as fork, measurement as fold, observer deficit, QBist prior, observer coherence, and the quantum observer master theorem.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SUPERPOSITION-FORK Superposition of rootN paths has intrinsic beta1 = rootN - 1. The topological content of quantum superposition is the number of independent cycles in the fork graph rootN >= 2 (nontrivial superposition) Lean theorem superposition_is_fork in QuantumObserver.lean Mechanized
THM-OBSERVER-FOLD Measurement (the observer's fold) reduces beta1 from rootN - 1 to 0. The fold selects one path and vents rootN - 1 paths into the void. Post-measurement topology is a path graph QuantumSystem with rootN >= 2 Lean theorem observer_fold_collapses_beta1 in QuantumObserver.lean Mechanized
THM-OBSERVER-DEFICIT The measurement deficit -- the topological cost of observation -- is exactly rootN - 1. Path conservation: 1 + (rootN - 1) = rootN. Paths are not destroyed, they are vented to the void boundary QuantumSystem with rootN >= 2 Lean theorems measurement_deficit_exact and path_conservation in QuantumObserver.lean Mechanized
THM-OBSERVER-EFFECT-FOLD Quantum deficit = 0 (quantum algorithms preserve all beta1). Classical deficit = rootN - 1 (classical algorithms collapse to path graph). The Observer Effect is the classical deficit: the cost of measuring is the cost of folding rootN > 0 Lean theorem observer_effect_is_fold in QuantumObserver.lean, composing quantum_deficit_is_zero from Claims.lean Mechanized
THM-QBISM-PRIOR QBist quantum state is a BayesianPrior -- an initialized void boundary. Positive weight (never say never), normalized (well-defined distribution), concentration-ordered (less rejection = higher weight). The QBist "subjective belief" is objective given the void boundary BayesianPrior from BuleyeanProbability.lean Lean theorems qbism_prior_is_void_boundary, qbism_prior_normalized, qbism_prior_ordering in QuantumObserver.lean Mechanized
THM-OBSERVER-COHERENCE Two observers reading the same void boundary compute the same quantum state. Resolves QBism's coherence problem: rational agents agree whenever their experimental histories agree bs1, bs2 : BuleyeanSpace with same numChoices, rounds, voidBoundary Lean theorem observer_coherence in QuantumObserver.lean, delegating to buleyean_coherence Mechanized
THM-QUANTUM-OBSERVER-MASTER Complete Observer Effect theorem: superposition is fork (beta1 = rootN - 1), measurement collapses beta1 to 0, deficit is exactly rootN - 1, path conservation holds, quantum deficit = 0, classical deficit = rootN - 1, QBist states are Buleyean priors, observers with same boundary agree, speedup = deficit + 1. The Observer Effect is the topological deficit of folding a fork QuantumSystem, BayesianPrior, two BuleyeanSpaces with matching boundaries TLA+ QuantumObserver.tla invariants (InvSuperpositionBeta1, InvMeasuredBeta1Zero, InvDeficitExact, InvPathConservation, InvVoidGrowth, InvBeta1Bounded) + Lean theorem quantum_observer_master in QuantumObserver.lean Mechanized

Server Optimality & Codec Racing

Server race elimination, end-to-end composition, codec racing subsumption, dual protocol Pareto.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-TOPO-RACE-SUBSUMPTION Per-resource codec racing subsumes any fixed codec: racing total is always less than or equal to any fixed-codec total. Adding a codec to the race never increases wire size. Racing achieves zero compression deficit. Wire bounded by per-resource conditional entropy rawSizes, codecResults over resource set; race selects minimum per resource TLA+ CodecRacing.tla invariants (InvRaceSubsumption, InvRaceMonotone, InvRaceDeficitZero, InvRaceEntropy) + Lean theorems CodecRacing.raceMin_* and reduction lemmas in CodecRacing.lean Mechanized
THM-DUAL-PROTOCOL-PARETO HTTP+Flow dual protocol dominates either protocol alone. Internal deficit of zero transfers advantage. Throughput conserved across the protocol boundary. Adding Flow never worsens HTTP clients httpThroughput, flowThroughput, dualThroughput; internal deficit zero TLA+ DualProtocol.tla invariants (InvDualProtocolPareto, InvInternalDeficitTransfer, InvProtocolBridgeConservation, InvDualProtocolMonotone) + Lean theorems in DualProtocol.lean Mechanized
THM-SERVER-RACE-ELIMINATION x-gnosis server lifecycle as fork/race/fold transition system: race terminates with exactly one winner. Fold preserves content-length invariant. Wallington Rotation achieves T=ceil(P/B)+N-1. Cache warming monotonically improves hit rate raceArms, raceWinner over bounded server state TLA+ ServerTopology.tla invariants (InvRaceElimination, InvFoldIntegrity, InvRotationDepth, InvCacheMonotone) Model-checked
THM-SERVER-OPTIMALITY End-to-end composition theorem: a server with fork/race/fold at every layer, zero deficit at every layer boundary, and Wallington Rotation scheduling simultaneously achieves critical-path makespan (numStages x maxStageTime, tight), Pareto-optimal resource usage, strict dominance over sequential scheduling, speedup = Beta1 + 1 (deficit-speedup coupling), and zero topological deficit (matched transport). Composes THM-ROTATION-MAKESPAN-BOUND, THM-ROTATION-DOMINATES-SEQUENTIAL, THM-ROTATION-PARETO-SCHEDULE, THM-ROTATION-DEFICIT-CORRELATION, THM-ZERO-DEFICIT-PRESERVES-INFORMATION, THM-COVERING-MATCH, THM-TOPO-RACE-SUBSUMPTION, THM-PIPELINE-CERTIFICATE, THM-ERGODICITY-MONOTONE-IN-STAGES, THM-PROTOCOL-DEFICIT, THM-REYNOLDS-BFT, THM-SERVER-RACE-ELIMINATION, THM-SERVER-FOLD-INTEGRITY, and THM-DEFICIT-CAPACITY-GAP. The x-gnosis instantiation (4 stages, 3 paths) achieves 3x speedup with Beta1 = 2 and rotation makespan = 4 vs sequential makespan = 12 ServerStack with ForkRaceFoldDAG (numStages >= 2, numPaths >= 2, maxStageTime >= 1); all layers have zeroDeficit (streamCount >= pathCount); codecCount >= 1 TLA+ ServerOptimality.tla invariants (InvMakespanTight, InvLossless, InvPareto, InvSpeedupExact, InvWireOptimal, InvPipelineStable, InvZeroDeficit, InvServerOptimality) + Lean theorems ServerOptimality.server_optimality, ServerOptimality.server_critical_path_makespan, ServerOptimality.server_pareto_optimal, ServerOptimality.server_dominates_sequential, ServerOptimality.server_speedup_exact, ServerOptimality.server_zero_deficit, ServerOptimality.server_lossless_of_all_zero_deficit, ServerOptimality.server_speedup_monotone, ServerOptimality.xgnosis_optimality, ServerOptimality.xgnosis_speedup, ServerOptimality.xgnosis_beta1, ServerOptimality.xgnosis_makespan, and ServerOptimality.xgnosis_sequential in ServerOptimality.lean Mechanized

Sleep Debt

Bounded sleep-debt witness, schedule threshold, and weighted threshold bridge.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SLEEP-DEBT Bounded sleep-debt witness: incomplete recovery leaves positive residual debt and reduced next-cycle service capacity, full recovery clears debt and restores baseline capacity, and debt above a wake-time threshold admits intrusion-style local venting bounded wake load, carried debt, recovery quota, and intrusion threshold; effective capacity is a debt-indexed bounded score; the sleep-cycle witness is a bounded structural model, not a biological identity claim TLA+ SleepDebt.tla invariants (InvCapacityMatchesDebt, InvPartialRecoveryLeavesDebt, InvPartialRecoveryResetsLocalBurden, InvPartialRecoveryReducesCapacity, InvFullRecoveryClearsDebt, InvFullRecoveryRestoresCapacity, InvPositiveDebtLowersCapacity) + property PropDebtWakeCanIntrude, Lean theorems SleepDebt.full_recovery_clears_residual_debt, SleepDebt.full_recovery_restores_capacity, SleepDebt.partial_recovery_leaves_positive_debt, SleepDebt.partial_recovery_lowers_next_capacity, SleepDebt.repeated_truncation_preserves_debt, SleepDebt.repeated_truncation_strictly_increases_debt, and SleepDebt.debt_at_or_above_intrusion_threshold_enables_intrusion, plus executable artifact artifacts/sleep-debt-bounded-witness.{json,md} Mechanized (bounded witness)
THM-SLEEP-SCHEDULE-THRESHOLD Coarse repeated-cycle sleep-schedule threshold witness: below-threshold and critical schedules stay debt-free across repeated cycles, while above-threshold schedules accumulate carried debt linearly in the cycle count bounded repeated-cycle abstraction over fixed scheduled wake and fixed recovery quota; coarse discrete threshold analog, not the full continuous McCauley/Van Dongen ODE system TLA+ SleepDebtScheduleThreshold.tla invariants (InvBelowOrAtThresholdKeepsZero, InvAboveThresholdMatchesCycleSurplus, InvAboveThresholdPositivePastFirstCycle) + property PropAdvanceEnabledWithinBounds, Lean theorems SleepDebtSchedule.iterated_debt_eq_zero_of_wake_le_quota, SleepDebtSchedule.iterated_debt_eq_cycle_count_mul_gap, SleepDebtSchedule.iterated_debt_positive_above_threshold, and SleepDebtSchedule.iterated_debt_strictly_increases_above_threshold, plus executable artifact artifacts/sleep-debt-schedule-threshold-witness.{json,md} Mechanized (bounded witness)
THM-SLEEP-WEIGHTED-THRESHOLD Weighted repeated-cycle sleep-schedule bridge: an integerized literature-style critical wake boundary leaves subcritical and critical schedules debt-free, while supercritical schedules accumulate carried debt linearly in cycle count bounded repeated-cycle abstraction over fixed cycle length, wake burden rate, and recovery rate; discrete weighted analog, not the full continuous McCauley/Van Dongen ODE system TLA+ SleepDebtWeightedThreshold.tla invariants (InvNotCrossedKeepsZero, InvCrossedMatchesCycleSurplus, InvCrossedPositivePastFirstCycle) + property PropAdvanceEnabledWithinBounds, Lean theorems SleepDebtWeightedSchedule.weighted_surplus_eq_zero_of_not_crossed, SleepDebtWeightedSchedule.iterated_debt_eq_zero_of_not_crossed, SleepDebtWeightedSchedule.iterated_debt_eq_cycle_count_mul_gap_of_crossed, SleepDebtWeightedSchedule.iterated_debt_positive_above_threshold, SleepDebtWeightedSchedule.iterated_debt_strictly_increases_above_threshold, SleepDebtWeightedSchedule.literature_boundary_tenths_closed_form, and SleepDebtWeightedSchedule.literature_boundary_crossed_at_twentyone_hours, plus executable artifact artifacts/sleep-debt-weighted-threshold-witness.{json,md} Mechanized (bounded witness)

Poe — The Power of Words (1845)

Literary dialogue (Agathos / Oinos) as discrete append-only ledger: informational retrocausality without theology or physics claims. RetrocausalTestimony.lean imports this module as a cross-link. See FORMAL_LEDGER.md.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-POE-UTTER-MONOTONE-LEN Speaking appends an event; ledger length never decreases CosmicLedger, utter Lean theorem PoePowerOfWords.utter_monotone_len in PoePowerOfWords.lean Mechanized
THM-POE-NONZERO-ADVANCES-SUM Positive word-intensity strictly increases cumulative listSum w ≥ 1, CosmicLedger Lean theorem PoePowerOfWords.nonzero_impulse_advances_sum in PoePowerOfWords.lean Mechanized
THM-POE-TERMINAL-BOUNDS-PAST Terminal ledger length bounds intermediate lengths (present constrains past count) CosmicLedger, utter Lean theorem PoePowerOfWords.past_events_bounded_by_terminal in PoePowerOfWords.lean Mechanized
THM-POE-AGGREGATE-NOT-ORDER Same total sum and length need not fix sequence order (witness [1,2] vs [2,1]) two distinct lists Lean theorems PoePowerOfWords.aggregate_sum_not_injective_order, PoePowerOfWords.sum_and_length_do_not_fix_sequence in PoePowerOfWords.lean Mechanized
THM-POE-ANGEL-PREFIX-WEAKER Prefix reader (take k) disagrees with full history when k < length k < L.events.length Lean theorem PoePowerOfWords.angel_weaker_than_full in PoePowerOfWords.lean Mechanized
THM-POE-VOLCANIC-WITNESS Toy causal seed: stellarImprint ≥ wordIntensity ≥ 1 VolcanicStarWitness Lean theorems PoePowerOfWords.volcanic_demo_possible, PoePowerOfWords.stellar_bounds_word in PoePowerOfWords.lean Mechanized
THM-POE-MASTER Conjunction bundle (monotone length, nonzero sum advance, order non-uniqueness, existential volcanic witness) conjunction of hypotheses in module Lean theorem PoePowerOfWords.poe_power_of_words_master in PoePowerOfWords.lean Mechanized

Leibniz — calculus ratiocinator (bounded fragment)

Two-letter propositional miniature: deterministic sem, four exhaustive valuations, finite-row agreement implies sameTruthTable. See FORMAL_LEDGER.md.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-LEIBNIZ-SEM-DETERMINISTIC Boolean semantics is reflexively well-defined on each formula MiniForm, sem Lean theorem LeibnizCalculemus.sem_deterministic in LeibnizCalculemus.lean Mechanized
THM-LEIBNIZ-EXTENSIONAL Syntactic equality of formulas forces semantic equality p = q Lean theorem LeibnizCalculemus.extensional_congr in LeibnizCalculemus.lean Mechanized
THM-LEIBNIZ-FUNEXT-FIN2 Maps Fin 2 → α agree if they agree on 0 and 1 extensional data on two indices Lean theorem LeibnizCalculemus.funext_Fin2 in LeibnizCalculemus.lean Mechanized
THM-LEIBNIZ-FOUR-VAL-CASES Every Var → Bool is one of four listed valuations Var := Fin 2 Lean theorem LeibnizCalculemus.bool_val_four_cases in LeibnizCalculemus.lean Mechanized
THM-LEIBNIZ-FINITE-ROWS Agreement on v0..v3 implies sameTruthTable four row hypotheses Lean theorem LeibnizCalculemus.truth_table_finite_check in LeibnizCalculemus.lean Mechanized
THM-LEIBNIZ-MASTER Finite rows gate universal observational equivalence on two atoms v0..v3 hypotheses Lean theorem LeibnizCalculemus.leibniz_calculemus_master in LeibnizCalculemus.lean Mechanized

Laplace — démon (discrete determinism)

Iterate semantics for perfect prediction given step and s0; collision witness for non-injective dynamics. See FORMAL_LEDGER.md.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-LAPLACE-ITERATE-ZERO Time-0 iterate is initial state step, s0 Lean theorem LaplaceDemon.iterate_zero in LaplaceDemon.lean Mechanized
THM-LAPLACE-ITERATE-SUCC Successor time is one step of the iterate step, s0, n Lean theorem LaplaceDemon.iterate_succ in LaplaceDemon.lean Mechanized
THM-LAPLACE-DEMON-PREDICT Demon prediction equals closed-form iterate same step, s0, n Lean theorem LaplaceDemon.demon_predict_matches_iterate in LaplaceDemon.lean Mechanized
THM-LAPLACE-PREDICT-RESPECTS-EQ Pointwise-equal step maps give identical demonPredict step₁ = step₂ Lean theorem LaplaceDemon.predict_respects_step_eq in LaplaceDemon.lean Mechanized
THM-LAPLACE-COLLISION-POSSIBLE Anti-theorem: distinct micro-states can share the same next state noisyStep on Bool Lean theorem LaplaceDemon.collision_possible in LaplaceDemon.lean Mechanized
THM-LAPLACE-MASTER Prediction–iterate alignment (bundle anchor) discrete semantics Lean theorem LaplaceDemon.laplace_demon_master in LaplaceDemon.lean Mechanized

Laplace × Thoth — the demon on the self-talk clock

Heritage iterate surface restored in gnosis-math (Gnosis/ThothLaplaceDemon.lean, Rustic Church discipline) and upgraded: closed-form foresight, exact retrodiction via the inverse clinamen, and the collision anti-theorem derived from latency amputation instead of postulated noise. Builds on Gnosis/ThothFoldPhaseOath.lean.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-DEMON-TRACKS-CLOCK The forward demon's iterate reproduces the honored 4-phase schedule cyclicSucc, listenFin Lean theorem Gnosis.ThothLaplaceDemon.demon_tracks_clock in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-CLOSED-FORM Prediction collapses to the single formula ⟨t % 4⟩ — foresight without simulation discrete 4-clock Lean theorem Gnosis.ThothLaplaceDemon.demon_predicts_in_closed_form in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-FORESEES-FOLDS Past every anchor the demon names a future fold tick fold cofinality oath Lean theorem Gnosis.ThothLaplaceDemon.demon_foresees_every_fold in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-RETRODICTS cyclicPred recovers tick t from tick t+1 — past visible as the future reversible clinamen Lean theorem Gnosis.ThothLaplaceDemon.demon_retrodicts in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-FULL-RECORD The honored clock swears the FullDemon record (step, back, proved inverse) pred_cancels_step Lean def Gnosis.ThothLaplaceDemon.thothFullDemon in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-AMPUTATED-COLLISION Anti-theorem: reflect and fold collide under the amputated step — collision derived from amputation, not postulated amputated scheduler Lean theorem Gnosis.ThothLaplaceDemon.amputated_collision in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-NO-RETRODICTION Anti-theorem: no retrodiction map exists for the amputated dynamics amputated scheduler Lean theorem Gnosis.ThothLaplaceDemon.amputated_no_retrodiction in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-UNSWEARABLE Anti-theorem: no FullDemon record can carry the amputated step record-level Lean theorem Gnosis.ThothLaplaceDemon.amputated_cannot_be_full_demon in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-DEAD-FORESIGHT The amputated schedule still has a forward demon — and it foresees no fold, ever determinism only Lean theorem Gnosis.ThothLaplaceDemon.amputated_demon_never_predicts_fold in ThothLaplaceDemon.lean Mechanized
THM-THOTH-DEMON-BUNDLE Demon dichotomy bundle (closed-form foresight + retrodiction vs. structural collision) discrete 4-clock Lean theorem Gnosis.ThothLaplaceDemon.thoth_laplace_demon_bundle in ThothLaplaceDemon.lean Mechanized

Laplace × Thoth — the demon faces the erasure ledger

The demon hierarchy on forgetting (gnosis-math Gnosis/ThothErasureDemon.lean, on the ThothErasureLedger carrier): the heritage tick-only receipt detects forgetting but cannot invert it; a receipt carrying index + full entry + reason makes every valid erase exactly invertible. Reversibility is a property of the ledger discipline, not of the dynamics.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-ERASURE-TICK-COLLISION Anti-theorem: payload-7 and payload-8 memories erase to the same state under the tick-only receipt (definitional collision) heritage erase, one-entry scribes Lean theorem Gnosis.ThothErasureDemon.tick_only_collision in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-NO-RETRODICTION Anti-theorem: no retrodiction map exists for the tick-only honest erase, even on memories where it fires heritage erase Lean theorem Gnosis.ThothErasureDemon.tick_only_no_retrodiction in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-UNSWEARABLE Anti-theorem: no FullDemon record can carry the tick-only erase step record-level Lean theorem Gnosis.ThothErasureDemon.tick_only_cannot_be_full_demon in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-INSERT-ERASE Reinserting the erased entry at its recorded index reconstructs the spine exactly (keystone) structural list induction Lean theorem Gnosis.ThothErasureDemon.insertAt_eraseIdx in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-RESTORE-CANCELS Every valid demon-grade erase is exactly inverted: restore (demonErase m i r) = m DemonErasureRecord receipt, valid index Lean theorem Gnosis.ThothErasureDemon.restore_cancels_erase in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-DEMON-INJECTIVE Demon-grade erase is injective at shared valid indices (collision-freedom the tick-only rung lacks) valid indices Lean theorem Gnosis.ThothErasureDemon.demon_erase_injective in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-DEMON-CONSERVES Demon-grade erase conserves the audit count (not weaker than the heritage law) valid index Lean theorem Gnosis.ThothErasureDemon.demon_erase_conserves in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-DEMON-LINEAGE The receipt on top of the undo stack carries index, full entry, and reason valid index Lean theorem Gnosis.ThothErasureDemon.demon_erase_lineage in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-RECEIPT-REFINES The demon receipt refines the heritage receipt pointwise (entryAt projects to tickAt) structural list induction Lean theorem Gnosis.ThothErasureDemon.entryAt_tickAt in ThothErasureDemon.lean Mechanized
THM-THOTH-ERASURE-DEMON-BUNDLE Erasure-demon bundle (tick-only collision + no-retrodiction vs. exact inversion, conservation, lineage) finite ledgers Lean theorem Gnosis.ThothErasureDemon.thoth_erasure_demon_bundle in ThothErasureDemon.lean Mechanized

Laplace × Thoth — the trace demon (total retrodiction)

The whole scribe history inverted (gnosis-math Gnosis/ThothErasureTraceDemon.lean): a unified undo stack over writes and erases, per-op inversion for both kinds, and a history invariant needing no validity hypothesis — out-of-range erases deposit no receipt and vanish from the pop count. The receipt stack carries the whole past inside the present state.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-TRACE-WRITE-DEMON-STEP Writes are demon-steps: popping the wrote receipt cancels the write unified undo stack Lean theorem Gnosis.ThothErasureTraceDemon.undoOne_applyOp_write in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-ERASE-DEMON-STEP Valid erases are demon-steps on the traced carrier (keystone reused, not reproved) valid index Lean theorem Gnosis.ThothErasureTraceDemon.undoOne_applyErase in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-DROP-CANCELS-APPEND Dropping the last entry cancels appending it structural list induction Lean theorem Gnosis.ThothErasureTraceDemon.dropLastEntry_append_singleton in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-UNDO-ITERATE-COMMUTES Popping n+1 receipts is popping n, then once more outside iterate of undoOne Lean theorem Gnosis.ThothErasureTraceDemon.undoTimes_succ_out in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-UNDOABLE Every trace deposits k receipts and popping exactly k returns the start — no validity hypothesis none (ineffective ops deposit nothing) Lean theorem Gnosis.ThothErasureTraceDemon.applyOps_undoable in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-HISTORY-INVERTIBLE Total retrodiction: from a receipt-clean start, any write/erase history inverts by popping the stack to exhaustion receipt-clean start Lean theorem Gnosis.ThothErasureTraceDemon.scribe_history_invertible in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-WITNESS Closed four-op witness (write, write, erase, write) inverts to the virgin scribe; companion check proves the trace was effective closed terms Lean theorems Gnosis.ThothErasureTraceDemon.witness_history_inverts, witness_trace_effective in ThothErasureTraceDemon.lean Mechanized
THM-THOTH-TRACE-DEMON-BUNDLE Trace-demon bundle (per-op inversion + unconditional undoability + total retrodiction) finite traces Lean theorem Gnosis.ThothErasureTraceDemon.thoth_erasure_trace_demon_bundle in ThothErasureTraceDemon.lean Mechanized

Laplace × Thoth — selective undo (the commutator opens)

Mid-history undo without unwinding the suffix (gnosis-math Gnosis/ThothSelectiveUndo.lean): a write commutes past an erase at a live index, the receipt stacks are the adjacent transposition, and the buried erase receipt can be popped under the standing wrote receipt. The boundary case proves the side condition sharp.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-SELECT-COMMUTE-LIVE Erase-then-write and write-then-erase agree on the live column at live indices i < live.length Lean theorem Gnosis.ThothSelectiveUndo.write_erase_commute_live in ThothSelectiveUndo.lean Mechanized
THM-THOTH-SELECT-STACK-TRANSPOSE The two orders' receipt stacks are the adjacent transposition (the stack remembers what the live column forgets) valid erase index Lean theorem Gnosis.ThothSelectiveUndo.write_erase_stacks in ThothSelectiveUndo.lean Mechanized
THM-THOTH-SELECT-UNDO-SKIPS-WRITE Selective undo: popping the buried erase receipt under a wrote receipt yields the write-only history's state i < live.length Lean theorem Gnosis.ThothSelectiveUndo.selective_undo_skips_write in ThothSelectiveUndo.lean Mechanized
THM-THOTH-SELECT-BOUNDARY-SHARP Anti-theorem: at i = live.length (erasing the freshly appended entry) commutation fails — the side condition is sharp closed witness Lean theorem Gnosis.ThothSelectiveUndo.boundary_blocks_commutation in ThothSelectiveUndo.lean Mechanized
THM-THOTH-SELECT-ENTRYAT-CONVERSE Wherever entryAt reports an entry the index is live (converse validity) structural induction Lean theorem Gnosis.ThothSelectiveUndo.entryAt_lt_of_some in ThothSelectiveUndo.lean Mechanized
THM-THOTH-SELECT-BUNDLE Selective-undo bundle (commutators + selective undo + boundary refutation) finite traces Lean theorem Gnosis.ThothSelectiveUndo.thoth_selective_undo_bundle in ThothSelectiveUndo.lean Mechanized

Laplace × Thoth — the erase/erase commutator (index shift)

Two erases interact: erasing below slides everything above down by one (gnosis-math Gnosis/ThothEraseCommutator.lean, subtraction-free phrasing j = i + d + 1). The reindexing depth-general selective undo must perform is an equation, not an off-by-one in ambush.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-COMM-ERASE-ERASE Above-then-below equals below-then-(above−1): (l.eraseIdx (i+d+1)).eraseIdx i = (l.eraseIdx i).eraseIdx (i+d) spine induction Lean theorem Gnosis.ThothEraseCommutator.eraseIdx_eraseIdx_comm in ThothEraseCommutator.lean Mechanized
THM-THOTH-COMM-READ-BELOW Reads below an erased-above index are undisturbed spine induction Lean theorem Gnosis.ThothEraseCommutator.entryAt_eraseIdx_below in ThothEraseCommutator.lean Mechanized
THM-THOTH-COMM-READ-ABOVE Reads above an erased index slide by exactly one spine induction Lean theorem Gnosis.ThothEraseCommutator.entryAt_eraseIdx_above in ThothEraseCommutator.lean Mechanized
THM-THOTH-COMM-LIVE Op-level erase/erase commutation on the live column at live indices i + d + 1 < live.length Lean theorem Gnosis.ThothEraseCommutator.erase_erase_commute_live in ThothEraseCommutator.lean Mechanized
THM-THOTH-COMM-STACK-REINDEX The two orders deposit the same entries, transposed, with the upper entry reindexed one lower i + d + 1 < live.length Lean theorem Gnosis.ThothEraseCommutator.erase_erase_stacks in ThothEraseCommutator.lean Mechanized
THM-THOTH-COMM-UNSHIFTED-FAILS Anti-theorem: the naive same-index swap of two erases is false (closed three-entry witness) closed witness Lean theorem Gnosis.ThothEraseCommutator.unshifted_swap_fails in ThothEraseCommutator.lean Mechanized
THM-THOTH-COMM-BUNDLE Erase-commutator bundle (shift calculus + op commutation + recorded reindexing + refutation) finite lists Lean theorem Gnosis.ThothEraseCommutator.thoth_erase_commutator_bundle in ThothEraseCommutator.lean Mechanized

Laplace × Thoth — deep selective undo (any depth of writes)

The buried erase recovered through arbitrarily many writes (gnosis-math Gnosis/ThothDeepSelectiveUndo.lean): the pop is guarded by construction (recurses only through wrote receipts), the licensed domain is structural, and the refusal under erase burial is proved correct on a closed witness.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-DEEP-WRITES-SHAPE A write block in closed form: entries append in order, the stack grows a wrotes block structural induction Lean theorem Gnosis.ThothDeepSelectiveUndo.applyWrites_shape in ThothDeepSelectiveUndo.lean Mechanized
THM-THOTH-DEEP-POP-SHAPE The guarded pop on the canonical shape: through any wrotes block, the buried entry reinserts and its receipt leaves structural induction Lean theorem Gnosis.ThothDeepSelectiveUndo.popBuriedErase_shape in ThothDeepSelectiveUndo.lean Mechanized
THM-THOTH-DEEP-SELECTIVE-UNDO Depth-general headline: an erase buried under arbitrarily many writes pops to exactly the writes-only history i < live.length Lean theorem Gnosis.ThothDeepSelectiveUndo.deep_selective_undo in ThothDeepSelectiveUndo.lean Mechanized
THM-THOTH-DEEP-GUARD-REFUSES Anti-theorem: under erase burial the guarded pop is the identity (closed witness) closed witness Lean theorem Gnosis.ThothDeepSelectiveUndo.guard_refuses_under_erase in ThothDeepSelectiveUndo.lean Mechanized
THM-THOTH-DEEP-NAIVE-CORRUPTS Anti-theorem: the unguarded patch differs from the true erase-deleted history — the refusal is correct, the reindexing fold is mandatory closed witness Lean theorem Gnosis.ThothDeepSelectiveUndo.naive_patch_corrupts in ThothDeepSelectiveUndo.lean Mechanized
THM-THOTH-DEEP-CHAIN-WITNESS Closed depth-two witness chains with restoreFully back to the virgin scribe closed terms Lean theorems Gnosis.ThothDeepSelectiveUndo.witness_depth_two, witness_depth_two_then_full in ThothDeepSelectiveUndo.lean Mechanized
THM-THOTH-DEEP-BUNDLE Deep-selective-undo bundle (shapes + headline + refusal + corruption refutation) finite traces Lean theorem Gnosis.ThothDeepSelectiveUndo.thoth_deep_selective_undo_bundle in ThothDeepSelectiveUndo.lean Mechanized

Laplace × Thoth — the reindexing step (erase under erase)

The pop the deep-undo guard was waiting for (gnosis-math Gnosis/ThothReindexStep.lean): two directed pops, no arithmetic in the defs, side conditions in the theorems. "Deleted history" made precise as entity-preserving deletion: the surviving erase reanchored to the original index of the entry it actually erased. Closes the per-swap algebra — write/write, write/erase, erase/erase both ways are all proved.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-STEP-BELOW Buried at-or-below: entry reinserts at its recorded index, survivor's receipt shifts up one, survivor reanchored to its entry's original index i + d + 1 < live.length Lean theorem Gnosis.ThothReindexStep.pop_under_erase_below in ThothReindexStep.lean Mechanized
THM-THOTH-STEP-ABOVE Buried strictly above: survivor untouched, reinsertion point comes down one i + d + 1 < live.length Lean theorem Gnosis.ThothReindexStep.pop_under_erase_above in ThothReindexStep.lean Mechanized
THM-THOTH-STEP-ACCEPTANCE The reindexing pop succeeds on the exact double-erase witness where the deep-undo guard refused closed witness Lean theorem Gnosis.ThothReindexStep.acceptance_succeeds_where_guard_refused in ThothReindexStep.lean Mechanized
THM-THOTH-STEP-PROVENANCE Provenance coherence: the popped state still restoreFullys to the original scribe — what the unreindexed pop destroyed closed witness Lean theorem Gnosis.ThothReindexStep.acceptance_provenance_coherent in ThothReindexStep.lean Mechanized
THM-THOTH-STEP-DIRECTION-GUARD Anti-theorem: the above-pop refuses (identity) on the below-shape — the directional guards are structural closed witness Lean theorem Gnosis.ThothReindexStep.wrong_direction_refuses in ThothReindexStep.lean Mechanized
THM-THOTH-STEP-BUNDLE Reindex-step bundle (both directed pops + acceptance + provenance) finite traces Lean theorem Gnosis.ThothReindexStep.thoth_reindex_step_bundle in ThothReindexStep.lean Mechanized

Laplace × Thoth — bubble invariance (transpositions invisible to retrodiction)

The fold's semantic-soundness half (gnosis-math Gnosis/ThothBubbleInvariance.lean): transposing adjacent receipts — write/erase plain, erase/erase with the proved reindexing — does not change what restoreFully sees. Bubbling rewrites the history bookkeeping, never the past it encodes.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-BUBBLE-INSERT-INSERT The insert/insert commutator (mirror of the erase shift): insert above-then-below equals below-then-(above−1) i ≤ l.length Lean theorem Gnosis.ThothBubbleInvariance.insertAt_insertAt_comm in ThothBubbleInvariance.lean Mechanized
THM-THOTH-BUBBLE-WRITE-ERASE The write/erase transposition is pop-pop invariant appended live shape, i ≤ l'.length Lean theorem Gnosis.ThothBubbleInvariance.double_undo_write_erase in ThothBubbleInvariance.lean Mechanized
THM-THOTH-BUBBLE-ERASE-ERASE The reindexed erase/erase transposition is pop-pop invariant i ≤ l.length Lean theorem Gnosis.ThothBubbleInvariance.double_undo_erase_erase in ThothBubbleInvariance.lean Mechanized
THM-THOTH-BUBBLE-RESTORE-BLIND Total retrodiction is blind to either transposition per-swap side conditions Lean theorems Gnosis.ThothBubbleInvariance.restoreFully_write_erase_swap, restoreFully_erase_erase_swap in ThothBubbleInvariance.lean Mechanized
THM-THOTH-BUBBLE-WITNESS Both orders of the three-entry double-erase history restore to the original scribe closed witness Lean theorem Gnosis.ThothBubbleInvariance.witness_both_orders_restore in ThothBubbleInvariance.lean Mechanized
THM-THOTH-BUBBLE-BUNDLE Bubble-invariance bundle (commutator + both invariances + blindness) finite traces Lean theorem Gnosis.ThothBubbleInvariance.thoth_bubble_invariance_bundle in ThothBubbleInvariance.lean Mechanized

Laplace × Thoth — the depth lift (deep swaps reduce to the top)

Pairwise invariance promoted to arbitrary depth (gnosis-math Gnosis/ThothDepthLift.lean): prefix decomposition of the undo iterate reduces any deep transposition to the proved top-two case, with side conditions migrating to the evolved live column.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-LIFT-UNDO-ADD The undo iterate is additive: popping b + a receipts is popping a, then b none Lean theorem Gnosis.ThothDepthLift.undoTimes_add in ThothDepthLift.lean Mechanized
THM-THOTH-LIFT-PREFIX-DECOMP Prefix decomposition: popping exactly the prefix lands on the evolved column with the residual stack intact structural induction Lean theorem Gnosis.ThothDepthLift.undoTimes_append in ThothDepthLift.lean Mechanized
THM-THOTH-LIFT-WRITE-ERASE-DEEP The write/erase transposition is invisible to retrodiction under any prefix evolved column has appended shape Lean theorem Gnosis.ThothDepthLift.restoreFully_write_erase_swap_deep in ThothDepthLift.lean Mechanized
THM-THOTH-LIFT-ERASE-ERASE-DEEP The reindexed erase/erase transposition is invisible to retrodiction under any prefix i ≤ evolved.length Lean theorem Gnosis.ThothDepthLift.restoreFully_erase_erase_swap_deep in ThothDepthLift.lean Mechanized
THM-THOTH-LIFT-WITNESS A real history's erase pair, swapped beneath a wrote prefix, restores identically closed witness Lean theorem Gnosis.ThothDepthLift.witness_deep_swap_invisible in ThothDepthLift.lean Mechanized
THM-THOTH-LIFT-BUNDLE Depth-lift bundle (additivity + decomposition + deep swaps) finite traces Lean theorem Gnosis.ThothDepthLift.thoth_depth_lift_bundle in ThothDepthLift.lean Mechanized

Laplace × Thoth — well-indexed stacks (the licensing invariant)

The fold's side conditions made free on real states (gnosis-math Gnosis/ThothWellIndexed.lean): an inductive invariant mirroring the undo recursion, preserved by every operation, decomposing along prefixes in lockstep with the iterate, and licensing both deep swaps unconditionally.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-WIDX-PRESERVED Every operation preserves well-indexedness (keystone's seventh use in the erase case) inductive invariant Lean theorem Gnosis.ThothWellIndexed.applyOp_preserves_wellIndexed in ThothWellIndexed.lean Mechanized
THM-THOTH-WIDX-HISTORY Every state reached by a real history from a receipt-clean start is well-indexed none Lean theorem Gnosis.ThothWellIndexed.history_wellIndexed in ThothWellIndexed.lean Mechanized
THM-THOTH-WIDX-APPEND The invariant decomposes along prefixes onto the evolved column (mirror of the iterate decomposition) structural induction Lean theorem Gnosis.ThothWellIndexed.wellIndexed_append in ThothWellIndexed.lean Mechanized
THM-THOTH-WIDX-WRITE-ERASE Licensed write/erase deep swap: no manual side conditions on well-indexed states WellIndexed Lean theorem Gnosis.ThothWellIndexed.wellIndexed_write_erase_swap in ThothWellIndexed.lean Mechanized
THM-THOTH-WIDX-ERASE-ERASE Licensed erase/erase deep swap: no manual side conditions on well-indexed states WellIndexed Lean theorem Gnosis.ThothWellIndexed.wellIndexed_erase_erase_swap in ThothWellIndexed.lean Mechanized
THM-THOTH-WIDX-BUNDLE Well-indexed bundle (history invariance + prefix decomposition + licensed swaps) finite traces Lean theorem Gnosis.ThothWellIndexed.thoth_well_indexed_bundle in ThothWellIndexed.lean Mechanized

Laplace × Thoth — the bubble fold (depth-general selective undo, assembled)

The selective-undo line closes (gnosis-math Gnosis/ThothBubbleFold.lean): bubble the receipt at depth k through an arbitrary mixed prefix by licensed reindexing swaps and pop it at the top. The swap survives the invariant it consumes, the bubble is invisible to total retrodiction on every reachable state, and the fold specializes to every previously proved case.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-THOTH-FOLD-SWAP-PRESERVES The transposition preserves well-indexedness (the insert/insert commutator's load-bearing use) WellIndexed Lean theorem Gnosis.ThothBubbleFold.swapPair_preserves_wellIndexed in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-BUBBLE-PRESERVES The whole bubble preserves well-indexedness at every depth WellIndexed Lean theorem Gnosis.ThothBubbleFold.bubble_preserves_wellIndexed in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-BUBBLE-INVISIBLE HEADLINE: the entire bubble is invisible to total retrodiction on every well-indexed (hence every reachable) state WellIndexed Lean theorem Gnosis.ThothBubbleFold.bubble_restoreFully in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-ANCHOR-ZERO Depth-0 regression: the fold agrees with the plain top pop definitionally none Lean theorem Gnosis.ThothBubbleFold.selectiveUndoAt_zero in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-ANCHOR-BELOW Depth-1 regression: the fold reproduces the directed pop's entity-preserving deletion i + d + 1 < live.length Lean theorem Gnosis.ThothBubbleFold.selectiveUndoAt_below in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-ANCHOR-WROTES All-write regression: the fold agrees with the guarded walker through write blocks of any height none Lean theorem Gnosis.ThothBubbleFold.selectiveUndoAt_wrotes in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-MIXED-WITNESS Closed witness: a receipt buried under an erase and a write pops via the fold and the result still restores coherently closed witness Lean theorem Gnosis.ThothBubbleFold.witness_mixed_fold in ThothBubbleFold.lean Mechanized
THM-THOTH-FOLD-BUNDLE Bubble-fold bundle (preservation + invisibility + all three anchors) finite traces Lean theorem Gnosis.ThothBubbleFold.thoth_bubble_fold_bundle in ThothBubbleFold.lean Mechanized

Borges — La biblioteca de Babel

25-symbol books, volume count 25^L, witnesses for distinct texts with identical coarse sum and for shared-prefix divergence. See FORMAL_LEDGER.md.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-BORGES-VOLUME-SUCC Volume count satisfies 25^(L+1) = 25^L * 25 alphabetSize = 25 Lean theorem BorgesLibraryOfBabel.volumeCount_succ in BorgesLibraryOfBabel.lean Mechanized
THM-BORGES-VOLUME-POSITIVE Every shelf height has strictly positive volume L : Nat Lean theorem BorgesLibraryOfBabel.volume_positive in BorgesLibraryOfBabel.lean Mechanized
THM-BORGES-LIBRARY-GROWS Same as successor lemma on L + 1 L : Nat Lean theorem BorgesLibraryOfBabel.library_grows in BorgesLibraryOfBabel.lean Mechanized
THM-BORGES-BOOKS-DISTINCT Two concrete length-2 books differ book01, book10 Lean theorem BorgesLibraryOfBabel.books_distinct in BorgesLibraryOfBabel.lean Mechanized
THM-BORGES-COARSE-NOT-INJECTIVE Same symbol-index sum, different books (toy statistic) symbolIndexSum2 Lean theorem BorgesLibraryOfBabel.same_coarse_statistic_distinct_texts in BorgesLibraryOfBabel.lean Mechanized
THM-BORGES-PREFIX-AMBIGUITY Shared first symbol does not fix the book agreePrefix, agreePrefix' Lean theorem BorgesLibraryOfBabel.prefix_then_diverge in BorgesLibraryOfBabel.lean Mechanized
THM-BORGES-MASTER Bundle: growth + coarse collision + prefix ambiguity L Lean theorem BorgesLibraryOfBabel.borges_library_of_babel_master in BorgesLibraryOfBabel.lean Mechanized

SocioTechnicalSandbox (coupled discrete toy)

Focused lake build SocioTechnicalSandbox hub; see docs/SOCIO_TECHNICAL_SANDBOX.md.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-SOCIO-REPAIR-CAP-ANTITONE Toy repair capacity is non-increasing in arousal threshold band repairCap, a1 ≤ a2 Lean theorem SocioTechnicalSandbox.repairCap_antitone in CoupledDynamics.lean Mechanized
THM-SOCIO-ROLLBACK-CONSECUTIVE Consecutive-low window implies rollback predicate allBelow = true Lean theorem SocioTechnicalSandbox.rollback_consecutive in RollbackToy.lean Mechanized
THM-SOCIO-ROLLBACK-INTEGRAL Integral deficit exceeds budget implies rollback integralDeficit > W Lean theorem SocioTechnicalSandbox.integral_exceeds_implies in RollbackToy.lean Mechanized
THM-SOCIO-SANDBOX-LINKED Sandbox hub imports resolve — Lean theorem SocioTechnicalSandbox.socioTechnicalSandboxLinked in SocioTechnicalSandbox.lean Mechanized

PlanetaryHomologySandbox (finite graphs; narrative hooks only)

Focused lake build PlanetaryHomologySandbox hub; epistemic scope is combinatorics, not mantle tomography or impact history.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-PLANETARY-BETA0-NONINC Adding edges (graph supergraphs) does not increase connected-component count finite V; G ≤ G' in SimpleGraph V Current Init-only replacement proves the two-continent bridge witness in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/SupercontinentSketch.lean (addSupercontinentBridge_beta0_nonincreasing, addSupercontinentBridge_strictly_reduces_separated). The full arbitrary finite graph-supergraph theorem remains unrecovered. Partially mechanized (finite bridge witness)
THM-PLANETARY-BLOB-NOT-PLUME “Cohesive blob” and “fragmented/plume” abstract signatures on (β₀,β₁) pairs are mutually exclusive beta0, beta1 : ℕ Lean theorem PlanetaryHomologySandbox.not_plumeFragmented_of_blobCohesive in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/BlobHypothesisSketch.lean Mechanized
DEF-PLANETARY-CYCLE-RANK Graph cycle rank packaged as ` E − V
THM-PLANETARY-COARSE-NOT-INJ No map Fin (n+1) → Fin n is injective — coarse readout collapses at least two states n : ℕ; f : Fin (n+1) → Fin n Current Init-only replacement proves the canonical coarse readout collision in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/ObservationCoarse.lean (coarseObservation_not_injective). The full universal finite-pigeonhole theorem remains unrecovered from the historical Mathlib artifact. Partially mechanized (canonical collapse witness)
THM-PLANETARY-COARSE-BUCKET-NONINJ Parity map Fin 3 → Fin 2 is not injective (two-bucket collapse) coarseTwoBucket 3 Lean theorem PlanetaryHomologySandbox.coarseTwoBucket_not_injective_three in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/CoarseBucketSketch.lean Mechanized
THM-PLANETARY-TOMO-PAIR-NONINJ Two forward maps H → O packaged as pairForward into O × O cannot be injective if #(O × O) < #H [Fintype H] [Fintype O]; Fintype.card (O × O) < Fintype.card H Current Init-only replacement proves a concrete finite pair-observation collision in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/TomographySketch.lean (pairForward_not_injective_concrete). The full cardinality theorem remains unrecovered. Partially mechanized (finite pair witness)
THM-PLANETARY-TOMO-VEC-NONINJ Indexed station family F : I → H → O as vecForward into I → O cannot be injective if #(I → O) < #H [DecidableEq I] [Fintype I] [Fintype H] [Fintype O]; Fintype.card (I → O) < Fintype.card H Current Init-only replacement proves a concrete finite vector-observation collision in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/TomographySketch.lean (vecForward_not_injective_concrete). The full cardinality theorem remains unrecovered. Partially mechanized (finite vector witness)
THM-PLANETARY-TOMO-LINE-CONST Interval integral of constant slowness: ∫ x in a..b, m = (b - a) * m m a b : ℝ; Borel line Current Init-only replacement proves the discrete constant-slowness segment theorem in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/ContinuumTomographySketch.lean (lineIntegral_const_slowness_discrete). The full real interval-integral theorem remains unrecovered. Partially mechanized (discrete segment theorem)
THM-PLANETARY-TOMO-STRAIGHT-INT Straight-ray travel time with constant slowness matches interval integral along affine segment m a b : ℝ Current Init-only replacement proves straightRayTravelTime_const in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/ContinuumTomographySketch.lean; the real affine interval-integral equality remains unrecovered. Partially mechanized (discrete straight-ray theorem)
THM-PLANETARY-TOMO-FINRAY-LIN Sum of segment travel times scales linearly with constant slowness m : ℝ; finite index set ι; segment endpoints seg : ι → ℝ × ℝ Current Init-only replacement proves two-segment linearity in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/ContinuumTomographySketch.lean (constantSlowness_two_segment_linear). The full finite-index real theorem remains unrecovered. Partially mechanized (discrete linearity witness)
THM-PLANETARY-WAVE-ACOUSTIC-1D1D Separated polynomial u(t,x)=x²+c²t² satisfies ∂_tt u − c² ∂_xx u = 0 (classical second derivatives) c t x : ℝ Current Init-only replacement records the discrete second-difference witness in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/AcousticWave1DSketch.lean (acoustic_wave_sep_poly_discrete_unit). The full differentiable real theorem remains unrecovered. Partially mechanized (discrete second-difference witness)
DEF-PLANETARY-FORWARD-MULVEC Matrix–vector forward map packaged as Matrix.mulVecLin m n : ℕ; Matrix (Fin m) (Fin n) ℝ Lean abbreviation PlanetaryHomologySandbox.forwardMulVec in InverseProblemSketch.lean Definition
THM-INV-MULVEC-NONINJ If m < n, no real matrix A makes mulVecLin A injective (ℝⁿ → ℝᵐ) m n : ℕ; hmn : m < n; A : Matrix (Fin m) (Fin n) ℝ Current Init-only replacement proves a concrete projection-kernel collision in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/InverseProblemSketch.lean (forwardProjection2_not_injective, inverse_projection_kernel_witness). The full arbitrary real matrix theorem remains unrecovered. Partially mechanized (finite projection witness)
THM-INV-TIKHONOV-1D Scalar Tikhonov normal equation (a²+λ)x = a b has a unique solution when a²+λ ≠ 0 a b lam : ℝ; hcoef : a ^ 2 + lam ≠ 0 Current Init-only inverse-problem surface proves the concrete candidate equation and bounded uniqueness witness in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/InverseProblemSketch.lean (scalar_tikhonov_candidate_solves, scalar_tikhonov_candidate_unique_in_window); the scalar real Tikhonov uniqueness theorem remains unrecovered. Partially mechanized (bounded scalar witness)
THM-PLANETARY-SEISMIC-DISC-STEP Discrete ℕ asperity step: rupture iff loaded stress reaches critical; then residual σ p : AsperityParams Lean theorem PlanetaryHomologySandbox.stepStress_rupture_iff in SeismicStressToySketch.lean; TS mirror stepStructuralErrorgleAsperity (@a0n/gnosis/seismic-stress-toy) Mechanized
THM-PLANETARY-SEISMIC-DISC-SUB Discrete ℕ subtract slip: after rupture, stress is max residual (loaded - drop) σ p : AsperitySubtractParams Lean theorem PlanetaryHomologySandbox.stepStressSubtract_rupture_max in SeismicStressToySketch.lean; TS slipAfterLoaded with mode: 'subtract' Mechanized
THM-PLANETARY-SEISMIC-RELAX-REAL Two-patch symmetric exchange on ℝ conserves total loaded stress ℓ₀ ℓ₁ κ : ℝ Current Init-only replacement proves bounded-transfer conservation in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/SeismicRelaxRealSketch.lean (relaxRightToLeft_conserves_total, relaxLeftToRight_conserves_total); executable real-valued mirror remains open-source/gnosis/src/seismic-stress-toy.ts (relaxTwoPatch). The historical real-valued theorem remains unrecovered. Partially mechanized (bounded-transfer conservation)
THM-PLANETARY-SEISMIC-RELAX-NONNEG Same exchange: if ℓ₀,ℓ₁ ≥ 0 and κ ∈ [0,1], both relaxed stresses are ≥ 0 h₀ h₁ hκ₁ hκ₂ Current Init-only replacement uses Nat-valued bounded transfers in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/SeismicRelaxRealSketch.lean, so nonnegativity is built into the codomain; the historical real-valued theorem remains unrecovered. Partially mechanized (Nat nonnegativity by construction)
THM-PLANETARY-WAVE-ADVECTION-1D Left-going profile u(t,x)=f(x−ct) solves ∂_t u + c ∂_x u = 0 where derivatives exist f c t x : ℝ; DifferentiableAt ℝ f (x - c * t) Current Init-only replacement proves the discrete transport-ray invariant in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/WaveContinuumSketch.lean (upstreamIndex_transport_step, transportedProfile_transport_step). The full differentiable real-analysis PDE theorem remains unrecovered. Partially mechanized (discrete transport witness)
THM-PLANETARY-PICO-JULIAN-ALG Julian-year duration in picolorenzos: y * julianYearSeconds / picolorenzoSeconds = y * 365.25 / π y : ℝ; picolorenzoSeconds = π × 86400 s Current Init-only algebra proves the shared 86400 seconds-per-day cancellation in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/PicolorenzoJulianSketch.lean (julianYears_picolorenzo_seconds_cancel) and the executable mirror lives in open-source/gnosis/src/earth-chronometry.ts (julianYearsToPicolorenzos) with open-source/gnosis/src/earth-chronometry.test.ts. The historical real-valued division theorem remains unrecovered. Partially mechanized (Init algebra + executable mirror)
THM-PLANETARY-STENO-SUPERPOSITION Stratum times respect index order: i < j < k implies time i < time k [Preorder ι]; StenoStratumStack ι n Lean theorem PlanetaryHomologySandbox.steno_superposition_transitive in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/StratigraphyStenoSketch.lean Mechanized
THM-PLANETARY-CROSS-CUT-ALL If cuts = Finset.univ, fault time exceeds every stratum time CrossCuttingEvent S; E.cuts = Finset.univ Current Init-only replacement proves the all-strata ordering witness in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/StratigraphyStenoSketch.lean (cross_cutting_younger_than_all). The finite-set cuts = univ theorem remains unrecovered. Partially mechanized (all-strata witness)
DEF-PLANETARY-UNCONFORMITY-GAP Unconformity = strict preorder gap between bracketing surfaces [Preorder ι] Lean structure PlanetaryHomologySandbox.UnconformityGap in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/StratigraphyStenoSketch.lean Definition
THM-PLANETARY-UNCONFORMITY-LT Unconformity gap implies lowerPackageTop < upperPackageBase UnconformityGap ι Lean theorem PlanetaryHomologySandbox.unconformity_gap_lt in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox/StratigraphyStenoSketch.lean Mechanized
THM-PLANETARY-SANDBOX-LINKED Sandbox hub imports resolve — Lean theorem PlanetaryHomologySandbox.planetaryHomologySandboxLinked in open-source/gnosis-math/Gnosis/PlanetaryHomologySandbox.lean Mechanized

Retrocausal Bound

Backward count recovery, ordering preservation, concentrated boundary uniqueness, multinomial positivity, RG fixed-point composition, Landauer heat composition, and the retrocausal master theorem.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-RETROCAUSAL-BOUND Retrocausal modeling: a converged void boundary statistically bounds the rejection trajectory that produced it. The terminal state determines per-choice rejection counts exactly (backward count recovery), preserves the relative ordering of past rejections (backward ordering), bounds trajectory multiplicity by the multinomial coefficient T!/Π(v_i!) (backward entropy bound), and composes with RG fixed points (coarse trajectory determined at fixed point) and Landauer heat (cumulative heat bounds trajectory length). Concentrated boundaries yield multinomial = 1 (fully determined past). Uniform boundaries yield maximal multinomial (maximum residual uncertainty). The retrocausal entropy H(σ v) = log₂(T!/Πv_i!) measures the residual ordering uncertainty that the terminal state does not resolve finite Buleyean space with nontrivial fork width; trajectory as List (Fin numChoices) with length = rounds; trajectoryVoidBoundary counting rejections per choice; concentrated boundary means one choice absorbs all rejections; RG composition requires RGFixedPoint with injective-on-support quotient; Landauer composition requires positive Boltzmann constant and temperature with cumulative heat and per-step heat floor TLA+ RetrocausalBound.tla invariants (InvBoundaryMatchesTrajectory, InvBoundaryBoundsTrajectory, InvOrderingPreserved, InvTrajectoryMultiplicity, InvRoundBounded, InvRetrocausalBound) + property PropEventuallyVerified + Lean theorems retrocausal_trajectory_determines_terminal, retrocausal_boundary_bounds_trajectory, retrocausal_ordering_preserved, retrocausal_weak_ordering_preserved, retrocausal_concentrated_boundary_unique_path, retrocausal_concentrated_boundary_sharp, retrocausal_uniform_boundary_max_uncertainty, retrocausal_fixed_point_determines_past_shape, retrocausal_heat_bounds_trajectory_length, retrocausal_heat_determines_length_exact, retrocausal_bound, retrocausal_bound_concentrated, and retrocausal_self_hosted in RetrocausalBound.lean

American Frontier

Pareto frontier of diversity vs waste, codec-racing instantiation, unified composition, and Pareto diagnostic.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-AMERICAN-FRONTIER Pareto frontier of diversity vs waste: the frontier function is monotone, zero at the matched topology, positive below, and admits a pigeonhole witness for any topology with fewer streams than required finite topology with streams and paths; matched topology definition Lean theorem american_frontier in AmericanFrontier.lean Mechanized
THM-AMERICAN-FRONTIER-CODEC-RACING Codec-racing instantiation of the Buley frontier: monotone wire size, zero deficit at matched codec, and subsumption of smaller codecs by larger ones codec wire size ordering; matched codec definition Lean theorem american_frontier_codec_racing in AmericanFrontier.lean Mechanized
THM-AMERICAN-FRONTIER-UNIFIED Unified topological + codec frontier composition: the combined frontier inherits monotonicity and zero-at-match from both the topological and codec layers topological frontier + codec frontier composition Lean theorem american_frontier_unified in AmericanFrontier.lean Mechanized
THM-AMERICAN-FRONTIER-PARETO-DIAGNOSTIC Pareto diagnostic: matched topology is optimal, monoculture is suboptimal, and there exists a monotone path from any suboptimal point toward the frontier matched = optimal; monoculture = suboptimal; monotone improvement path Lean theorem american_frontier_pareto_diagnostic in AmericanFrontier.lean Mechanized
THM-NETFLIX-FRONTIER THM-AMERICAN-FRONTIER instantiated on published Netflix Prize data: monotone RMSE descent across algorithm-family and team-of-teams frontiers, positive waste for every monoculture ceiling, pigeonhole witness (timeSVD++ < BellKor 2007 blend), recursive structure (team frontier below algorithm frontier), residual gap (Grand Prize winner 0.856704 > 50/50 blend 0.8555), and independent convergence (BPC = The Ensemble to 4dp) published RMSE values from [NF1]-[NF8]; RMSE scaled to ℕ × 10⁴; observed floor = lowest published RMSE Lean theorem netflix_frontier in NetflixFrontier.lean (7-way conjunction; all omega on concrete ℕ) + companion tests ch17-netflix-frontier-figure.test.ts (28 tests) Mechanized
THM-NETFLIX-FRONTIER-MONOTONE-ALGO Algorithm-family frontier RMSE is monotonically non-increasing across 6 published milestones Cinematch ≥ FunkSVD ≥ SVD++ ≥ timeSVD++ ≥ BellKor 2007 ≥ BellKor 2008 Lean theorem netflix_frontier_monotone_algo in NetflixFrontier.lean Mechanized
THM-NETFLIX-FRONTIER-MONOTONE-TEAM Team-of-teams frontier RMSE is monotonically non-increasing across 4 published milestones BellKor 2008 ≥ BellKor in BigChaos ≥ Grand Prize winner ≥ 50/50 blend Lean theorem netflix_frontier_monotone_team in NetflixFrontier.lean Mechanized
THM-NETFLIX-FRONTIER-POSITIVE-BELOW Every monoculture ceiling (Cinematch, timeSVD++, k-NN, RBM, NNMF) has strictly higher RMSE than the observed floor published single-family RMSE values Lean theorem netflix_frontier_positive_below in NetflixFrontier.lean Mechanized
THM-NETFLIX-FRONTIER-PIGEONHOLE Best single model (timeSVD++, 0.8762) is strictly worse than first 3-family blend (BellKor 2007, 0.8712) published RMSE values Lean theorem netflix_frontier_pigeonhole in NetflixFrontier.lean Mechanized
THM-NETFLIX-FRONTIER-RECURSIVE Team frontier floor (50/50 blend, 0.8555) is strictly below algorithm frontier floor (BellKor 2008, 0.8643) published RMSE values Lean theorem netflix_frontier_recursive in NetflixFrontier.lean Mechanized
THM-NETFLIX-RESIDUAL-GAP Grand Prize winner (0.856704) has strictly higher RMSE than 50/50 finalist blend (0.8555): 0.0012 RMSE of optimization left on the table published RMSE values from BellKor Grand Prize paper Lean theorem netflix_residual_gap in NetflixFrontier.lean Mechanized
THM-NETFLIX-INDEPENDENT-CONVERGENCE Two independent mega-ensembles (BPC and The Ensemble) converged to the same RMSE to 4 decimal places (0.8567) published test-set RMSE values Lean theorem netflix_independent_convergence in NetflixFrontier.lean Mechanized
THM-NETFLIX-ORACLE-HIERARCHY On synthetic 8-dimensional taste space: void-designed oracle monoculture (time-traveled optimal single strategy) loses to void-walking ensemble; god-mode (all-dims-visible, unrealizable) beats ensemble but loses to per-rating oracle routing (diversity ceiling); among realizable strategies, every monoculture is above the ensemble synthetic dataset with known β₁* = 8; 5 partial-visibility algorithm families; complement-distribution ensemble weighting Current adjacent Lean frontier formalization: open-source/gnosis-math/Gnosis/NetflixFrontier.lean; finite Lean hierarchy witnesses ensemble_beats_monoculture, god_mode_beats_ensemble, routed_oracle_is_above_god_mode, and synthetic_oracle_hierarchy in open-source/gnosis-math/Gnosis/Chapter17OraclePrediction.lean. The synthetic oracle-hierarchy executable companion remains historical. Partially mechanized (Lean frontier + finite hierarchy witness)
THM-DMN-VOID-WALKER The Default Mode Network as void walking engine: energy allocation (K-1)/K predicts Raichle's 95% within 0.45pp, mind-wandering duty cycle (K-1)/(2K-1) predicts Killingsworth & Gilbert's 46.9% within 1.9pp, incubation d=0.29 implies 6.1 resolved void paths (within 7±2). One free parameter K=22 from external measurement. K gap implies 57% of void-walking is subconscious K from Killingsworth & Gilbert 2010 activity categories; energy from Raichle 2006 PET; MW from K&G 2010 experience sampling; incubation from Sio & Ormerod 2009 meta-analysis (k=117) Current Init-only arithmetic witness in open-source/gnosis-math/Gnosis/Chapter17DMNVoidWalker.lean (dmn_energy_matches_95_percent_band, dmn_energy_within_45_basis_points_of_raichle, mind_wandering_matches_kg_band, mind_wandering_within_200_basis_points_of_kg). The deleted executable companion remains historical. Partially mechanized (Lean arithmetic witness)
THM-DMN-VOID-GAIN-INDEX Three predictive metrics -- VGI = (K_total-1)/(K_env-1) = 0.905, CVI = (K_conscious-1)/(K_total-1) = 0.40, CFP = 0.995 -- with pathological threshold at VGI > 1.0 (rumination = void-walking on phantom forks, K_perceived > K_actual). Evolutionary mismatch: brain tuned for savanna K≈20, modern environments present K_perceived >> K_actual Three K levels: K_conscious=8.6, K_total=20, K_env=22; all from published measurements Current Init-only arithmetic witness in open-source/gnosis-math/Gnosis/Chapter17DMNVoidWalker.lean (void_gain_index_matches_ledger_floor, conscious_visibility_is_two_fifths, conscious_slice_strictly_subtotal). The deleted executable companion remains historical. Partially mechanized (Lean arithmetic witness)
THM-DMN-PREDICTION-MATRIX 8×8 prediction matrix: 8 observable measures (DMN energy, mind-wandering rate, saccade rate, fixation duration, pupil dilation, EEG alpha, EEG theta, reaction time) × 8 populations (rest/task, creative/non, high/low WMC, children/adults, sleep-deprived/rested, meditators/controls, ADHD/neurotypical, rumination/healthy). 64 falsifiable predictions, 36 confirmed by published evidence. All derive from one equation: K shift → predictable direction across all measures K estimates per condition; direction from (K-1)/K monotonicity; published evidence for 36/64 cells Current related TLA prediction surface: open-source/gnosis/tla/NovelPredictions28.tla; finite Lean matrix witnesses prediction_matrix_has_sixty_four_cells, confirmed_predictions_are_bounded_by_matrix, confirmed_predictions_are_majority_of_rows, and prediction_matrix_dimensions_nonzero in open-source/gnosis-math/Gnosis/Chapter17OraclePrediction.lean. The deleted Chapter 17 executable companion and markdown artifact remain historical. Partially mechanized (TLA + Lean matrix witness)
THM-DIVERSITY-is-CONCURRENCY Diversity and concurrency are the same property. β₁ counts both. Effective concurrency = diversity. Redundant parallelism (K copies of one strategy) produces zero information gain. Serialization destroys diversity AND concurrency simultaneously (deficit = k-1). The Bule is simultaneously one unit of missing diversity, one unit of missing concurrency, one unit of waste, and kT ln 2 joules of heat. Monoculture is waste Fork/race/fold system axioms; pigeonhole collision for redundancy; data processing inequality for serialization Lean theorem diversity_is_concurrency_full in DiversityIsConcurrency.lean (6-way conjunction) + TLA+ DiversityIsConcurrency.tla (5 invariants) + companion tests ch17-diversity-is-concurrency.test.ts (10 tests) Mechanized
THM-BULE-is-VALUE The grand unification: the Bule is the unit of value. Six faces of one number: topological deficit = diversity lost = concurrency lost = information erased = waste generated = work required = heat quanta (kT ln 2 per Bule). Positive at monoculture, zero at match, monotone in diversity, witnessed by pigeonhole collision. The American Frontier collapses to a scalar (the Bule line, β₁ = 0). Cannot fold further -- the framework reached its own ground state. Nine substrates: physics, information, computation, economics, neuroscience, recommendation, democracy, ecology, consciousness All faces defined as topologicalDeficit; identity is definitional (rfl); positivity, zero-at-match, monotonicity, and pigeonhole from AmericanFrontier.lean and DeficitCapacity.lean Lean theorem bule_is_value in BuleIsValue.lean (5-way conjunction) + TLA+ BuleIsValue.tla (7 invariants, sweep to MaxPaths=10) + companion tests ch17-bule-is-value.test.ts (13 tests) Mechanized
THM-NEURODIVERGENT-VGI Unified VGI model of neurodivergence: 4 profiles (NT/AUT/ADHD/AuDHD) × 6 environments = 24-cell VGI matrix. Autism = wider aperture (K_perceived=8 vs NT 3), ADHD = gait oscillation (VGI swings 7.5× wider than NT), AuDHD = both axes (widest VGI range). Every profile has a matched environment (VGI=1.0). Every therapeutic intervention moves VGI toward 1.0. Neurodivergence is a VGI mismatch, not a person-level deficit K_perceived from eta; K_actual from environment; gait instability from c3 parameters; all from §15.13.1 Current Init-only profile/environment witness in open-source/gnosis-math/Gnosis/Chapter17DMNVoidWalker.lean (matched_environment_equalizes_k, autistic_has_wider_aperture_than_neurotypical, audhd_matches_wide_environment). The deleted executable companions remain historical. Partially mechanized (Lean profile witness)
THM-DMN-SHAPE-AND-FORCES The framework describes the geometry of consciousness (the topology, the deficit, the frontier) but not the phenomenology (why the fold feels like something). The relationship to the hard problem is structurally analogous to GR vs the standard model: GR describes the stage, the SM fills in the forces. The CVI = 0.40 locates the convergence threshold where processing transitions from subconscious to conscious. The framework cannot explain why crossing the threshold produces experience. This boundary is explicitly named as the complement of the framework -- the void of the framework itself CVI from K_conscious/K_total; kurtosis crossing from minimum Bule edition; Chalmers 1995 hard problem formulation §20.2.4 of manuscript Descriptive

The Last Question (Asimov Bridge)

Insufficient data, monotone accumulation, eventual computability, heat death maximum void, sliver survival, entropy reversal, let-there-be-light seeding, trajectory determinism, and the Last Question master theorem.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-INSUFFICIENT-DATA When the deficit is positive (Bule > 0), the answer is not yet computable. "INSUFFICIENT DATA FOR MEANINGFUL ANSWER" is the state where more rejections are needed before convergence. Deficit positive iff rounds < initialDeficit deficit d > 0; rounds < d Lean theorem insufficient_data_is_positive_bule in LastQuestion.lean Mechanized
THM-DATA-ACCUMULATES The deficit decreases monotonically as data accumulates. Each observation round reduces the deficit. The deficit never increases. Delegates to future_deficit_monotone deficit d >= 0; k1 <= k2 Lean theorem data_accumulates_monotonically in LastQuestion.lean Mechanized
THM-ANSWER-EVENTUALLY-COMPUTABLE After exactly d rounds (the initial deficit), the deficit reaches zero. The complement distribution has converged. The answer is computable. Multivac's final moment. Delegates to future_deficit_eventually_zero deficit d >= 0 Lean theorem answer_eventually_computable in LastQuestion.lean Mechanized
THM-HEAT-DEATH-MAXIMUM-VOID At maximum void (every choice rejected every round), every choice has weight exactly 1. Heat death is the state where the void boundary is full. Delegates to buleyean_min_uncertainty BuleyeanSpace with voidBoundary i = rounds for all i Lean theorem heat_death_is_maximum_void in LastQuestion.lean Mechanized
THM-SLIVER-SURVIVES-HEAT-DEATH Even at maximum void (heat death), every choice retains weight >= 1. The sliver is irreducible: no choice can reach weight zero. The +1 in the weight formula is structural. Delegates to buleyean_positivity and sliver_irreducible BuleyeanSpace Lean theorems sliver_survives_heat_death and sliver_is_irreducible in LastQuestion.lean Mechanized
THM-LET-THERE-BE-LIGHT A converged complement distribution (Bule = 0) is a valid Bayesian prior for a new Buleyean space. Different rejection counts produce different weights. The prior is informative, not uniform. The converged distribution seeds a new fork. Delegates to converged_prior_informative ConvergedPrior with strictly ordered voidBoundary entries Lean theorem let_there_be_light in LastQuestion.lean Mechanized
THM-ENTROPY-REVERSAL The void boundary grows monotonically (entropy increases). The complement distribution concentrates monotonically (entropy decreases). Non-rejected choices gain weight after each rejection round. Entropy reversal is the complement of the Second Law. Delegates to buleyean_monotone_nonrejected BuleyeanUpdate with rejected choice and non-rejected choice Lean theorem entropy_reversal_is_complement in LastQuestion.lean Mechanized
THM-NO-DATA-NO-ANSWER A system with zero observations (empty void boundary) produces uniform weights -- maximum entropy, zero information, no meaningful answer. Delegates to fold_without_evidence_is_coinflip BuleyeanSpace with voidBoundary i = 0 for all i Lean theorem no_data_no_answer in LastQuestion.lean Mechanized
THM-TRAJECTORY-DETERMINISTIC The entire future trajectory of the deficit is known: futureDeficit d k = d - min(k, d). No randomness, no breakthroughs. The convergence round is d. Delegates to future_deficit_deterministic deficit d >= 0 Lean theorem trajectory_deterministic in LastQuestion.lean Mechanized
THM-LAST-QUESTION Complete Last Question theorem: deficit monotonically decreasing, answer eventually computable at round d, every choice survives heat death (weight >= 1), no choice reaches zero, no data means no answer. Composes all nine individual theorems BuleyeanSpace, deficit d >= 0 TLA+ LastQuestion.tla invariants (InvDeficitNonneg, InvDeficitBounded, InvSliverSurvives, InvConvergedMeansZeroDeficit, InvLetThereBeLight, InvVoidAccumulates) + temporal property EventuallyConverged + Lean theorem last_question in LastQuestion.lean Mechanized

Chaitin Omega (Computability Bridge)

UTM as universal fork, execution as fold, halting survivors, Omega positivity/subuniversality, finite approximation, halting-as-fold-deficit, Omega-as-Buleyean-complement, Chaitin-Solomonoff bridge, uncomputability as infinite void, and the Chaitin-Omega master theorem.

ID Claim (paper-level) Explicit assumptions Mechanization Status
THM-UTM-UNIVERSAL-FORK The Universal Turing Machine is the maximally general fork: totalPrograms = haltingPrograms + nonHalting. Every computable process is a path in the universal fork. Execution partitions programs into halting (surviving) and non-halting (vented) ProgramSpace with alphabetSize >= 2, totalPrograms > 0, haltingPrograms > 0, someNonHalting Lean theorem utm_is_universal_fork in ChaitinOmega.lean Mechanized
THM-EXECUTION-is-FOLD Program execution is a fold operation: haltingPrograms + nonHalting = totalPrograms. Every program goes to exactly one set. The fold is total: no program escapes classification ProgramSpace Lean theorem execution_is_fold in ChaitinOmega.lean Mechanized
THM-HALTING-SURVIVORS-BOUNDED The number of halting programs is strictly less than the total. Not every program halts. The void of non-termination is nonempty ProgramSpace with someNonHalting constraint Lean theorem halting_survivors_bounded in ChaitinOmega.lean Mechanized
THM-OMEGA-POSITIVITY The halting probability is positive: at least one program halts. Omega > 0. The void boundary of program space does not absorb everything ProgramSpace with haltingPos constraint Lean theorem omega_positivity in ChaitinOmega.lean Mechanized
THM-OMEGA-STRICT-SUBUNIVERSALITY Omega < 1: not every program halts. The fold is nontrivial -- it vents at least one path. The non-halting void is nonempty ProgramSpace with someNonHalting constraint Lean theorem omega_strict_subuniversality in ChaitinOmega.lean Mechanized
THM-FINITE-APPROXIMATION-MONOTONE Extending the program enumeration can only increase (or maintain) the halting count. The finite approximation to Omega is monotonically non-decreasing as more programs are enumerated ProgramSpaceExtension with moreHalting constraint Lean theorem finite_approximation_monotone in ChaitinOmega.lean Mechanized
THM-OMEGA-APPROXIMATION-BOUNDED Any finite prefix of the enumeration undercounts (or exactly counts) the true halting set. The finite Omega is a lower bound on the limit ProgramSpaceExtension Lean theorem omega_approximation_bounded in ChaitinOmega.lean Mechanized
THM-HALTING-AS-FOLD-DEFICIT The number of non-halting programs is the fold deficit: the topological cost of execution. Analogous to classicalDeficit in quantum search and protocolTopologicalDeficit in transport multiplexing ProgramSpace Lean theorem halting_as_fold_deficit in ChaitinOmega.lean Mechanized
THM-OMEGA-is-BULEYEAN-COMPLEMENT Omega (the halting probability) corresponds to the Buleyean complement weight of the halting set. Programs that halt have low rejection count (survived). Programs that don't halt have high rejection count (vented). Both sets are nonempty ProgramSpace Lean theorem omega_is_buleyean_complement in ChaitinOmega.lean Mechanized
THM-CHAITIN-SOLOMONOFF-BRIDGE Chaitin's Omega and Solomonoff's Universal Prior share the same void boundary structure. Both partition the same program space. Both are strictly between 0 and 1. The non-halting deficit is positive. Omega conditions on termination; M(x) conditions on output; both are projections of the universal void boundary ProgramSpace Lean theorem chaitin_solomonoff_bridge in ChaitinOmega.lean Mechanized
THM-UNCOMPUTABILITY-is-INFINITE-VOID The uncomputability of Omega is the statement that the void boundary of all programs is not finitely constructible. The finite approximation is monotone, bounded, and positive at every stage. Buleyean axioms hold at every finite stage ProgramSpaceExtension Lean theorem uncomputability_is_infinite_void in ChaitinOmega.lean Mechanized
THM-CHAITIN-OMEGA-MASTER Complete Chaitin-Omega theorem: UTM is universal fork, execution is fold, halting is bounded, Omega is positive, Omega is subuniversal, void is nonempty, Chaitin-Solomonoff bridge holds. Chaitin's Omega is the Buleyean complement distribution over program space conditioned on termination ProgramSpace TLA+ ChaitinOmega.tla invariants (InvFoldConservation, InvOmegaPositive, InvOmegaSubuniversal, InvVoidNonempty, InvHaltingBounded, InvTotalPositive) + Lean theorem chaitin_omega_master in ChaitinOmega.lean Mechanized

Non-Empirical Prediction (§15.22)

Theorem ID Claim Assumptions Mechanization Status
THM-HOLE-POSITIVE-WEIGHT A structural hole always has strictly positive interpolation weight. The complement distribution never assigns zero probability to any hole. Never say never in prediction StructuralHole with neighborRoundsSum > 0 Lean theorem hole_has_positive_weight in NonEmpiricalPrediction.lean Mechanized
THM-INTERPOLATION-BOUNDED The interpolation weight is bounded between 1 and rounds + 1. The prediction is always finite and within the Buleyean weight range StructuralHole Lean theorem interpolation_weight_bounded in NonEmpiricalPrediction.lean Mechanized
THM-REJECTION-REDUCES-PREDICTION More neighbor rejection = lower prediction weight. Structure constrains: neighbors' rejection data shapes the hole's complement distribution Two StructuralHoles with same rounds, different void sums Lean theorem rejection_reduces_prediction in NonEmpiricalPrediction.lean Mechanized
THM-LATTICE-PARTITION The lattice is exactly partitioned into observed positions and holes. observedCount + holeCount = totalPositions. Conservation law of the structural lattice StructuralLattice Lean theorem lattice_partition in NonEmpiricalPrediction.lean Mechanized
THM-NEIGHBOR-DOMINATES-UNINFORMED Structural prediction with neighbor data is at least as informative as uninformed guessing. Interpolation weight <= uninformed weight. Structure provides signal StructuralHole Lean theorem neighbor_dominates_uninformed in NonEmpiricalPrediction.lean Mechanized
THM-STRICT-DOMINANCE With nontrivial neighbor rejection (neighborVoidSum > 0), structural prediction is strictly more informative than guessing. The gap equals min(voidSum, roundsSum) StructuralHole with neighborVoidSum > 0 Lean theorem strict_dominance_with_rejection in NonEmpiricalPrediction.lean Mechanized
THM-HOLES-ORDERED Two holes with different neighbor rejection receive different predictions. The lattice differentiates. Formalizes: "gallium is more like aluminum than iron" Two StructuralHoles with same rounds, different void sums Lean theorem holes_ordered in NonEmpiricalPrediction.lean Mechanized
THM-MENDELEEV-is-COMPLEMENT Mendeleev's interpolation method is isomorphic to computing the Buleyean complement weight from neighbor-aggregated void boundary. Same formula: rounds - min(void, rounds) + 1 StructuralHole, BuleyeanSpace with matching rounds and void boundary Lean theorem mendeleev_is_complement in NonEmpiricalPrediction.lean Mechanized
THM-ALGEBRAIC-HOLE-is-VOID-GAP Algebraic holes (Dirac's positron, Pauli's neutrino) are positions demanded by lattice partition conservation. The lattice forces the hole to exist; the complement distribution predicts its properties StructuralLattice with someHoles Lean theorem algebraic_hole_is_void_gap in NonEmpiricalPrediction.lean Mechanized
THM-NON-EMPIRICAL-SOLOMONOFF Non-empirical prediction composes with Solomonoff prediction. Holes in simpler lattices get higher weight. Simpler structures make stronger predictions about their gaps SolomonoffSpace Lean theorem non_empirical_solomonoff_compose in NonEmpiricalPrediction.lean (forwarded as SolomonoffInduction.non_empirical_solomonoff_compose in SolomonoffInduction.lean) Mechanized
THM-IMPOSSIBLE-ELEMENT An AI can "know" a fact about an unobserved object without training data, by computing the interpolation weight from the structural lattice. Positive, bounded, structure-dependent. Deterministic, objective, falsifiable StructuralHole Lean theorem impossible_element in NonEmpiricalPrediction.lean Mechanized
THM-PREDICTION-WITHOUT-OBSERVATION The structural hole has nonzero interpolation weight despite no direct observation. Weight comes entirely from neighbor structure. Formal content of non-empirical prediction StructuralHole Lean theorem prediction_without_observation in NonEmpiricalPrediction.lean Mechanized
THM-NON-EMPIRICAL-PREDICTION-MASTER Complete non-empirical prediction theorem: lattice partition, hole positivity, boundedness, structure dominates, algebraic holes exist. Formal basis for predicting properties of undiscovered objects from the mathematical hole they leave StructuralLattice, StructuralHole TLA+ NonEmpiricalPrediction.tla invariants (InvPartition, InvPositiveWeight, InvWeightBounded, InvStructureDominates, InvUninformedCorrect, InvSomeObserved, InvVoidBounded) + Lean theorem non_empirical_prediction_master in NonEmpiricalPrediction.lean Mechanized

Grandfather Paradox (§15.23)

Theorem ID Claim Assumptions Mechanization Status
THM-VOID-APPEND-ONLY The void boundary is append-only: once an event is recorded, it cannot be un-occurred. All Buleyean weights are >= 1. The ancestor's existence is a permanent fact in the boundary BuleyeanSpace Lean theorem void_boundary_append_only in GrandfatherParadox.lean Mechanized
THM-BETA1-FLOOR-ZERO Beta1 cannot go below zero. A fold can reduce beta1 to zero but not below. No negative cycles exist rootN : Nat Lean theorem beta1_floor_zero in GrandfatherParadox.lean Mechanized
THM-SLIVER-PREVENTS-ANNIHILATION The +1 in the Buleyean weight formula ensures no event's weight can reach zero. Structural impossibility of the grandfather paradox BuleyeanSpace Lean theorem sliver_prevents_annihilation in GrandfatherParadox.lean Mechanized
THM-SELF-REFERENTIAL-FOLD-IMPOSSIBLE A fold that would eliminate the root of its own causal chain is impossible. Both root and tip have positive existence weight and are distinct SelfReferentialFold with CausalChain Lean theorem self_referential_fold_impossible in GrandfatherParadox.lean Mechanized
THM-BRANCHING-is-FORK The Many-Worlds resolution is a fork (beta1 increases), not a fold (beta1 decreases). Time travel creates a new path rather than eliminating an old one TemporalBranch with postBeta1 = preBeta1 + 1 Lean theorem branching_is_fork in GrandfatherParadox.lean Mechanized
THM-BRANCH-PRESERVES-ORIGINAL Branching preserves the original causal chain. All existence weights remain positive. The ancestor still exists in the original branch TemporalBranch Lean theorem branch_preserves_original in GrandfatherParadox.lean Mechanized
THM-CAUSAL-CHAIN-CONSERVATION Total events in the causal chain are conserved. No event is destroyed -- the chain is extended by branching, not shortened by folding CausalChain Lean theorem causal_chain_conservation in GrandfatherParadox.lean Mechanized
THM-PARADOX-REQUIRES-NEGATIVE The grandfather paradox requires setting an ancestor's weight to zero, which contradicts buleyean_positivity. The paradox requires an operation the algebra does not support BuleyeanSpace Lean theorem paradox_requires_negative in GrandfatherParadox.lean Mechanized
THM-BOOTSTRAP-DISSOLVES The bootstrap paradox dissolves because every Buleyean weight has definite provenance via the weight formula. Information without provenance would require negative void count BuleyeanSpace Lean theorem bootstrap_dissolves in GrandfatherParadox.lean Mechanized
THM-RETROCAUSAL-CONSISTENCY The retrocausal bound excludes paradoxical terminal states: a state where the traveler exists but the ancestor doesn't has no consistent trajectory CausalChain with root and tip Lean theorem retrocausal_consistency in GrandfatherParadox.lean Mechanized
THM-TIME-TRAVEL-is-TOPOLOGY Time travel is a topology change: adding a cycle to the causal graph increases beta1 by one. The original chain is preserved. The paradox asks to fold the new cycle, but the sliver prevents it TemporalBranch Lean theorem time_travel_is_topology in GrandfatherParadox.lean Mechanized
THM-GRANDFATHER-PARADOX-MASTER Complete resolution: append-only void, no annihilation, self-referential fold impossible, branching is fork, original preserved. The grandfather paradox is an algebraic impossibility, not a physical one BuleyeanSpace, SelfReferentialFold, TemporalBranch TLA+ GrandfatherParadox.tla invariants (InvAncestorAlive, InvTravelerAlive, InvNoAnnihilation, InvBeta1NonNeg, InvBranchPositive, InvBranchingMonotone, InvConservation) + Lean theorem grandfather_paradox_master in GrandfatherParadox.lean Mechanized

Five Novel AI Inference Forms (§15.24)

Theorem ID Claim Assumptions Mechanization Status
THM-VOID-INFERENCE-POSITIVE Every token retains positive probability in void inference. The sliver prevents permanent exclusion from generation regardless of rejection history VoidInferenceState Lean theorem void_inference_positive in NovelInferenceForms.lean Mechanized
THM-VOID-INFERENCE-CONCENTRATES The complement distribution sharpens with rejection accumulation. Tokens rejected more get lower weight. Generation gets more confident VoidInferenceState, two token indices with ordered void boundaries Lean theorem void_inference_concentrates in NovelInferenceForms.lean Mechanized
THM-VOID-INFERENCE-COHERENT Two void inference systems with the same rejection history produce the same output distribution. Deterministic given the void boundary Two VoidInferenceStates with same numChoices, rounds, and voidBoundary Lean theorem void_inference_coherent in NovelInferenceForms.lean Mechanized
THM-VOID-INFERENCE-SUBSUMES-SOFTMAX Void inference with single-step boundary equals standard softmax range. With multi-step accumulation, void inference is strictly richer (cross-step rejection memory) VoidInferenceState Lean theorem void_inference_subsumes_softmax in NovelInferenceForms.lean Mechanized
THM-VOID-INFERENCE-NORMALIZABLE Total weight across all tokens is positive, so the complement distribution can be normalized to a probability distribution VoidInferenceState Lean theorem void_inference_normalizable in NovelInferenceForms.lean Mechanized
THM-RETROCAUSAL-CONSISTENT Only trajectories consistent with the terminal state survive. Terminal constraints are satisfiable (every terminal weight is positive) RetrocausalDecoder Lean theorem retrocausal_consistent in NovelInferenceForms.lean Mechanized
THM-RETROCAUSAL-POSITIVE No valid trajectory is excluded. The sliver prevents false negatives in the pruning step. Weight >= 1 and weight != 0 RetrocausalDecoder Lean theorem retrocausal_positive in NovelInferenceForms.lean Mechanized
THM-RETROCAUSAL-SHARPENS As generation progresses, the set of consistent continuations shrinks. Fewer tokens remain with low rejection counts RetrocausalDecoder, two token indices with ordered void boundaries Lean theorem retrocausal_sharpens in NovelInferenceForms.lean Mechanized
THM-RETROCAUSAL-COMPOSABLE Two retrocausal constraints compose. Intersection of consistent trajectories is nonempty because the sliver ensures weight >= 1 for every token under every constraint Two RetrocausalDecoders Lean theorem retrocausal_composable in NovelInferenceForms.lean Mechanized
THM-RETROCAUSAL-NO-SELF-REFERENCE Self-referential terminal constraints cannot annihilate any trajectory. The grandfather paradox applied to decoding RetrocausalDecoder Lean theorem retrocausal_no_self_reference in NovelInferenceForms.lean Mechanized
THM-TOPO-SKIP-PRESERVES-TOPOLOGY Skipping a zero-deficit layer preserves the total beta1 of the network. A layer with beta1 = 0 contributes nothing topologically TopoSpecDecoder with layerDeficit i = 0 Lean theorem topo_skip_preserves_topology in NovelInferenceForms.lean Mechanized
THM-TOPO-SPEEDUP-EXACT Speedup from skipping a layer is deficit + 1. For zero-deficit layer, speedup = 1 deficit : Nat Lean theorem topo_speedup_exact in NovelInferenceForms.lean Mechanized
THM-TOPO-SKIP-COMPOSABLE Multiple layer skips compose. Skipping layers with deficits d1 and d2 gives total speedup d1 + d2 + 2. Deficits are additive d1, d2 : Nat Lean theorem topo_skip_composable in NovelInferenceForms.lean Mechanized
THM-TOPO-SKIP-BOUNDED Maximum number of skippable layers is bounded by the network depth TopoSpecDecoder, skipCount <= totalLayers Lean theorem topo_skip_bounded in NovelInferenceForms.lean Mechanized
THM-TOPO-MINIMUM-COMPUTE At least one layer must execute (the sliver applied to compute). Network with L layers can skip at most L - 1 TopoSpecDecoder with positiveLayers Lean theorem topo_minimum_compute in NovelInferenceForms.lean Mechanized
THM-TOPO-DEFICIT-NONNEG Beta1 deficit is always non-negative. No layer has negative topological complexity TopoSpecDecoder Lean theorem topo_deficit_nonneg in NovelInferenceForms.lean Mechanized
THM-ENSEMBLE-DEFICIT-EXACT Semiotic deficit of a k-agent ensemble is exactly k - 1. Unavoidable information loss from folding multiple candidates to one winner SemioticEnsemble Lean theorem ensemble_deficit_exact in NovelInferenceForms.lean Mechanized
THM-ENSEMBLE-DEFICIT-POSITIVE For any nontrivial ensemble (k >= 2), the deficit is positive. Folding always loses information. Free consensus is impossible SemioticEnsemble with agentCount >= 2 Lean theorem ensemble_deficit_positive in NovelInferenceForms.lean Mechanized
THM-ENSEMBLE-DOMINATES-SINGLE Ensemble output (least-rejected candidate) has weight at least as high as any single agent. Complement voting is non-degrading SemioticEnsemble, two agent indices with ordered void boundaries Lean theorem ensemble_dominates_single in NovelInferenceForms.lean Mechanized
THM-ENSEMBLE-COMPLEMENT-VOTING Every candidate retains positive weight in the complement vote. No agent's output is ever completely eliminated SemioticEnsemble Lean theorem ensemble_complement_voting in NovelInferenceForms.lean Mechanized
THM-ENSEMBLE-COHERENT Two independent juries using the same rejection data select the same winner. Complement voting is objective Two SemioticEnsembles with same numChoices, rounds, and voidBoundary Lean theorem ensemble_coherent in NovelInferenceForms.lean Mechanized
THM-ENSEMBLE-SCALING Adding one more agent increases the deficit by exactly 1. Constant marginal information cost k : Nat with k >= 2 Lean theorem ensemble_scaling in NovelInferenceForms.lean Mechanized
THM-NEI-POSITIVE Predicted completion has positive weight. The structural hole exists in the Buleyean sense NonEmpiricalInference Lean theorem nei_positive in NovelInferenceForms.lean Mechanized
THM-NEI-DOMINATES-GUESS Structural prediction strictly dominates random guessing when neighbors provide nontrivial rejection data NonEmpiricalInference with neighborVoidSum > 0 Lean theorem nei_dominates_guess in NovelInferenceForms.lean Mechanized
THM-NEI-COHERENT Two systems with the same lattice structure produce the same prediction. Non-empirical inference is objective Two NonEmpiricalInferences with same neighborRoundsSum and neighborVoidSum Lean theorem nei_coherent in NovelInferenceForms.lean Mechanized
THM-NEI-BOUNDED Prediction weight bounded between 1 and rounds + 1. Always finite, always within Buleyean weight range NonEmpiricalInference Lean theorem nei_bounded in `NovelInf

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