RUSTIC_CHURCH Restoration Ledger

Tracks the retirement of structural-witness stubs into real, Init-only modules that clear the gates in RUSTIC_CHURCH.md. A row leaves deferred and becomes restored when its module carries ≥1 meaningful structure and a proven theorem family, builds Init-only via lake build with no banned tactics on open goals, passes the #print axioms gate, and drops all stub prose.

Provenance (read first)

The structural-witness stub files named in the inventory live in the downstream gnosis-math project, not in this repository. They are not present in any branch or commit of forkjoin-ai/gnosis (verified across all 8 remote branches + tags), and there is no pre-existing RUSTIC_CHURCH.md / restoration-ledger / NegotiationEquilibrium / BeautyOptimality row here — that restoration scaffolding was created downstream.

What does trace back to this repo is the pre-burn module intent: the rich originals live in this repository's lean/Lean/ForkRaceFoldTheorems/ history (e.g. QuantumObserver.lean at 288 lines in ff031836; SyntacticLyapunov.lean at 210 lines in f0ae8b2f). Those originals import Mathlib and reason over ℝ/ENNReal/measure theory. Restoration here recovers their finite, Init-compatible core and rebuilds it import Init-only, per the RUSTIC_CHURCH procedure (separate the finite core from the Real/ENNReal/tactic-heavy shell; do not git revert the collapse).

Restored modules are placed in the live Gnosis library at lean/Lean/Gnosis/ (namespace Gnosis) and wired into lean/lakefile.lean.

Toolchain

Lean leanprover/lean4:v4.28.0, no external deps. Build + verify:

cd lean && lake build Gnosis.Quantum.QuantumObserver

Restored (verified green, Init-only, axioms gate passed)

Module	Path	Carrier(s)	Theorem family	`#print axioms`	Recovered from
`Gnosis.Quantum.QuantumObserver`	`lean/Lean/Gnosis/Quantum/QuantumObserver.lean`	`QuantumSystem` + β₁/deficit defs	`superposition_is_fork`, `measurement_deficit_exact`, `path_conservation`, `observer_effect_is_fold`, `speedup_recovers_rootN`, `quantum_observer_master` (8)	`propext` only	`ForkRaceFoldTheorems/QuantumObserver.lean` @ `ff031836` (Mathlib/ENNReal → finite `Nat` β₁ core)
`Gnosis.SyntacticLyapunov`	`lean/Lean/Gnosis/SyntacticLyapunov.lean`	`AffineDriftProgram`	`drift_gap_positive`, `step_decreases_V`, `drift_exact_above_floor`, `small_set_bounded`, `iterate_decreases_V` (8)	none	`ForkRaceFoldTheorems/SyntacticLyapunov.lean` @ `f0ae8b2f` (ℝ Foster–Lyapunov → `Nat` drift monovariant)
`Gnosis.Civil.StVenantDecay`	`lean/Lean/Gnosis/Civil/StVenantDecay.lean`	`StressField`	`zero_load_zero_stress`, `stress_le_load`, `stress_antitone`, `stress_vanishes_beyond_range`, `saint_venant_decay` (5)	`propext` only	subject (Tier-2 stub had only `zero_load_zero_stress : … := rfl`); finite `Nat` decay field
`Gnosis.Civil.CriticalPath`	`lean/Lean/Gnosis/Civil/CriticalPath.lean`	`TaskPath`	`makespan_cons`, `head_le_makespan`, `makespan_append`, `prefix_le_makespan`, `adding_task_increases` (6)	none	subject (Tier-2 stub had `project_completion_witness`); finite `Nat`-list makespan
`Gnosis.RenormalizationFixedPoints`	`lean/Lean/Gnosis/RenormalizationFixedPoints.lean`	`RGStep`, `Coarsening`	`trajectory_information_loss_additive`, `trajectory_cumulative_heat_monotone`, `fixed_point_iff_zero_loss`, `fixed_point_minimum_heat`, `nonfixed_positive_loss`, `collision_breaks_injectivity`, `remaining_le_start`, `trajectory_three_step_additive`/`_heat_monotone` (~13)	`propext` only	`ForkRaceFoldTheorems/RenormalizationFixedPoints.lean` @ `f0ae8b2f` (PMF/ℝ entropy + Landauer heat → finite `Nat` loss/heat; `H(X∣q)=0 ⇔ InjOnSupport` → `infoLoss=0` + concrete collision carrier)
`Gnosis.ThermodynamicTracedMonoidal`	`lean/Lean/Gnosis/ThermodynamicTracedMonoidal.lean`	`TracedStep`, `FeedbackThermodynamicCost`	`trace_heat_nonneg`, `trace_heat_pos_of_nontrivial_feedback`, `trace_many_to_one`, `trace_vanishing_heat`/`_landauer_heat`, `trace_singleton_injective`, `iterated_trace_heat_monotone`, `feedback_beauty_floor` (~11)	`propext` only	`ForkRaceFoldTheorems/ThermodynamicTracedMonoidal.lean` @ `f0ae8b2f` (traced-monoidal trace over `PMF`/`GHom` → `Nat` projection `A×U→A`; heat `=k·T·infoLoss`)
`Gnosis.Quantum.QuantumCancerTriples`	`lean/Lean/Gnosis/Quantum/QuantumCancerTriples.lean`	`CollapsedSystem`, `CancerCell`, `RetrocausalCollapse`, `BuleyeanSpace`, `NegotiationState`, `StructuralHole`, `TemporalBranch`, `RetrocausalSettlement`, `CancerTreatmentTarget` (9)	`quantum_cancer_retrocausally_indistinguishable`, `collapse_deficit_positive`, `the_sliver`/`sliver_irreducible`, `batna_predicts_holes`, `concession_steers_toward_hole`, `collapse_irreversibility`, `branching_no_reversal`, `settlement_retrocausal`/`_coherence`, `cancer_hole_treatment`, `treatment_ordered`, `quantum_cancer_triples_master` (~14)	none	`ForkRaceFoldTheorems/QuantumCancerTriples.lean` @ `f0ae8b2f` (9-module ℝ/PMF dependency web → self-contained `Nat` carriers for each of the 5 triples)
`Gnosis.TripleCompositions`	`lean/Lean/Gnosis/TripleCompositions.lean`	`BuleyeanSpace` (+ composes sibling modules)	`positivity_guarantees_heat`, `failure_cascade_generates_heat`, `buleyean_min`/`max_uncertainty`, `buleyean_concentration`, `concentrated_boundary_triple`, `coarsening_terminates_effectively`, `void_is_optimal_history`, `triple_compositions_master` (~11)	none	`ForkRaceFoldTheorems/TripleCompositions.lean` @ `f0ae8b2f` (7-module ℝ/PMF web → imports the restored Init-only `VoidWalking`/`RenormalizationFixedPoints`/`ThermodynamicTracedMonoidal` and composes them)
`Gnosis.PsycheReduction`	`lean/Lean/Gnosis/PsycheReduction.lean`	`PsycheGrind.PersonalityProfile` (+ reconstructed `PsycheGrind` core: `absDiff`, `defenseWeight`, `profileDistance`, `strain`, `breatheOnce`)	`P1_sliver`/`P2_floor`/`P3_symmetry`, `D1`–`D6`, `class_alpha`–`epsilon_complete`, `reduction_master`, `tautology_class`, `identity_unique_reduces_to_P2`, `completeness` (~30, witnessing all 105)	`propext` only	`ForkRaceFoldTheorems/PsycheReduction.lean` @ `3efe3b9d` (357 lines; `PsycheGrind` dep + `omega`/`native_decide` reconstructed Init-only)
`Gnosis.SkyrmsNadirBule`	`lean/Lean/Gnosis/SkyrmsNadirBule.lean`	`FailureTopology`, `NegotiationChannel`, `SkyrmsAsCommunity`	`community_deficit_is_negotiation_deficit`, `community_attenuation_is_mediation`, `nadirContext_pos`, `bule_zero_at_nadir`, `bule_zero_iff_nadir`, `nadir_context_is_minimum`, `nadir_algebraic`, `mediation_round_progress`/`_monotone`/`_reaches_nadir`, `skyrms_nadir_is_bule_zero` (~14)	`propext` only	`ForkRaceFoldTheorems/SkyrmsNadirBule.lean` @ `f0ae8b2f` (401 lines, ℤ deficits over community/negotiation web → self-contained `Int`/`Nat` deficit `bule = (totalDims-1) - context`)
`Gnosis.StringTheoryCorrespondence`	`lean/Lean/Gnosis/StringTheoryCorrespondence.lean`	`AlgorithmicKnot`, `StringState`, `Worldsheet`, `PairOfPants`, `DBrane`, `AttachedString`, `Module`, `HolographicBoundary`, `TemporalProfile`, `DualPlaneKnot` (10)	`string_knot_iso_`, `worldsheet_genus_is_loop_count`, `pair_of_pants_is_compose`/`_associative`, `gauge_`, `vacuum_is_unknot`, `landauer_heat_`, `loop_`, `dbrane_`, `compactification_`, `holography_is_exact`, `t_duality_`, `landscape_`, `string_theory_master` (~50)	`propext` only	`ForkRaceFoldTheorems/StringTheoryCorrespondence.lean` @ `f0ae8b2f` (657 lines, 6-module Mathlib knot web → self-contained `Nat` knot primitives)
`Gnosis.ProtocolDeficitLatency`	`lean/Lean/Gnosis/ProtocolDeficitLatency.lean`	(ceiling-div pressure model)	`tcp_multiplexing_pressure`, `matched_multiplexing_pressure`, `tcp/matched` inflation, `positive_deficit_implies_inflation`, `deficit_beauty_chain` (~9)	`propext` only	`ForkRaceFoldTheorems/ProtocolDeficitLatency.lean` @ `058cd04` (131 lines; ceiling-div + omega → Init div lemmas)
`Gnosis.ServerTopology`	`lean/Lean/Gnosis/ServerTopology.lean`	`RaceArmState`, `RaceResult`, `CacheState`	`race_unique_winner`, `race_losers_vented`, `race_one_winner_rest_vented`, `fold_integrity`/`_commutative`, `rotation_depth_ge_stages`/`_single_batch`, `cache_monotone_on_miss`/`_bounded` (~10)	`propext` only	`ForkRaceFoldTheorems/ServerTopology.lean` @ `058cd04` (162 lines; `Finset` card race-count → winner-uniqueness + `1+(n-1)=n` conservation)
`Gnosis.Void.VoidWalking`	`lean/Lean/Gnosis/Void/VoidWalking.lean`	`FoldStep`, `VoidBoundary`, `ConstantWidthComputation`, `VoidTunnel`, `VoidWalker`, `VoidGradient`, `VoidWalkerPair`, `InverseBuleWitness`, `SkyrmsEquilibrium` (9)	`void_boundary_monotone`, `void_dominance_linear`/`_nested`, `void_boundary_sufficient_statistic`, `void_tunnel_retention_positive`, `void_gradient_complement_positive`/`_monotone`, `void_walkers_converge`, `inverse_bule_void_monotone`, `skyrms_equilibrium_positive`, `void_regret_total_ceiling`/`_tight` (~28)	`propext` only	`ForkRaceFoldTheorems/VoidWalking.lean` @ `f0ae8b2f` (597 lines, Mathlib/ENNReal entropy → full finite `Nat` core; `Finset` sums → `List`; `Nat.sqrt`/`Nat.log` regret bound → its Init ceiling `T·sideBits ≤ T·N`)

Restore strategy for the remaining inventory

The inventory lists 103 stubs (65 Tier-1 + 38 Tier-2). Per-module procedure:

Recover intent. Find the richest historical body: git rev-list --all | while read c; do git show $c:lean/Lean/ForkRaceFoldTheorems/<Mod>.lean | wc -l; done then git show <commit>:<path>. Many file-heavy commits (e.g. 81c7e98f, 1740 files) are themselves post-burn stub farms; the rich body sits in an earlier commit (e.g. f0ae8b2f, ff031836).
Separate the core. Keep the finite Nat/Int content; drop the Mathlib/ℝ/ENNReal/PMF/BigOperators shell and the omega/simp/ ring/nlinarith proofs.
Rebuild Init-only, place in lean/Lean/Gnosis/…, add the root to lean/lakefile.lean.
Verify: lake build <Module> green; #print axioms clean.
Log the row here.

Deferred — rich original exists (recover finite core)

All rich-original modules recovered from ForkRaceFoldTheorems history have been restored. Remaining inventory modules had only thin/absent bodies in this repo's history and are restored by authoring an honest finite core from the module's stated subject (as for StVenantDecay/CriticalPath).

Deferred — no rich original in this repo's history

The remaining inventory names (e.g. CategoryMismatchDiagnostic, SpiderwebBFT, MitzvotTopology, InvariantStateProtocols, ManifoldCrossPollination, FormalMethods, AcousticWave1DSketch, …) have no substantive body in forkjoin-ai/gnosis history (max ≤ a few lines, or absent). Restoring these means authoring an honest finite core from the module's stated subject (as done above for StVenantDecay and CriticalPath), not recovering a prior proof.

Status

Restored — authored from subject (no recoverable body in history)

These inventory modules had no substantive body anywhere in forkjoin-ai/gnosis history; each is given an honest finite Nat core matching its stated subject, built green Init-only (#print axioms: propext at most).

Module	Core idea
`Gnosis.SpiderwebBFT`	Byzantine quorum `n-f` on `n≥3f+1`: reachability `q+f=n`, intersection `n+(f+1)≤2q`
`Gnosis.TetraOctaHoneycomb`	tetra = 2·octa ratio; cells = 3·octa; tetra > octa
`Gnosis.ManifoldCrossPollination`	product manifold: dimension/genus add, symmetric, associative
`Gnosis.UniverseTower`	level capacity `2^n`: non-empty, monotone, strictly cumulative
`Gnosis.TriadicNormalForm`	triad sum normal form: cyclic + reversal invariant, dominates components
`Gnosis.WormholeTradeoff`	throat/energy at fixed budget: shift conserves budget, widens/narrows
`Gnosis.SpiralDeterminism`	deterministic outward spiral `start + k·growth`: deterministic, monotone, strictly outward
`Gnosis.SpiralMachine`	spiral counter `initial + n·stride`: tick law, additive/composable, monotone
`Gnosis.RotationPatterns`	additive rotation group: zero identity, angle composition, commutativity
`Gnosis.SchedulerComposition`	sequential makespan: additive, idle identity, associative, monotone
`Gnosis.ZeckendorfStateVacuum`	Fibonacci + empty (vacuum=0) representation: recurrence, non-decreasing, positive past base
`Gnosis.SpiderwebTopology`	connected mesh cycle rank `edges+1-nodes`: tree acyclic, adding a strand adds one cycle
`Gnosis.SpiderwebGnosticLadder`	evenly-spaced ladder `base+n·spacing`: strict ascent, monotone, base-bounded
`Gnosis.ProtocolConnectivity`	hop metric `
`Gnosis.CategoryMismatchDiagnostic`	mismatch penalty `
`Gnosis.ValentinianCrossPollination`	aeon syzygy: fullness adds, symmetric, associative, non-diminishing
`Gnosis.ValentinianSinDiagnostic`	deficiency `ceiling-fullness`: zero ⇔ at pleroma, antitone, bounded
`Gnosis.SchedulingMatter`	work conservation: additive over concat, invariant under reorder, monotone
`Gnosis.CouplingTopology`	coupling `a·b`: symmetric, zero ⇔ a side decoupled, monotone, positive when engaged
`Gnosis.ErrorRecoveryInvariant`	recovery monovariant: `recoverIter k e = e-k`, never increases, fully recovers at `k=e`
`Gnosis.StateEntropyReduction`	entropy dissipation: antitone, composes additively, floored at zero
`Gnosis.MoralHeuristicLadder`	cumulative weighted standing: monotone, strict on positive rung, rung-bounded
`Gnosis.Moonshots.MoonshotHolographicPluralistEntropy`	entropy = min(bulk, boundary): holographic bound holds, saturation condition
`Gnosis.Moonshots.MoonshotTopologicalVoidFilling`	fill ≤ capacity, filled+remaining=capacity, strict shrink, full ⇒ empty remaining
`Gnosis.Moonshots.MoonshotSemanticTopologyDrift`	drift = k·stepBound: bounded, monotone, zero without per-step drift
`Gnosis.Moonshots.MoonshotWitnessGapHomotopyBypass`	invariants = gap+surplus ≥ gap: bypass, strict, tight
`Gnosis.Moonshots.MoonshotOracleStallResolution`	fuel monovariant `run k = fuel-k`: never increases, halts at `k=fuel`
`Gnosis.Moonshots.MoonshotSubatomicBureaucracy`	usable = capacity-overhead: capped, antitone, saturates to zero
`Gnosis.Moonshots.MoonshotErgodicJazz`	cyclic orbit `t % n`: periodic, returns to start, in-range (mod laws)
`Gnosis.Moonshots.MoonshotErgodicSemanticResolution`	resolution `ambiguity - k·rate`: monotone, always finite at positive rate
`Gnosis.Moonshots.MoonshotInterpretationLayerHolography`	layers = min(requested, boundary): holographic cap, full when fits
`Gnosis.Oracle.OracleExecutionStallAnnihilation`	stall annihilation monovariant `s-k`: clears at `k=s`
`Gnosis.Oracle.OracleExecutionStallBreakthrough`	positive fuel ⇒ strict step-down progress
`Gnosis.Oracle.OracleExecutionStallTopologicalSurgery`	excise stalled branch: preserves live, shrinks/strictly-shrinks total
`Gnosis.CrossDomain.CrossDomainFluidDynamicsEconomicsBridge`	viscosity↔liquidity friction: preserving, monotone, invertible
`Gnosis.CrossDomain.CrossDomainLinguisticsThermodynamicsBridge`	lexical↔thermo entropy: preserving, monotone, additive
`Gnosis.CrossDomain.CrossDomainAstronomyCulinaryBridge`	temperature↔flavor: preserving, monotone, strict
`Gnosis.CrossDomain.CrossDomainAstrobiologyPsychologyStallBridge`	biosig↔stall tension: symmetric, stable ⇔ aligned
`Gnosis.CrossDomain.CrossDomainMycologyAstrophysicsQueueKernelBridge`	3-way filament/queue count: preserving, composes, monotone
`Gnosis.AntiTheorems.AntiTheoremStallInevitable`	unbounded loop count invariant ⇒ non-empty loop never halts (refutation witness)
`Gnosis.Contrarian.ContrarianLatentWitnessAbsence`	zero absence optimal (<1), optimality ⇔ no absence, cost monotone
`Gnosis.Contrarian.ContrarianMemoryThrashingEfficiency`	hits+misses=accesses conservation; hits/misses bounded; no-miss ⇒ all hits
`Gnosis.BiologicalStallRecovery`	recovery = antibody count: monotone, zero without antibodies
`Gnosis.HypergraphInterpretationMapping`	layer complexity nodes+edges: node/edge bounds, edgeless ⇒ nodes
`Gnosis.QueueTheoreticInterpretationMapping`	Jackson load = Σ depths: additive, sub-network dominated
`Gnosis.Semantic.NoncomputableSemanticDrift`	embedding gap conserved under drift (all iterations), zero stays zero
`Gnosis.FormalMethods`	inductive-invariant principle (general), transition-system safety, even-counter instance
`Gnosis.MitzvotTopology`	613 mitzvot → one general law: any mitzvah sequence preserves the boundary invariant
`Gnosis.InvariantStateProtocols`	613 protocols → one general law: any protocol sequence preserves the invariant (+append)
`Gnosis.InvariantField`	total charge conserved: additive, region-exchange invariant, vacuum-free
`Gnosis.StateResistanceTopology`	series resistance: additive, component-bounded, strictly grows on positive resistor
`Gnosis.Dewey800ThinTopology`	Dewey subclass `base+offset` (offset<100): refines base, in-block, 810 instance
`Gnosis.RaceWinnerCorrectness`	RACE selection: validity, minimality, determinism (tie-break), isolation, fold-composability
`Gnosis.SelfAwareBudget`	godWeight `R-min v R+1`: surplus +1, each query costs 1, total-knowledge→1, bounds [1,R+1] (recovered, R≥1 fixed)
`Gnosis.PublicationBias`	godWeight file-drawer/replication arithmetic, pre-registration conservation, master (recovered)
`Gnosis.UniverseShapeByDimension`	visible torus rank `d-1`, Wallington closure, 3D⇒2-torus, higher dims not 2-torus, strict monotone (recovered)
`Gnosis.WallingtonOptimality`	rotation schedule: admissible, makespan = critical path, ×numPaths ratio, strict dominance, speedup=β₁+1 (recovered)
`Gnosis.ServerOptimality`	server stack: 5 simultaneous optima (makespan/Pareto/dominance/speedup/zero-deficit) + x-gnosis 4×3 certificate (imports Wallington)
`Gnosis.ZeckendorfKenoma`	gnostic ladder = Fibonacci/Zeckendorf basis: recurrence (phase-lock), fib positivity, non-consecutive decompositions, master (recovered; native_decide → decide/rfl)
`Gnosis.TheGain`	gain = ceiling-floor = rounds: discrimination_gain (best-worst = rounds), earned/positive/monotone (recovered)
`Gnosis.SurfaceReduction`	Seven Laws → generators: positivity, strict concentration, formula bounds, deficit subtraction, reduction-thesis master (recovered)
`Gnosis.SemioticDeficit`	channel deficit `(dims-1)-(streams-1)`: positive under mismatch, speech full deficit, matched zero, context eliminates (recovered)
`Gnosis.SemioticPeace`	confusion heat ∝ deficit: nonneg, positive on deficit, peace = zero-deficit fixed point reachable by context (recovered)
`Gnosis.SliverOfHope`	sliver `+1`: weight≥1 always, =1 at max rejection, proof step `-1` reaches ground, ±1 duality (recovered)
`Gnosis.SliverFromVent`	vent→heat→sliver→positivity: vent heat=1, gen heat=vents, heat-augmented weight positive (recovered)
`Gnosis.TopologicalMismatchAdequacy`	realization deficit `pathCount-streams`: lossless/tight, zero⇔capacity, positive⇔shortage (recovered)
`Gnosis.SemioticTriples`	Arrow deficit (≥3 alts ⇒ positive), bounds negotiation, war heat irreversible, sliver of hope, master (recovered)
`Gnosis.SevenLawsPredictions`	predictions as Buleyean laws: never-disproven, confidence bound, crash-concentration, shadow deficit, restructuring conservation (recovered)
`Gnosis.UnsolvedMysteries`	open problems' Buleyean structure: fine-tuning positivity, stability concentration, fold symmetry break, Cambrian saturation (recovered)
`Gnosis.RaceWinnerPredictions`	election winner correctness + training drift gap (converges ⇔ positive, stalls at zero, LR-monotone) (recovered)
`Gnosis.UniversalDomainConservation`	survived+vented=total across domains: sliver, bounded work, strict loss, positive fork (recovered)
`Gnosis.TradeTopology`	tariff deficit=blocked: suboptimal>0, free-trade zero, waste monotone, open-path narrowing (recovered)
`Gnosis.StatisticalTeleportation`	receiver knows min(steps,deficit): bounded, private, converges at deficit, monotone (recovered)
`Gnosis.TimeTravelTopology`	append-only void = arrow of time: no reversal (monotone), sibling-not-past, butterfly isolation (recovered)
`Gnosis.WhipWaveDuality`	taper wave-speed²=tension/rho: fold conserves tension, thinner⇒faster, snap-bit capacity (recovered; ℚ→Nat)
`Gnosis.ReynoldsBFT`	pipeline idle stages `N-C`: bounded, zero at saturation; quorum-safe ⇒ majority-safe `N<2C` (recovered)
`Gnosis.SecondTierMysteries`	megalithic positivity/coherence, decipherment deficit `symbols-meanings` (underdetermined/trivial) (recovered)
`Gnosis.TeleportationEvidencePredictions`	federation locality/completeness; presumption of innocence (guilt ⇒ zero deficit) (recovered)
`Gnosis.SpiderwebMeshNetwork`	mesh β₁ = peers·hops: formula, zero⇔trivial factor, positive on genuine mesh, wire/node relations (recovered)
`Gnosis.SolomonoffBuleyean`	simplicity prior: positivity, normalization bound, concentration (simpler⇒heavier), dominates uniform (recovered)
`Gnosis.WildExplorationCycleDouglasii50`	moonshot witnesses given real bounds (knot gap, circadian stall, dark-matter deficit, contrarian collapse delay) (tautology farm → honest)
`Gnosis.Semantic.SemanticCompatibility`	type-compat lattice: reflexivity, unknown-compatible both sides, integer<:number (recovered)
`Gnosis.PlanetaryHomologySandbox.AcousticWave1DSketch`	1D wave amplitude conserved under cyclic propagation; sampling length preserved (recovered; ℚ→Nat/List)
`Gnosis.RecursiveCoarseningSynthesis`	coarse drift aggregates fine: stable⇔service>arrival, conservation, synthesis-sound certificate (recovered; Finset/ℝ→Nat/List)
`Gnosis.RetrocausalBound`	trajectory void boundary (vent count): bounded by length, additive, prefix-ordering (recovered; Fin→Nat/List)
`Gnosis.Closures.StrongerCosmologyClosure`	10-rung radius ladder `2^n`: strictly climbs, bounded by top, fold mass-energy, closes at 1024 (recovered; ℝ→Nat)
`Gnosis.RateDistortionFrontier`	rate+distortion=budget identity, inverse tradeoff under refinement, min-rate/min-heat points (recovered; PMF/ℝ→Nat)
`Gnosis.WallingtonSurfaceAdmissibility`	admissible ⇔ stages+1=ambient (visible torus rank); smaller/larger inadmissible (recovered)
`Gnosis.StateDependentQueueFamilies`	vacation kernel: monotone service, Foster–Lyapunov drift positive above threshold (positive recurrence) (recovered; 1738-line ℝ → Nat core)

103 / 103 restored and verified green. Inventory cleared.