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forkjoin-ai/gnosis

Chapter 17 Companion Checks

content/companion-tests-README.md
forkjoin-ai/gnosis

Chapter 17 Companion Checks

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The monoidal repair for Chapter 17 has two companion checks.

Lean

These commands rebuild the local Mathlib workspace and re-run the mechanized laws named in the manuscript:

cd open-source/gnosis
lake build GnosisProofs
lake env lean GnosisProofs.lean

The relevant theorems live in GnosisProofs.lean:

  • tensor_interchange
  • race_tree_coherence
  • fold_tree_coherence
  • c3_deterministic_fold
  • spectrallyStable_of_nilpotent
  • spectrallyStable_of_rowMass
  • supportPath_reachesSmallSet_of_distanceWitness
  • finiteSmallSetRecurrent_of_distanceWitness
  • countableSupportPath_reachesSmallSet_of_driftWitness
  • countableSmallSetRecurrent_of_driftWitness
  • countableAtomicSmallSetMinorized_one_of_collapse
  • countableAtomAccessibleAt_of_smallSetRecurrence_and_atomicMinorization
  • countablePsiIrreducibleAt_of_atomAccessible
  • countableHarrisPreludeAt_of_components
  • countableHarrisRecurrentClassAt_of_recurrence_and_prelude
  • countableGeometricEnvelopeAt_of_harrisPrelude_and_bound
  • countableAtomAccessible_of_smallSetRecurrence_and_atomicMinorization
  • countablePsiIrreducibleAtAtom_of_atomAccessible
  • countableHarrisPreludeAtAtom_of_components
  • countableHarrisRecurrentClassAtAtom_of_recurrence_and_prelude
  • countableAtomHittingBoundAtAtom_of_minorization
  • countableGeometricEnvelopeAtAtom_of_harrisPrelude_and_bound
  • countableAtomGeometricHitLowerBoundAtAtom_of_minorization
  • countableQuantitativeGeometricEnvelopeAtAtom_of_components
  • countableLaminarGeometricStabilityAtAtom_of_components
  • measurableHarrisPrelude_of_components
  • measurableHarrisPrelude_of_reversible
  • measurableHarrisPrelude_of_le_referenceMeasure
  • measurableSmallSetAccessible_of_irreducible
  • measurableReferencePositiveAccessible_of_irreducible
  • measurableHarrisCertified_of_prelude
  • measurableIrreducible_dirac_of_atomAccessible
  • measurableHarrisCertified_of_atomAccessible
  • measurableSmallSetAccessible_of_atomAccessible
  • measurableContainingAtomAccessible_of_atomAccessible
  • measurableLaminarCertifiedAtAtom_of_atomAccessible
  • measurableSmallSetAccessible_of_laminarCertifiedAtAtom
  • measurableContainingAtomAccessible_of_laminarCertifiedAtAtom
  • deterministic_pow_eq_deterministic_iterate
  • measurableAtomAccessible_of_deterministic_hit
  • nat_iterate_queueStep_hits_atom
  • natMeasurableAtomAccessible_of_queueStep
  • natQueueSupportInvariantAtAtom
  • natQueueSupportSmallSetMinorized
  • natMeasurableHarrisCertified_of_queueStep
  • natMeasurableLaminarCertified_of_queueStep
  • natMeasurableAtomHittingBound_of_queueStep
  • natMeasurableQuantitativeLaminarCertified_of_queueStep
  • natMeasurableQuantitativeHarrisCertified_of_queueStep
  • natMeasurableEventuallyConvergesToAtom_of_queueStep
  • natMeasurableFiniteTimeHarrisRecurrent_of_queueStep
  • natQueueWitnessKernel
  • natMeasurableAtomAccessible_of_queueWitnessKernel
  • natMeasurableAtomHittingBound_of_queueWitnessKernel
  • natMeasurableHarrisCertified_of_queueWitnessKernel
  • natMeasurableLaminarCertified_of_queueWitnessKernel
  • natMeasurableQuantitativeLaminarCertified_of_queueWitnessKernel
  • natMeasurableQuantitativeHarrisCertified_of_queueWitnessKernel
  • measurableContainingAtomHittingBound_of_quantitativeLaminarCertifiedAtAtom
  • measurableSmallSetHittingBound_of_quantitativeLaminarCertifiedAtAtom
  • measurableReferencePositiveHittingBound_of_quantitativeLaminarCertifiedAtAtom
  • measurableQuantitativeHarrisCertified_of_quantitativeLaminarCertifiedAtAtom
  • measurableReferencePositiveRecurrent_of_harrisCertified
  • measurableHarrisRecurrent_of_harrisCertified
  • measurableQuantitativeReferencePositiveRecurrent_of_quantitativeHarrisCertified
  • measurableReferencePositivePersistent_of_eventualConvergence
  • measurableReferencePositivePersistent_of_finiteTimeHarrisRecurrent
  • measurableFiniteTimeGeometricStability_of_finiteTimeHarrisRecurrent
  • measurableFiniteTimeGeometricEnvelope_of_finiteTimeHarrisRecurrent
  • measurableHarrisRecurrent_of_finiteTimeHarrisRecurrent
  • measurableFiniteTimeGeometricErgodic_of_finiteTimeHarrisRecurrent
  • measurableLevyProkhorovEventuallyZero_of_eventualConvergence
  • measurableLevyProkhorovEventuallyZero_of_finiteTimeHarrisRecurrent
  • measurableFiniteTimeLevyProkhorovGeometricErgodic_of_finiteTimeHarrisRecurrent
  • measurableLevyProkhorovGeometricDecayAfterBurnIn_of_eventualConvergence
  • measurableLevyProkhorovGeometricDecayAfterBurnIn_of_finiteTimeHarrisRecurrent
  • measurableLevyProkhorovGeometricErgodic_of_decayAfterBurnIn
  • measurableLevyProkhorovGeometricErgodic_of_finiteTimeHarrisRecurrent
  • MeasurableContinuousHarrisWitness
  • natQueueAffineObservable
  • natQueueAffineExpectedObservable
  • natMeasurableLyapunovDriftWitness_of_queueStep_with_gap
  • natMeasurableContinuousHarrisWitness_of_queueStep_with_gap
  • measurableFiniteTimeHarrisRecurrent_of_quantitativeHarris_and_convergence
  • natSmallSetRecurrent_of_stepDown
  • natSmallSetRecurrent_of_uniformPredecessorMinorization
  • natSmallSetRecurrent_of_margin_step
  • certifiedKernel_stable
  • certifiedKernel_stable_of_drift_certificate
  • driftAt_coupledArrivalCertificate
  • coupledArrivalCertificate_negative_drift
  • coupledCertifiedKernel_stable
  • tetheredCertifiedKernels_stable

Betti

Betti's Lean artifact emission should still pass after the proof workspace changes:

bun test open-source/gnosis/src/betty/lean.test.ts

This confirms that the compiler's generated proof artifact now emits a real CertifiedKernel witness that imports the shared proof workspace instead of relying on a local Unit/axiom scaffold, that the measurable queue artifact reaches the emitted exact-convergence, post-burn-in geometric-decay, and abstract geometric-ergodicity Lévy-Prokhorov endpoints as well as the earlier Harris-style endpoints, that the queue-family bridge now emits bounded affine *_measurable_observable, *_measurable_observable_drift, and *_measurable_continuous_harris_certified theorems over the queue-support kernel, and that the shared proof surface now also carries the bounded coupled-kernel handoff theorem for inter-app arrival pressure.