AutoSamplingTheory.SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

id : String (explicit)

Stable obligation identifier.

sald.general_moving_target_discrete.cycle119_canonical_barB_weak_fp_consumer_middle

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 119 middle follows the refreshed dynamic leaf for appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport is now the canonical-barB weak-FP consumer boundary. The lower route should instantiate barB by SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface, keep the canonical condDistrib guide-plus-score field from appendix.tex:1368-1377, and consume SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff plus the cycle-94 barB source-sign handoffs. The remaining named theorem is not hbarBCondExp: it is the EM pointwise path-derivative/local-domination package and the canonical source-action identities driftAction = weakGradPairing canonicalBarB, weakGradPairing canonicalBarB = -driftDiv by no-boundary divergence, diffusionAction = sigmaCoeff • laplacian, and, for the normalized source-sign consumer, the corresponding law-derivative/partialS identification.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
2. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
6. ASTIS.SALD.cycle118.lower_ready.direct_canonical_barB_em_state_event_interface
7. ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport
8. Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le
9. Mathlib.Probability.Kernel.CondDistrib
10. appendix.tex:1368-1377
11. appendix.tex:1379-1387
12. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Illness-area refiner middle packet. It rejects another hbarBCondExp or named-representative wrapper, broad source-index or theorem-route audit, non-EM fallback, SLT import, Lake dependency change, theorem-status promotion, fake closure, and sald_version_2 content.

def cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle119_canonical_barB_weak_fp_consumer_middle"
  statement := "Cycle 119 middle follows the refreshed dynamic leaf for appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport is now the canonical-barB weak-FP consumer boundary. The lower route should instantiate barB by SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface, keep the canonical condDistrib guide-plus-score field from appendix.tex:1368-1377, and consume SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff plus the cycle-94 barB source-sign handoffs. The remaining named theorem is not hbarBCondExp: it is the EM pointwise path-derivative/local-domination package and the canonical source-action identities driftAction = weakGradPairing canonicalBarB, weakGradPairing canonicalBarB = -driftDiv by no-boundary divergence, diffusionAction = sigmaCoeff • laplacian, and, for the normalized source-sign consumer, the corresponding law-derivative/partialS identification."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "ASTIS.SALD.cycle118.lower_ready.direct_canonical_barB_em_state_event_interface",
    "ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport",
    "Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le",
    "Mathlib.Probability.Kernel.CondDistrib",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner middle packet. It rejects another hbarBCondExp or named-representative wrapper, broad source-index or theorem-route audit, non-EM fallback, SLT import, Lake dependency change, theorem-status promotion, fake closure, and sald_version_2 content."

/-- Cycle-119 lower obligation for the canonical `barB` weak-FP consumer.

This is a proof-producing lower packet, not a theorem-status promotion.  It
compiles the consumer that takes the canonical conditional-drift/state-event
package accepted in cycle 118 and uses it inside the dominated named-law weak
derivative route.  The remaining source-cited theorem boundary is still the
EM path derivative/domination and source-action package.
-/