AutoSamplingTheory.SALD.cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation

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 cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation :
    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.cycle129_em_diffusion_source_lower

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 129 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Stale hpathDeriv work is rejected as wrapper churn because cycle 125 compiled SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated, and cycle 126 compiled the derivative-value continuation. The exact boundary narrowed here is the supplied hdiffusionSource input in SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated: the compiled continuation removes that direct premise and replaces it with the two source-facing facts consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction, namely the EM/Brownian diffusion generator contribution equals the named weak diffusion action, and the weak Laplacian integration-by-parts theorem identifies that action with sigmaCoeff • laplacian phi.

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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated
4. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated
5. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated
6. appendix.tex:1379-1387
7. 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 packet. It does not reassign lower work to hpathDeriv, hderivValue, hdriftBarBAction, hpairMeas, hdivNoBoundary, or hcanonicalBarBMeas, all of which already have compiled follow-on theorems. It proves only the local composition into the canonical consumer. It does not prove the Brownian generator theorem, weak Laplacian integration by parts, gradient-bound regularity, weak-test-gradient measurability, law-derivative/partialS uniqueness, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, or sald_version_2 content.

def cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle129_em_diffusion_source_lower"
  statement := "Cycle 129 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Stale hpathDeriv work is rejected as wrapper churn because cycle 125 compiled SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated, and cycle 126 compiled the derivative-value continuation. The exact boundary narrowed here is the supplied hdiffusionSource input in SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated: the compiled continuation removes that direct premise and replaces it with the two source-facing facts consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction, namely the EM/Brownian diffusion generator contribution equals the named weak diffusion action, and the weak Laplacian integration-by-parts theorem identifies that action with sigmaCoeff • laplacian phi."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet. It does not reassign lower work to hpathDeriv, hderivValue, hdriftBarBAction, hpairMeas, hdivNoBoundary, or hcanonicalBarBMeas, all of which already have compiled follow-on theorems. It proves only the local composition into the canonical consumer. It does not prove the Brownian generator theorem, weak Laplacian integration by parts, gradient-bound regularity, weak-test-gradient measurability, law-derivative/partialS uniqueness, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, or sald_version_2 content."

/-- Cycle-129 proof-DAG pane for the remaining diffusion source-action
boundary inside the canonical EM weak-FP backend. -/