AutoSamplingTheory.SALD.cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation

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 cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation :
    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.cycle130_em_laplacian_ibp_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 130 middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts and SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hlaplacianAction premise consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction is replaced by the source-facing hdiffusionLaplacianTerm and hweakLaplacianIbP facts. The EM/Brownian hdiffusionAction premise remains separate.

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.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction
4. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated
5. appendix.tex:1379-1387
6. 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 rejects wrapper churn around the already narrowed hdiffusionSource consumer and targets only the hlaplacianAction sub-boundary. It does not reassign lower work to hsampleInt, hsampleDerivMeas, hsampleDerivBound, hboundInt, hpathDeriv, hderivValue, hdriftBarBAction, raw hpairMeas, hcanonicalBarBMeas, or direct hdiffusionSource. It does not prove Brownian construction, density regularity, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, or sald_version_2 content.

def cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle130_em_laplacian_ibp_lower"
  statement := "Cycle 130 middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts and SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hlaplacianAction premise consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction is replaced by the source-facing hdiffusionLaplacianTerm and hweakLaplacianIbP facts. The EM/Brownian hdiffusionAction premise remains separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet. It rejects wrapper churn around the already narrowed hdiffusionSource consumer and targets only the hlaplacianAction sub-boundary. It does not reassign lower work to hsampleInt, hsampleDerivMeas, hsampleDerivBound, hboundInt, hpathDeriv, hderivValue, hdriftBarBAction, raw hpairMeas, hcanonicalBarBMeas, or direct hdiffusionSource. It does not prove Brownian construction, density regularity, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, or sald_version_2 content."

/-- Cycle-130 lower_1 scout obligation for narrowing the weak Laplacian IBP
identity to the two Green-identity steps visible in the source proof. -/