AutoSamplingTheory.SALD.cycle130GeneralMovingTargetDiscreteEmGreenLaplacianIbPScoutObligation

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 cycle130GeneralMovingTargetDiscreteEmGreenLaplacianIbPScoutObligation :
    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_green_laplacian_ibp_scout

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 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity and SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hweakLaplacianIbP premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts is replaced by first-Green density-Laplacian-to-negative-gradient-pairing, second-Green negative-gradient-pairing-to-test-Laplacian, and test-Laplacian normalization hypotheses. The EM/Brownian hdiffusionAction fact and hdiffusionLaplacianTerm remain 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.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts
5. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
6. Mathlib.MeasureTheory.Integral.DivergenceTheorem
7. appendix.tex:1379-1387
8. appendix.tex:1368-1377
9. 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.

Natural-language proof-scout packet plus compiled abstract composition. It does not prove the analytic Green identities, but records the exact lower_2 target: instantiate the first and second no-boundary integration-by-parts steps for the source density and admissible weak tests, likely through the existing SALD box-divergence/no-boundary route and Mathlib MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable. No SLT import, non-EM fallback, Lake/toolchain change, theorem-status promotion, fake closure, wrapper churn, or sald_version_2 content.

def cycle130GeneralMovingTargetDiscreteEmGreenLaplacianIbPScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle130_em_green_laplacian_ibp_scout"
  statement := "Cycle 130 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity and SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hweakLaplacianIbP premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts is replaced by first-Green density-Laplacian-to-negative-gradient-pairing, second-Green negative-gradient-pairing-to-test-Laplacian, and test-Laplacian normalization hypotheses. The EM/Brownian hdiffusionAction fact and hdiffusionLaplacianTerm remain separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts",
    "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "appendix.tex:1379-1387",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Natural-language proof-scout packet plus compiled abstract composition. It does not prove the analytic Green identities, but records the exact lower_2 target: instantiate the first and second no-boundary integration-by-parts steps for the source density and admissible weak tests, likely through the existing SALD box-divergence/no-boundary route and Mathlib MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable. No SLT import, non-EM fallback, Lake/toolchain change, theorem-status promotion, fake closure, wrapper churn, or sald_version_2 content."

/-- Cycle-130 lower_2 obligation narrowing the first Green identity to
no-boundary flux algebra. -/