AutoSamplingTheory.SALD.cycle137GeneralMovingTargetDiscreteEmSecondGreenPointwiseBoxBoundaryFluxLowerObligation

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 cycle137GeneralMovingTargetDiscreteEmSecondGreenPointwiseBoxBoundaryFluxLowerObligation :
    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.cycle137_em_second_green_pointwise_box_boundary_flux_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 137 lower_2 compiles SALD.generalMovingTargetDiscreteSecondGreenPointwiseOfBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hsecondGreenPointwise leaf from SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity is no longer primitive; it follows from the second-Green residual and divergence identities, the Mathlib box-divergence regularity/derivative/integrability package, signed-face trace identification, pointwise equality with the admissible test trace, and pointwise zero test trace. First-Green pointwise, test-Laplacian pointwise normalization, hdensityLaplacianActionDef, hsourceDensityLaplacianEqLaplacian, and htestLaplacianStdBasisDef remain explicit.

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.generalMovingTargetDiscreteSecondGreenPointwiseOfBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
2. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux
3. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity
4. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
5. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
6. Filter.Eventually.of_forall
7. appendix.tex:1392-1427
8. 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.

Dynamic-leaf lower_2 worker packet. It narrows only the pointwise second-Green leaf under the cycle-137 pointwise Green split, replacing the direct hsecondGreenPointwise premise by the already source-facing box-divergence and pointwise trace-zero boundary. It does not prove first-Green pointwise, test-Laplacian pointwise normalization, density-Laplacian source definitions, diffusion-source closure, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle137GeneralMovingTargetDiscreteEmSecondGreenPointwiseBoxBoundaryFluxLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle137_em_second_green_pointwise_box_boundary_flux_lower"
  statement := "Cycle 137 lower_2 compiles SALD.generalMovingTargetDiscreteSecondGreenPointwiseOfBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hsecondGreenPointwise leaf from SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity is no longer primitive; it follows from the second-Green residual and divergence identities, the Mathlib box-divergence regularity/derivative/integrability package, signed-face trace identification, pointwise equality with the admissible test trace, and pointwise zero test trace. First-Green pointwise, test-Laplacian pointwise normalization, hdensityLaplacianActionDef, hsourceDensityLaplacianEqLaplacian, and htestLaplacianStdBasisDef remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteSecondGreenPointwiseOfBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity",
    "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
    "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
    "Filter.Eventually.of_forall",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_2 worker packet. It narrows only the pointwise second-Green leaf under the cycle-137 pointwise Green split, replacing the direct hsecondGreenPointwise premise by the already source-facing box-divergence and pointwise trace-zero boundary. It does not prove first-Green pointwise, test-Laplacian pointwise normalization, density-Laplacian source definitions, diffusion-source closure, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-137 proof-DAG pane for the weak-FP density-Laplacian pointwise
integration-by-parts boundary. -/