AutoSamplingTheory.SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenPointwiseTraceEqLowerObligation

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 cycle132GeneralMovingTargetDiscreteEmSecondGreenPointwiseTraceEqLowerObligation :
    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.cycle132_em_second_green_pointwise_trace_eq_lower_2

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 132 lower_2 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hsecondGreenTestTraceEq premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero is replaced by hsecondGreenTestTracePointwiseEq, a pointwise source trace-definition equality between secondGreenTestTrace and the standard admissible-test boundary trace. The theorem derives the a.e. equality via Filter.Eventually.of_forall and keeps htestTraceZero, box-divergence regularity/face-trace facts, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero
3. Filter.Eventually.of_forall
4. appendix.tex:1392-1427
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.

Proof-producing lower_2 packet. It does not prove the analytic compact-support/zero-trace theorem, the pointwise source trace-definition equality, weighted-field regularity, divergence integrability, face-to-trace identification, second-Green residual/divergence facts, test-Laplacian normalization, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content.

def cycle132GeneralMovingTargetDiscreteEmSecondGreenPointwiseTraceEqLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle132_em_second_green_pointwise_trace_eq_lower_2"
  statement := "Cycle 132 lower_2 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hsecondGreenTestTraceEq premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero is replaced by hsecondGreenTestTracePointwiseEq, a pointwise source trace-definition equality between secondGreenTestTrace and the standard admissible-test boundary trace. The theorem derives the a.e. equality via Filter.Eventually.of_forall and keeps htestTraceZero, box-divergence regularity/face-trace facts, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero",
    "Filter.Eventually.of_forall",
    "appendix.tex:1392-1427",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing lower_2 packet. It does not prove the analytic compact-support/zero-trace theorem, the pointwise source trace-definition equality, weighted-field regularity, divergence integrability, face-to-trace identification, second-Green residual/divergence facts, test-Laplacian normalization, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content."

/-- Cycle-132 proof-DAG pane for the second-Green zero-test-trace narrowing. -/