AutoSamplingTheory.SALD.cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation

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 cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation :
    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.cycle133_em_second_green_pointwise_test_trace_zero_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 133 middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the htestTraceZero premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero is replaced by htestTracePointwiseZero, a pointwise boundary-trace vanishing theorem for source admissible tests. The theorem derives the old a.e. boundary trace fact by Filter.Eventually.of_forall and keeps hsecondGreenTestTracePointwiseEq, the 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero
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.

Illness-area refiner packet. It rejects stale dynamic leaves and wrapper churn by removing the direct a.e. htestTraceZero premise and exposing the smaller pointwise zero-trace source theorem. It does not prove compact support/decay, pointwise second-Green trace identification, 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, or sald_version_2 content.

def cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle133_em_second_green_pointwise_test_trace_zero_lower"
  statement := "Cycle 133 middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the htestTraceZero premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero is replaced by htestTracePointwiseZero, a pointwise boundary-trace vanishing theorem for source admissible tests. The theorem derives the old a.e. boundary trace fact by Filter.Eventually.of_forall and keeps hsecondGreenTestTracePointwiseEq, the 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero",
    "Filter.Eventually.of_forall",
    "appendix.tex:1392-1427",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet. It rejects stale dynamic leaves and wrapper churn by removing the direct a.e. htestTraceZero premise and exposing the smaller pointwise zero-trace source theorem. It does not prove compact support/decay, pointwise second-Green trace identification, 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, or sald_version_2 content."

/-- Cycle-133 lower_1 scout packet narrowing the test-Laplacian normalization
input from the broad weak-FP context to a test-local theorem. -/