AutoSamplingTheory.SALD.cycle135GeneralMovingTargetDiscreteEmSecondGreenStdBasisConsumerLowerObligation

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 cycle135GeneralMovingTargetDiscreteEmSecondGreenStdBasisConsumerLowerObligation :
    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.cycle135_em_second_green_std_basis_consumer_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 135 lower_2 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the downstream second-Green diffusion-source consumer no longer takes htestLaplacianActionDef and hweakFpLaplacianDef; it derives the old test-Laplacian normalization from htestLaplacianStdBasisDef plus hweakFpStdBasisDef through the cycle-135 standard-basis operator bridge. All second-Green, box-divergence, trace, diffusion, and first-Green leaves 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfStdBasisSourceFormula
2. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula
5. SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
6. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
7. appendix.tex:1379-1387
8. appendix.tex:1392-1427
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.

Dynamic-leaf worker packet. It does not prove htestLaplacianStdBasisDef or hweakFpStdBasisDef; it removes the older htestLaplacianActionDef/hweakFpLaplacianDef supplied hypotheses from the downstream second-Green consumer by deriving the required local test-Laplacian normalization from the two smaller standard-basis source formulas. No SLT import, non-EM fallback, broad audit, theorem-status promotion, fake closure, wrapper churn, Lake/toolchain change, or sald_version_2 content is introduced.

def cycle135GeneralMovingTargetDiscreteEmSecondGreenStdBasisConsumerLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle135_em_second_green_std_basis_consumer_lower"
  statement := "Cycle 135 lower_2 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the downstream second-Green diffusion-source consumer no longer takes htestLaplacianActionDef and hweakFpLaplacianDef; it derives the old test-Laplacian normalization from htestLaplacianStdBasisDef plus hweakFpStdBasisDef through the cycle-135 standard-basis operator bridge. All second-Green, box-divergence, trace, diffusion, and first-Green leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It does not prove htestLaplacianStdBasisDef or hweakFpStdBasisDef; it removes the older htestLaplacianActionDef/hweakFpLaplacianDef supplied hypotheses from the downstream second-Green consumer by deriving the required local test-Laplacian normalization from the two smaller standard-basis source formulas. No SLT import, non-EM fallback, broad audit, theorem-status promotion, fake closure, wrapper churn, Lake/toolchain change, or sald_version_2 content is introduced."

/-- Cycle-135 proof-DAG pane for the test-calculus standard-basis boundary. -/