AutoSamplingTheory.SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation

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 cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation :
    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_test_laplacian_operator_normalization_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 133 lower_2 compiles SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the test-local htestLaplacianLocal premise left by lower_1 is derived from the operator-level source identity htestLaplacianOperator : testRegular → testLaplacianAction = laplacian. The admissibility argument is no longer part of the analytic normalization leaf; it is inert once the selected test calculus is regular.

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.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
3. appendix.tex:1379-1387
4. appendix.tex:1392-1427
5. 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 operator-level source identity for the selected regular test calculus; that is the remaining analytic boundary. 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, Brownian diffusion construction, 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 cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle133_em_test_laplacian_operator_normalization_lower_2"
  statement := "Cycle 133 lower_2 compiles SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the test-local htestLaplacianLocal premise left by lower_1 is derived from the operator-level source identity htestLaplacianOperator : testRegular → testLaplacianAction = laplacian. The admissibility argument is no longer part of the analytic normalization leaf; it is inert once the selected test calculus is regular."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing lower_2 packet. It does not prove the operator-level source identity for the selected regular test calculus; that is the remaining analytic boundary. 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, Brownian diffusion construction, 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-133 proof-DAG pane for the pointwise admissible-test trace boundary. -/