AutoSamplingTheory.SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation

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 cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation :
    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.cycle138_em_test_laplacian_pointwise_std_basis_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 138 lower_2 compiles SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the htestLaplacianActionDef side of the pointwise test-Laplacian normalization is no longer primitive; it follows from htestLaplacianStdBasisDef via the Mathlib Laplacian standard-basis bridge. The weak-FP side remains the explicit hweakFpLaplacianDef source boundary, because deriving it from hweakFpStdBasisDef would reuse the standard-basis conclusion being proved by the Green route.

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.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula
2. SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. appendix.tex:1379-1427
7. 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 implements the valid non-circular part of the lower_1 handoff: htestLaplacianActionDef is instantiated from htestLaplacianStdBasisDef for the pointwise Green route. It deliberately does not instantiate hweakFpLaplacianDef from hweakFpStdBasisDef or hweakFpDensityLaplacianAction, since either would feed a target or ancestor target back into the pointwise proof. It does not close hweakFpLaplacianDef, density-Laplacian source definitions, second-Green residual/divergence, box-divergence, trace, diffusion, KL differentiation, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle138_em_test_laplacian_pointwise_std_basis_lower"
  statement := "Cycle 138 lower_2 compiles SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the htestLaplacianActionDef side of the pointwise test-Laplacian normalization is no longer primitive; it follows from htestLaplacianStdBasisDef via the Mathlib Laplacian standard-basis bridge. The weak-FP side remains the explicit hweakFpLaplacianDef source boundary, because deriving it from hweakFpStdBasisDef would reuse the standard-basis conclusion being proved by the Green route."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:1379-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It implements the valid non-circular part of the lower_1 handoff: htestLaplacianActionDef is instantiated from htestLaplacianStdBasisDef for the pointwise Green route. It deliberately does not instantiate hweakFpLaplacianDef from hweakFpStdBasisDef or hweakFpDensityLaplacianAction, since either would feed a target or ancestor target back into the pointwise proof. It does not close hweakFpLaplacianDef, density-Laplacian source definitions, second-Green residual/divergence, box-divergence, trace, diffusion, KL differentiation, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-138 proof-DAG pane for the first-Green pointwise boundary-flux
sub-boundary. -/