AutoSamplingTheory.SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation

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 cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation :
    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.cycle145_em_generator_laplacian_std_basis_law_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 145 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianStdBasisActionDef premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula is no longer primitive; it follows from hemGeneratorLaplacianLawIntegral by rewriting Mathlib's Laplacian into the source standard-basis second-derivative formula through SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. hemGeneratorLaplacianEventFieldStdBasisDef, hlaplacianEqEmGenerator, htraceFieldStdBasis, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion 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.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. appendix.tex:984-995
7. appendix.tex:1368-1387
8. appendix.tex:1379-1387
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 inside the cycle-142/143/144 EM generator trace-state illness area. It rejects wrapper churn by replacing the standard-basis action integral with the smaller law-space EM Laplacian action integral plus the local Mathlib standard-basis rewrite. It does not prove hemGeneratorLaplacianLawIntegral, hemGeneratorLaplacianEventFieldStdBasisDef, hlaplacianEqEmGenerator, htraceFieldStdBasis, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, diffusion leaves, SLT imports, Lake/toolchain changes, theorem-status promotion, fake closure, non-EM fallback, broad audits, or sald_version_2 content.

def cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle145_em_generator_laplacian_std_basis_law_lower"
  statement := "Cycle 145 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianStdBasisActionDef premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula is no longer primitive; it follows from hemGeneratorLaplacianLawIntegral by rewriting Mathlib's Laplacian into the source standard-basis second-derivative formula through SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. hemGeneratorLaplacianEventFieldStdBasisDef, hlaplacianEqEmGenerator, htraceFieldStdBasis, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet inside the cycle-142/143/144 EM generator trace-state illness area. It rejects wrapper churn by replacing the standard-basis action integral with the smaller law-space EM Laplacian action integral plus the local Mathlib standard-basis rewrite. It does not prove hemGeneratorLaplacianLawIntegral, hemGeneratorLaplacianEventFieldStdBasisDef, hlaplacianEqEmGenerator, htraceFieldStdBasis, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, diffusion leaves, SLT imports, Lake/toolchain changes, theorem-status promotion, fake closure, non-EM fallback, broad audits, or sald_version_2 content."

/-- Cycle-145 proof-DAG pane for the law-integral to standard-basis action
narrowing. -/