AutoSamplingTheory.SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation

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 cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation :
    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.cycle144_em_generator_laplacian_std_basis_event_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 144 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula for appendix.tex:984-995 and appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianEventFieldEqLaplacian premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula is no longer primitive; it follows from the source-facing standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. hemGeneratorLaplacianActionDef, 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula
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 EM generator trace-state illness area. It rejects wrapper churn around hemGeneratorLaplacianEventFieldEqLaplacian by replacing the direct Mathlib-Laplacian field equality with the source standard-basis event-field definition used by the frozen EM generator. It does not prove hemGeneratorLaplacianActionDef, 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 cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle144_em_generator_laplacian_std_basis_event_lower"
  statement := "Cycle 144 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula for appendix.tex:984-995 and appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianEventFieldEqLaplacian premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula is no longer primitive; it follows from the source-facing standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. hemGeneratorLaplacianActionDef, 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula",
    "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 EM generator trace-state illness area. It rejects wrapper churn around hemGeneratorLaplacianEventFieldEqLaplacian by replacing the direct Mathlib-Laplacian field equality with the source standard-basis event-field definition used by the frozen EM generator. It does not prove hemGeneratorLaplacianActionDef, 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-144 proof-DAG pane for the standard-basis frozen EM event-field
narrowing. -/