AutoSamplingTheory.SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation

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 cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation :
    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.cycle141_em_generator_std_basis_source_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 141 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the remaining hemGeneratorSourceActionDef premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional is no longer primitive; it follows from hemGeneratorStdBasisDef, the source-cited frozen EM generator standard-basis second-derivative action formula, plus the existing Mathlib selected-test Laplacian bridge. The theorem keeps hlaplacianEqEmGenerator, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence leaves, and diffusion leaves 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.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. appendix.tex:984-995
7. appendix.tex:1379-1387
8. 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.

Illness-area refiner packet. It narrows only hemGeneratorSourceActionDef to the smaller standard-basis source formula for the frozen EM generator Laplacian component. It does not prove hemGeneratorStdBasisDef, hlaplacianEqEmGenerator, source-field equality, source-field measurability, source-functional construction, test standard-basis formula, density-Laplacian source facts, Green/trace/box-divergence leaves, diffusion construction, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle141_em_generator_std_basis_source_lower"
  statement := "Cycle 141 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the remaining hemGeneratorSourceActionDef premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional is no longer primitive; it follows from hemGeneratorStdBasisDef, the source-cited frozen EM generator standard-basis second-derivative action formula, plus the existing Mathlib selected-test Laplacian bridge. The theorem keeps hlaplacianEqEmGenerator, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence leaves, and diffusion leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet. It narrows only hemGeneratorSourceActionDef to the smaller standard-basis source formula for the frozen EM generator Laplacian component. It does not prove hemGeneratorStdBasisDef, hlaplacianEqEmGenerator, source-field equality, source-field measurability, source-functional construction, test standard-basis formula, density-Laplacian source facts, Green/trace/box-divergence leaves, diffusion construction, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-141 lower_1 scout narrowing below the EM generator standard-basis leaf. -/