AutoSamplingTheory.SALD.cycle140GeneralMovingTargetDiscreteEmGeneratorSourceFunctionalLowerObligation

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 cycle140GeneralMovingTargetDiscreteEmGeneratorSourceFunctionalLowerObligation :
    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.cycle140_em_generator_source_functional_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 140 lower_2 compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the law-space hemGeneratorLawIntegral premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorLawIntegral is no longer primitive; it follows from a source-cited definition of the frozen EM generator Laplacian action as sourceLaplacianFunctional applied to Mathlib's selected-test Laplacian, together with the existing source-functional law integral definition. The theorem keeps hlaplacianEqEmGenerator, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence, 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorLawIntegral
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
4. Mathlib.Analysis.InnerProductSpace.Laplacian
5. appendix.tex:984-995
6. appendix.tex:1379-1387
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.

Lower_2 proof-producing packet inside the cycle-140 illness area. It narrows only the law-space frozen EM generator Laplacian integral to the smaller source-functional action definition plus the existing source functional as integration against hatRhoS. It does not prove 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 cycle140GeneralMovingTargetDiscreteEmGeneratorSourceFunctionalLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle140_em_generator_source_functional_lower"
  statement := "Cycle 140 lower_2 compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the law-space hemGeneratorLawIntegral premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorLawIntegral is no longer primitive; it follows from a source-cited definition of the frozen EM generator Laplacian action as sourceLaplacianFunctional applied to Mathlib's selected-test Laplacian, together with the existing source-functional law integral definition. The theorem keeps hlaplacianEqEmGenerator, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence, and diffusion leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorLawIntegral",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Lower_2 proof-producing packet inside the cycle-140 illness area. It narrows only the law-space frozen EM generator Laplacian integral to the smaller source-functional action definition plus the existing source functional as integration against hatRhoS. It does not prove 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-140 proof-DAG pane for the source-Laplacian state-integral boundary. -/