AutoSamplingTheory.SALD.cycle140GeneralMovingTargetDiscreteEmLaplacianSourceStateIntegralLowerObligation

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 cycle140GeneralMovingTargetDiscreteEmLaplacianSourceStateIntegralLowerObligation :
    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_laplacian_source_state_integral_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 middle compiles SALD.generalMovingTargetDiscreteLaplacianSourceStateIntegralOfEmGeneratorStateIntegral and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStateIntegral for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hlaplacianSourceStateIntegral premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral is no longer primitive; it follows from a source-cited equality identifying the weak-FP Laplacian action with the frozen EM generator's Laplacian component and a source integral formula for that generator component against the sample path hatXAtS. The theorem keeps 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.generalMovingTargetDiscreteLaplacianSourceStateIntegralOfEmGeneratorStateIntegral
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStateIntegral
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfStateIntegral
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 hlaplacianSourceStateIntegral to the smaller EM frozen-generator action/state-integral interface. It does not prove hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, the source functional definition, htestLaplacianStdBasisDef, density-Laplacian source facts, second-Green residual/divergence, box-divergence, trace, diffusion, 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 cycle140GeneralMovingTargetDiscreteEmLaplacianSourceStateIntegralLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle140_em_laplacian_source_state_integral_lower"
  statement := "Cycle 140 middle compiles SALD.generalMovingTargetDiscreteLaplacianSourceStateIntegralOfEmGeneratorStateIntegral and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStateIntegral for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hlaplacianSourceStateIntegral premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral is no longer primitive; it follows from a source-cited equality identifying the weak-FP Laplacian action with the frozen EM generator's Laplacian component and a source integral formula for that generator component against the sample path hatXAtS. The theorem keeps hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence, and diffusion leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteLaplacianSourceStateIntegralOfEmGeneratorStateIntegral",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStateIntegral",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfStateIntegral",
    "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 hlaplacianSourceStateIntegral to the smaller EM frozen-generator action/state-integral interface. It does not prove hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, the source functional definition, htestLaplacianStdBasisDef, density-Laplacian source facts, second-Green residual/divergence, box-divergence, trace, diffusion, 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 lower_1 law-integral scout for the frozen EM generator
Laplacian component. -/