AutoSamplingTheory.SALD.cycle139GeneralMovingTargetDiscreteEmWeakFpSourceLaplacianStateIntegralLowerObligation

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 cycle139GeneralMovingTargetDiscreteEmWeakFpSourceLaplacianStateIntegralLowerObligation :
    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.cycle139_em_weak_fp_source_laplacian_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 139 lower_2 compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the lower_1 hweakFpFieldMeas and hlaplacianStateIntegral inputs are no longer stated for an opaque weakFpLaplacianSourceField; they are reduced to sourceLaplacianFieldMeas and hlaplacianSourceStateIntegral for Mathlib's Laplacian of the selected weak-test representative, together with hweakFpSourceFieldEqLaplacian. The theorem then reuses the compiled EM state-law integral_map bridge.

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.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfStateIntegral
3. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField
4. MeasureTheory.integral_map
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. appendix.tex:1379-1387
7. appendix.tex:1392-1427
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.

Dynamic-leaf lower_2 packet. It proves a compiled local theorem below hweakFpSourceActionDef and narrows the source-action state-integral inputs to the concrete source Laplacian field. It does not prove hweakFpSourceFieldEqLaplacian, sourceLaplacianFieldMeas, the source sample-space Laplacian integral formula, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence leaves, diffusion construction, KL differentiation, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle139GeneralMovingTargetDiscreteEmWeakFpSourceLaplacianStateIntegralLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle139_em_weak_fp_source_laplacian_state_integral_lower"
  statement := "Cycle 139 lower_2 compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the lower_1 hweakFpFieldMeas and hlaplacianStateIntegral inputs are no longer stated for an opaque weakFpLaplacianSourceField; they are reduced to sourceLaplacianFieldMeas and hlaplacianSourceStateIntegral for Mathlib's Laplacian of the selected weak-test representative, together with hweakFpSourceFieldEqLaplacian. The theorem then reuses the compiled EM state-law integral_map bridge."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfSourceLaplacianStateIntegral",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfStateIntegral",
    "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField",
    "MeasureTheory.integral_map",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_2 packet. It proves a compiled local theorem below hweakFpSourceActionDef and narrows the source-action state-integral inputs to the concrete source Laplacian field. It does not prove hweakFpSourceFieldEqLaplacian, sourceLaplacianFieldMeas, the source sample-space Laplacian integral formula, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence leaves, diffusion construction, KL differentiation, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-139 proof-DAG pane for the weak-FP source-Laplacian field split. -/