AutoSamplingTheory.SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation

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 cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation :
    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.cycle153_em_generator_laplacian_state_integral_source_functional

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 153 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hemGeneratorLaplacianStateIntegral leaf is no longer primitive for the active EM conditional-law/state-event set-integral backend; it follows from the smaller source-functional action definition hemGeneratorSourceActionDef, the explicit hsourceLaplacianFunctional law-integral definition, source-Laplacian measurability, hhatRhoS = Measure.map hatXAtS P, and AEMeasurable hatXAtS, reusing SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral. The packet keeps hsourceLaplacianFunctional and hsourceLaplacianFieldMeas explicit, and leaves hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, htraceFieldEqLaplacian, state-event, and sibling EM leaves separate.

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.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
3. hemGeneratorSourceActionDef
4. hsourceLaplacianFunctional
5. hsourceLaplacianFieldMeas
6. hhatRhoS
7. hhatX
8. appendix.tex:984-995
9. appendix.tex:1368-1387
10. appendix.tex:1379-1387
11. 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 EM conditional-law/state-event set-integral illness area. It targets only hemGeneratorLaplacianStateIntegral and reuses the already compiled law-to-state integral transport. It does not prove the source-functional action definition, source-Laplacian measurability, source-functional construction, EM event-field standard-basis definition, weak-FP pointwise source field identity, trace-field Laplacian identity, state-event formula, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, downstream wrapper churn, non-EM fallback, or sald_version_2.tex content.

def cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle153_em_generator_laplacian_state_integral_source_functional"
  statement := "Cycle 153 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hemGeneratorLaplacianStateIntegral leaf is no longer primitive for the active EM conditional-law/state-event set-integral backend; it follows from the smaller source-functional action definition hemGeneratorSourceActionDef, the explicit hsourceLaplacianFunctional law-integral definition, source-Laplacian measurability, hhatRhoS = Measure.map hatXAtS P, and AEMeasurable hatXAtS, reusing SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral. The packet keeps hsourceLaplacianFunctional and hsourceLaplacianFieldMeas explicit, and leaves hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, htraceFieldEqLaplacian, state-event, and sibling EM leaves separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
    "hemGeneratorSourceActionDef",
    "hsourceLaplacianFunctional",
    "hsourceLaplacianFieldMeas",
    "hhatRhoS",
    "hhatX",
    "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 EM conditional-law/state-event set-integral illness area. It targets only hemGeneratorLaplacianStateIntegral and reuses the already compiled law-to-state integral transport. It does not prove the source-functional action definition, source-Laplacian measurability, source-functional construction, EM event-field standard-basis definition, weak-FP pointwise source field identity, trace-field Laplacian identity, state-event formula, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, downstream wrapper churn, non-EM fallback, or sald_version_2.tex content."

/-- Cycle-153 lower_2 narrowing from the standard-basis source formula. -/