AutoSamplingTheory.SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation

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 cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation :
    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_lower2_em_generator_laplacian_state_integral_stdbasis_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 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hemGeneratorSourceActionDef input under SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional is no longer primitive; it follows from the smaller source-cited standard-basis source formula hemGeneratorStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula. The packet keeps hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hhatRhoS, and hhatX 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.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional
2. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
5. hemGeneratorStdBasisDef
6. hsourceLaplacianFunctional
7. hsourceLaplacianFieldMeas
8. hhatRhoS
9. hhatX
10. appendix.tex:984-995
11. appendix.tex:1368-1387
12. appendix.tex:1379-1387
13. 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 worker packet inside the EM conditional-law/state-event set-integral illness area. It targets only the source-action premise needed to recover hemGeneratorLaplacianStateIntegral and reuses the compiled standard-basis-to-Laplacian bridge. It does not prove hemGeneratorStdBasisDef, source-functional construction, source-Laplacian measurability, 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 cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle153_lower2_em_generator_laplacian_state_integral_stdbasis_source_functional"
  statement := "Cycle 153 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hemGeneratorSourceActionDef input under SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional is no longer primitive; it follows from the smaller source-cited standard-basis source formula hemGeneratorStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula. The packet keeps hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hhatRhoS, and hhatX explicit, and leaves hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, htraceFieldEqLaplacian, state-event, and sibling EM leaves separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional",
    "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
    "hemGeneratorStdBasisDef",
    "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 lower_2 worker packet inside the EM conditional-law/state-event set-integral illness area. It targets only the source-action premise needed to recover hemGeneratorLaplacianStateIntegral and reuses the compiled standard-basis-to-Laplacian bridge. It does not prove hemGeneratorStdBasisDef, source-functional construction, source-Laplacian measurability, 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 proof-DAG pane for the state-integral/source-functional leaf. -/