AutoSamplingTheory.SALD.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceEventLowerObligation

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 cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceEventLowerObligation :
    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.cycle149_em_generator_total_event_stdbasis_source_event

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 149 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceAndEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hemGeneratorLaplacianEventFieldEqLaplacian premise in the cycle-149 total-event standard-basis source-functional route is no longer primitive; it follows from the smaller source-cited standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef via SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula. The packet keeps hemGeneratorStdBasisDef, hsourceLaplacianFunctional, htraceFieldEqLaplacian, and state-event equality when not supplied by pointwise rewriting 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceAndEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. hemGeneratorStdBasisDef
6. hemGeneratorLaplacianEventFieldStdBasisDef
7. hsourceLaplacianFunctional
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 lower_1 worker/scout packet in the EM conditional-law/state-event set-integral illness area. It reuses only local SALD declarations and the already-local Mathlib Laplacian standard-basis bridge; no SLT file was consulted, no SLT import or port claim is made, no sald_version_2 source is used, and no broad route audit, theorem-status/Lake/toolchain change, fake closure, non-EM fallback, or duplicate wrapper churn is introduced.

def cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle149_em_generator_total_event_stdbasis_source_event"
  statement := "Cycle 149 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceAndEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hemGeneratorLaplacianEventFieldEqLaplacian premise in the cycle-149 total-event standard-basis source-functional route is no longer primitive; it follows from the smaller source-cited standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef via SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula. The packet keeps hemGeneratorStdBasisDef, hsourceLaplacianFunctional, htraceFieldEqLaplacian, and state-event equality when not supplied by pointwise rewriting explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceAndEventFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "hemGeneratorStdBasisDef",
    "hemGeneratorLaplacianEventFieldStdBasisDef",
    "hsourceLaplacianFunctional",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_1 worker/scout packet in the EM conditional-law/state-event set-integral illness area. It reuses only local SALD declarations and the already-local Mathlib Laplacian standard-basis bridge; no SLT file was consulted, no SLT import or port claim is made, no sald_version_2 source is used, and no broad route audit, theorem-status/Lake/toolchain change, fake closure, non-EM fallback, or duplicate wrapper churn is introduced."

/-- Cycle-149 lower_1 proof-DAG pane for replacing the pointwise event-field
Laplacian identity by the standard-basis event-field source formula. -/