AutoSamplingTheory.SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation

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 cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation :
    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.cycle151_em_generator_total_event_trace_laplacian_state_integral_pointwise_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 151 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianEventFieldEqTraceField premise left by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula is no longer primitive; it follows from the smaller pointwise EM event-field identity hemGeneratorLaplacianEventFieldEqLaplacian and the already explicit htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields. The packet keeps hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, and htraceFieldEqLaplacian explicit, with 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
4. hemGeneratorLaplacianEventFieldEqLaplacian
5. htraceFieldEqLaplacian
6. hemGeneratorLaplacianStateIntegral
7. hsourceLaplacianFieldMeas
8. hsourceLaplacianFunctional
9. appendix.tex:984-995
10. appendix.tex:1368-1387
11. appendix.tex:1379-1387
12. 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 in the EM conditional-law/state-event set-integral illness area. It targets only the direct hemGeneratorLaplacianEventFieldEqTraceField leaf selected by the refreshed blueprint and derives it from the pointwise event-field Laplacian identity plus htraceFieldEqLaplacian. No SLT file was consulted or imported; no Lake/toolchain change, theorem-status promotion, non-EM fallback, broad audit, wrapper churn outside this direct leaf, fake closure, or sald_version_2.tex use.

def cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle151_em_generator_total_event_trace_laplacian_state_integral_pointwise_event"
  statement := "Cycle 151 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianEventFieldEqTraceField premise left by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula is no longer primitive; it follows from the smaller pointwise EM event-field identity hemGeneratorLaplacianEventFieldEqLaplacian and the already explicit htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields. The packet keeps hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, and htraceFieldEqLaplacian explicit, with state-event and sibling EM leaves separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
    "hemGeneratorLaplacianEventFieldEqLaplacian",
    "htraceFieldEqLaplacian",
    "hemGeneratorLaplacianStateIntegral",
    "hsourceLaplacianFieldMeas",
    "hsourceLaplacianFunctional",
    "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 in the EM conditional-law/state-event set-integral illness area. It targets only the direct hemGeneratorLaplacianEventFieldEqTraceField leaf selected by the refreshed blueprint and derives it from the pointwise event-field Laplacian identity plus htraceFieldEqLaplacian. No SLT file was consulted or imported; no Lake/toolchain change, theorem-status promotion, non-EM fallback, broad audit, wrapper churn outside this direct leaf, fake closure, or sald_version_2.tex use."

/-- Cycle-151 proof-DAG pane for the direct event-field/trace-field equality
leaf in the trace-Laplacian state total-event route. -/