AutoSamplingTheory.SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralSourceEventLowerObligation

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 cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralSourceEventLowerObligation :
    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.cycle150_em_generator_total_event_trace_laplacian_state_integral_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 150 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorTraceStateIntegral and htraceFieldMeas premises left by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula are no longer primitive; they follow from the smaller sample-space selected-test Laplacian integral hemGeneratorLaplacianStateIntegral, source-Laplacian measurability hsourceLaplacianFieldMeas, and the already explicit htraceFieldEqLaplacian through the local trace-field standard-basis and trace-state helper declarations. The packet keeps hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian explicit, and leaves state-event equality when not supplied by pointwise rewriting plus sibling EM/weak-FP 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas
4. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula
6. hemGeneratorLaplacianStateIntegral
7. hsourceLaplacianFieldMeas
8. hhatRhoS
9. hhatX
10. hsourceLaplacianFunctional
11. hemGeneratorLaplacianEventFieldEqTraceField
12. htraceFieldEqLaplacian
13. appendix.tex:984-995
14. appendix.tex:1368-1387
15. appendix.tex:1379-1387
16. 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 in the EM conditional-law/state-event set-integral illness area. It reuses only existing local SALD trace-field/Laplacian bridges and the already-local Mathlib standard-basis Laplacian bridge. It does not prove hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldEqLaplacian, hemGeneratorLaplacianStateEventEqLaplacian, hlaplacianEqEmGenerator, source-field leaves, density-Laplacian, Green/trace/box-divergence, diffusion leaves, import SLT, change Lake/toolchain files, use sald_version_2, close a theorem by fake proof, take a non-EM fallback, or promote theorem status.

def cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralSourceEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle150_em_generator_total_event_trace_laplacian_state_integral_source_event"
  statement := "Cycle 150 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorTraceStateIntegral and htraceFieldMeas premises left by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula are no longer primitive; they follow from the smaller sample-space selected-test Laplacian integral hemGeneratorLaplacianStateIntegral, source-Laplacian measurability hsourceLaplacianFieldMeas, and the already explicit htraceFieldEqLaplacian through the local trace-field standard-basis and trace-state helper declarations. The packet keeps hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian explicit, and leaves state-event equality when not supplied by pointwise rewriting plus sibling EM/weak-FP leaves separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula",
    "hemGeneratorLaplacianStateIntegral",
    "hsourceLaplacianFieldMeas",
    "hhatRhoS",
    "hhatX",
    "hsourceLaplacianFunctional",
    "hemGeneratorLaplacianEventFieldEqTraceField",
    "htraceFieldEqLaplacian",
    "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 in the EM conditional-law/state-event set-integral illness area. It reuses only existing local SALD trace-field/Laplacian bridges and the already-local Mathlib standard-basis Laplacian bridge. It does not prove hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldEqLaplacian, hemGeneratorLaplacianStateEventEqLaplacian, hlaplacianEqEmGenerator, source-field leaves, density-Laplacian, Green/trace/box-divergence, diffusion leaves, import SLT, change Lake/toolchain files, use sald_version_2, close a theorem by fake proof, take a non-EM fallback, or promote theorem status."

/-- Cycle-150 proof-DAG pane for reducing the total-event trace-action leaf to
the law-space trace integral. -/