AutoSamplingTheory.SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceStateIntegralSourceEventLowerObligation

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 cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceStateIntegralSourceEventLowerObligation :
    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_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_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorTraceLawIntegral premise left by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula is no longer primitive; it follows from the smaller sample-space trace integral hemGeneratorTraceStateIntegral, the law identity hhatRhoS, the measurability hhatX, and htraceFieldMeas via the existing map-integral helper SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral. 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula
4. hemGeneratorTraceStateIntegral
5. hhatRhoS
6. hhatX
7. htraceFieldMeas
8. hsourceLaplacianFunctional
9. hemGeneratorLaplacianEventFieldEqTraceField
10. htraceFieldEqLaplacian
11. appendix.tex:984-995
12. appendix.tex:1368-1387
13. appendix.tex:1379-1387
14. 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 proof-scout packet in the EM conditional-law/state-event set-integral illness area. It reuses the existing cycle-142 map-integral transport helper inside the current total-event trace-law route. It does not prove hemGeneratorTraceStateIntegral, htraceFieldMeas, 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 cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceStateIntegralSourceEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle150_em_generator_total_event_trace_state_integral_source_event"
  statement := "Cycle 150 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorTraceLawIntegral premise left by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula is no longer primitive; it follows from the smaller sample-space trace integral hemGeneratorTraceStateIntegral, the law identity hhatRhoS, the measurability hhatX, and htraceFieldMeas via the existing map-integral helper SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral. 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula",
    "hemGeneratorTraceStateIntegral",
    "hhatRhoS",
    "hhatX",
    "htraceFieldMeas",
    "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_1 proof-scout packet in the EM conditional-law/state-event set-integral illness area. It reuses the existing cycle-142 map-integral transport helper inside the current total-event trace-law route. It does not prove hemGeneratorTraceStateIntegral, htraceFieldMeas, 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 lower_2 narrowing for the trace-state premise left by the
current total-event trace-state route. -/