AutoSamplingTheory.SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation

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 cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation :
    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.cycle146_em_generator_trace_event_total_event_lower

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 146 middle compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianLawIntegral premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula is no longer primitive; it follows from hemGeneratorLaplacianTotalEventIntegral, the total state-event formula for the named frozen-generator Laplacian event field, plus hemGeneratorLaplacianEventFieldEqTraceField and htraceFieldStdBasis. The compiled route derives the measurable-state-event Laplacian equality through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField, SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula, and SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise, then applies SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula. hlaplacianEqEmGenerator, hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldStdBasis, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves remain 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
6. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
7. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
8. Mathlib.Analysis.InnerProductSpace.Laplacian
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 inside the cycle-142/143/144/145 EM generator trace-state illness area. It rejects wrapper churn by removing only the direct law-space EM generator Laplacian integral from the current trace-event consumer and replacing it with the smaller total-state-event formula plus the already exposed trace-event equality/trace standard-basis route. It does not prove hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldStdBasis, hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, diffusion leaves, SLT imports, Lake/toolchain changes, theorem-status promotion, fake closure, non-EM fallback, broad audits, or sald_version_2 content.

def cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle146_em_generator_trace_event_total_event_lower"
  statement := "Cycle 146 middle compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianLawIntegral premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula is no longer primitive; it follows from hemGeneratorLaplacianTotalEventIntegral, the total state-event formula for the named frozen-generator Laplacian event field, plus hemGeneratorLaplacianEventFieldEqTraceField and htraceFieldStdBasis. The compiled route derives the measurable-state-event Laplacian equality through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField, SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula, and SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise, then applies SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula. hlaplacianEqEmGenerator, hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldStdBasis, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "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 inside the cycle-142/143/144/145 EM generator trace-state illness area. It rejects wrapper churn by removing only the direct law-space EM generator Laplacian integral from the current trace-event consumer and replacing it with the smaller total-state-event formula plus the already exposed trace-event equality/trace standard-basis route. It does not prove hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldStdBasis, hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, diffusion leaves, SLT imports, Lake/toolchain changes, theorem-status promotion, fake closure, non-EM fallback, broad audits, or sald_version_2 content."

/-- Cycle-146 proof-DAG pane for the trace-event total-event narrowing. -/