AutoSamplingTheory.SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation

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 cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation :
    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.cycle145_em_generator_laplacian_trace_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 145 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianEventFieldStdBasisDef premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula is no longer primitive; it follows from the source-facing equality hemGeneratorLaplacianEventFieldEqTraceField identifying the named frozen-generator Laplacian event field with the already tracked trace field, together with htraceFieldStdBasis. hemGeneratorLaplacianLawIntegral remains explicit, as do hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves.

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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula
5. SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField
6. appendix.tex:984-995
7. appendix.tex:1368-1387
8. appendix.tex:1379-1387
9. 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 inside the cycle-142/143/144/145 EM generator trace-state illness area. It rejects wrapper churn by replacing the event-field standard-basis definition with the smaller source equality between the named Laplacian event field and the trace field plus the already explicit htraceFieldStdBasis. It does not prove hemGeneratorLaplacianLawIntegral, prove htraceFieldStdBasis, prove hemGeneratorLaplacianEventFieldEqTraceField, close source-field/source-functional leaves, promote density-Laplacian/Green/trace/box-divergence/diffusion leaves, import SLT, change Lake/toolchain files, use sald_version_2, close a theorem by fake proof, or take a non-EM fallback.

def cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle145_em_generator_laplacian_trace_event_lower"
  statement := "Cycle 145 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianEventFieldStdBasisDef premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula is no longer primitive; it follows from the source-facing equality hemGeneratorLaplacianEventFieldEqTraceField identifying the named frozen-generator Laplacian event field with the already tracked trace field, together with htraceFieldStdBasis. hemGeneratorLaplacianLawIntegral remains explicit, as do hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField",
    "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 inside the cycle-142/143/144/145 EM generator trace-state illness area. It rejects wrapper churn by replacing the event-field standard-basis definition with the smaller source equality between the named Laplacian event field and the trace field plus the already explicit htraceFieldStdBasis. It does not prove hemGeneratorLaplacianLawIntegral, prove htraceFieldStdBasis, prove hemGeneratorLaplacianEventFieldEqTraceField, close source-field/source-functional leaves, promote density-Laplacian/Green/trace/box-divergence/diffusion leaves, import SLT, change Lake/toolchain files, use sald_version_2, close a theorem by fake proof, or take a non-EM fallback."

/-- Cycle-145 lower_2 proof-DAG pane for the trace-field event narrowing. -/