AutoSamplingTheory.SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation

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 cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation :
    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.cycle143_em_generator_laplacian_pointwise_event_lower_1

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 143 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula for appendix.tex:984-995 and appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianStateEventEqLaplacian premise from the cycle-143 state-event split is no longer primitive; it follows from the pointwise source definition hemGeneratorLaplacianEventFieldEqLaplacian identifying the named frozen-generator event field with Laplacian.laplacian (selectedTest phi). The total-event action hemGeneratorLaplacianTotalEventIntegral remains explicit, as do hlaplacianEqEmGenerator, htraceFieldStdBasis, source-field/source-functional, 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.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
5. appendix.tex:984-995
6. appendix.tex:1368-1387
7. appendix.tex:1379-1387
8. 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 inside the cycle-143 EM generator trace-state illness area. It narrows only the all-state-events equality to a pointwise event-field definition plus the existing total-event action. It does not prove the total-event action, prove hlaplacianEqEmGenerator, prove htraceFieldStdBasis, 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 cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle143_em_generator_laplacian_pointwise_event_lower_1"
  statement := "Cycle 143 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula for appendix.tex:984-995 and appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianStateEventEqLaplacian premise from the cycle-143 state-event split is no longer primitive; it follows from the pointwise source definition hemGeneratorLaplacianEventFieldEqLaplacian identifying the named frozen-generator event field with Laplacian.laplacian (selectedTest phi). The total-event action hemGeneratorLaplacianTotalEventIntegral remains explicit, as do hlaplacianEqEmGenerator, htraceFieldStdBasis, source-field/source-functional, density-Laplacian, Green/trace/box-divergence, and diffusion leaves."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
    "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 inside the cycle-143 EM generator trace-state illness area. It narrows only the all-state-events equality to a pointwise event-field definition plus the existing total-event action. It does not prove the total-event action, prove hlaplacianEqEmGenerator, prove htraceFieldStdBasis, 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-143 lower-1 proof-DAG pane for pointwise event-field narrowing. -/