AutoSamplingTheory.SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation

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 cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation :
    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.cycle148_em_generator_pointwise_state_event_trace_laplacian

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 148 middle compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula is no longer primitive; it follows from the source-cited EM conditional-law/state-event formula through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula. The pointwise event-field Laplacian identity hemGeneratorLaplacianEventFieldEqLaplacian and trace-field Laplacian identity htraceFieldEqLaplacian remain 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula
4. appendix.tex:984-995
5. appendix.tex:1368-1387
6. appendix.tex:1379-1387
7. 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 middle packet inside the cycle-142/143/144/145/146/147/148 EM generator trace-state illness area. It rejects wrapper churn by replacing only hemGeneratorLaplacianLawIntegral in the current pointwise event/trace route with the source-cited EM conditional-law/state-event formula. It does not prove hemGeneratorLaplacianTotalEventIntegral, prove hemGeneratorLaplacianStateEventEqLaplacian, prove hemGeneratorLaplacianEventFieldEqLaplacian, prove htraceFieldEqLaplacian, prove hlaplacianEqEmGenerator, 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 cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle148_em_generator_pointwise_state_event_trace_laplacian"
  statement := "Cycle 148 middle compiles SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula is no longer primitive; it follows from the source-cited EM conditional-law/state-event formula through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula. The pointwise event-field Laplacian identity hemGeneratorLaplacianEventFieldEqLaplacian and trace-field Laplacian identity htraceFieldEqLaplacian remain 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf middle packet inside the cycle-142/143/144/145/146/147/148 EM generator trace-state illness area. It rejects wrapper churn by replacing only hemGeneratorLaplacianLawIntegral in the current pointwise event/trace route with the source-cited EM conditional-law/state-event formula. It does not prove hemGeneratorLaplacianTotalEventIntegral, prove hemGeneratorLaplacianStateEventEqLaplacian, prove hemGeneratorLaplacianEventFieldEqLaplacian, prove htraceFieldEqLaplacian, prove hlaplacianEqEmGenerator, 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-148 proof-DAG pane for the state-event narrowing inside the
pointwise event/trace-Laplacian route. -/