AutoSamplingTheory.SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutObligation

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 cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutObligation :
    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_lower_1_em_generator_state_event_pointwise_scout

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 lower_1 narrows the hemGeneratorLaplacianStateEventEqLaplacian boundary left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula. The state-event set-integral equality is not an independent lower_2 analytic target in the current branch: it follows from the already explicit source-cited pointwise identity hemGeneratorLaplacianEventFieldEqLaplacian via compiled SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise, by rewriting the integrand under every measurable state-event integral. The packet therefore rejects a new wrapper that merely restates SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula; lower_2 should spend implementation effort on the remaining genuine EM source leaves hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqLaplacian, and htraceFieldEqLaplacian.

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.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula
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 lower_1 proof-scout packet inside the cycle-142/143/144/145/146/147/148 EM generator trace-state illness area. It uses only local SALD declarations already compiled from the Mathlib set-integral rewrite shape; no SLT import or port claim, sald_version_2 use, non-EM fallback, broad route audit, theorem-status/Lake/toolchain change, fake closure, or new wrapper theorem is introduced.

def cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle148_lower_1_em_generator_state_event_pointwise_scout"
  statement := "Cycle 148 lower_1 narrows the hemGeneratorLaplacianStateEventEqLaplacian boundary left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula. The state-event set-integral equality is not an independent lower_2 analytic target in the current branch: it follows from the already explicit source-cited pointwise identity hemGeneratorLaplacianEventFieldEqLaplacian via compiled SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise, by rewriting the integrand under every measurable state-event integral. The packet therefore rejects a new wrapper that merely restates SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula; lower_2 should spend implementation effort on the remaining genuine EM source leaves hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqLaplacian, and htraceFieldEqLaplacian."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula",
    "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-142/143/144/145/146/147/148 EM generator trace-state illness area. It uses only local SALD declarations already compiled from the Mathlib set-integral rewrite shape; no SLT import or port claim, sald_version_2 use, non-EM fallback, broad route audit, theorem-status/Lake/toolchain change, fake closure, or new wrapper theorem is introduced."

/-- Cycle-148 lower_1 proof-DAG pane for reducing the state-event equality to
the pointwise event-field identity. -/