AutoSamplingTheory.SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalLowerObligation

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 cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalLowerObligation :
    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_2_em_generator_total_event_source_functional

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_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianTotalEventIntegral premise left by the cycle-148 state-event route is no longer primitive; it follows from the source-functional definition of the frozen EM generator Laplacian action, the source-functional law-integral definition hsourceLaplacianFunctional, and the already explicit pointwise event-field/Laplacian identity hemGeneratorLaplacianEventFieldEqLaplacian. The state-event equality, htraceFieldEqLaplacian, hlaplacianEqEmGenerator, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional
2. hemGeneratorSourceActionDef
3. hsourceLaplacianFunctional
4. hemGeneratorLaplacianEventFieldEqLaplacian
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_2 worker packet inside the cycle-142/143/144/145/146/147/148 EM generator trace-state illness area. It implements one genuine source leaf rather than adding a downstream wrapper: the theorem proves exactly hemGeneratorLaplacianTotalEventIntegral from the source-functional action definition and pointwise event-field identity. It does not prove hemGeneratorLaplacianStateEventEqLaplacian, htraceFieldEqLaplacian, hlaplacianEqEmGenerator, close 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 cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle148_lower_2_em_generator_total_event_source_functional"
  statement := "Cycle 148 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianTotalEventIntegral premise left by the cycle-148 state-event route is no longer primitive; it follows from the source-functional definition of the frozen EM generator Laplacian action, the source-functional law-integral definition hsourceLaplacianFunctional, and the already explicit pointwise event-field/Laplacian identity hemGeneratorLaplacianEventFieldEqLaplacian. The state-event equality, htraceFieldEqLaplacian, hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional",
    "hemGeneratorSourceActionDef",
    "hsourceLaplacianFunctional",
    "hemGeneratorLaplacianEventFieldEqLaplacian",
    "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-142/143/144/145/146/147/148 EM generator trace-state illness area. It implements one genuine source leaf rather than adding a downstream wrapper: the theorem proves exactly hemGeneratorLaplacianTotalEventIntegral from the source-functional action definition and pointwise event-field identity. It does not prove hemGeneratorLaplacianStateEventEqLaplacian, htraceFieldEqLaplacian, hlaplacianEqEmGenerator, close 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 lower_2 proof-DAG pane for reducing the total-event action
formula to the source-functional action definition. -/