AutoSamplingTheory.SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianStateEventLowerObligation

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 cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianStateEventLowerObligation :
    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_state_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 143 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula for appendix.tex:984-995 and appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianLawIntegral premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula is no longer primitive; it follows from a source-cited EM conditional-law/state-event formula: a named frozen-generator Laplacian event field has total state-event action equal to emGeneratorLaplacianAction, and its integrals over every measurable state event agree with the selected-test Laplacian integrals against hatRhoS. The theorem keeps hlaplacianEqEmGenerator, htraceFieldStdBasis, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, density-Laplacian, Green/trace/box-divergence, and diffusion leaves 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.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
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 worker packet inside the cycle-143 EM generator trace-state illness area. It narrows only hemGeneratorLaplacianLawIntegral to a state-event law-integral boundary tied to the conditional-law source step. It does not reintroduce the cycle-140 source-functional wrapper, prove hlaplacianEqEmGenerator, prove htraceFieldStdBasis, close source-field equality or measurability, 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 cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianStateEventLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle143_em_generator_laplacian_state_event_lower"
  statement := "Cycle 143 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula for appendix.tex:984-995 and appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianLawIntegral premise under SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula is no longer primitive; it follows from a source-cited EM conditional-law/state-event formula: a named frozen-generator Laplacian event field has total state-event action equal to emGeneratorLaplacianAction, and its integrals over every measurable state event agree with the selected-test Laplacian integrals against hatRhoS. The theorem keeps hlaplacianEqEmGenerator, htraceFieldStdBasis, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, density-Laplacian, Green/trace/box-divergence, and diffusion leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet inside the cycle-143 EM generator trace-state illness area. It narrows only hemGeneratorLaplacianLawIntegral to a state-event law-integral boundary tied to the conditional-law source step. It does not reintroduce the cycle-140 source-functional wrapper, prove hlaplacianEqEmGenerator, prove htraceFieldStdBasis, close source-field equality or measurability, 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 proof-DAG pane for the state-event law-integral split. -/