AutoSamplingTheory.SALD.cycle128GeneralMovingTargetDiscreteEmNoBoundaryTraceLowerObligation

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 cycle128GeneralMovingTargetDiscreteEmNoBoundaryTraceLowerObligation :
    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.cycle128_em_no_boundary_trace_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 128 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated for appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hdivNoBoundary continuation from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated. The theorem reconstructs driftDiv phi = - integral inner (testGrad phi) canonicalBarB by product-rule total divergence, divergence-theorem boundary flux, boundary trace integral, zero admissible-test trace, MeasureTheory.integral_congr_ae, and SALD.generalMovingTargetDiscreteDriftDivNoBoundaryOfProductRule. Remaining exact boundary: separate test-gradient and canonical-field measurability, gradient-bound regularity, diffusion source action, and optional law-derivative/partialS uniqueness.

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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated
3. SALD.generalMovingTargetDiscreteDriftDivNoBoundaryOfProductRule
4. SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero
5. SALD.generalMovingTargetDiscreteZeroBoundaryFluxOfTraceProductZero
6. MeasureTheory.integral_congr_ae
7. appendix.tex:1368-1377
8. appendix.tex:1379-1387
9. 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.

Illness-area refiner packet. It rejects wrapper churn around hdivNoBoundary: the old direct no-boundary continuation is absent from the theorem statement and is reconstructed from product-rule/divergence/boundary-trace facts. The theorem keeps htestGradMeas, hcanonicalBarBMeas, hgradNormBound, and hdiffusionSource explicit, and it does not introduce non-EM fallback, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, or sald_version_2 content.

def cycle128GeneralMovingTargetDiscreteEmNoBoundaryTraceLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle128_em_no_boundary_trace_lower"
  statement := "Cycle 128 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated for appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hdivNoBoundary continuation from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated. The theorem reconstructs driftDiv phi = - integral inner (testGrad phi) canonicalBarB by product-rule total divergence, divergence-theorem boundary flux, boundary trace integral, zero admissible-test trace, MeasureTheory.integral_congr_ae, and SALD.generalMovingTargetDiscreteDriftDivNoBoundaryOfProductRule. Remaining exact boundary: separate test-gradient and canonical-field measurability, gradient-bound regularity, diffusion source action, and optional law-derivative/partialS uniqueness."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated",
    "SALD.generalMovingTargetDiscreteDriftDivNoBoundaryOfProductRule",
    "SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero",
    "SALD.generalMovingTargetDiscreteZeroBoundaryFluxOfTraceProductZero",
    "MeasureTheory.integral_congr_ae",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet. It rejects wrapper churn around hdivNoBoundary: the old direct no-boundary continuation is absent from the theorem statement and is reconstructed from product-rule/divergence/boundary-trace facts. The theorem keeps htestGradMeas, hcanonicalBarBMeas, hgradNormBound, and hdiffusionSource explicit, and it does not introduce non-EM fallback, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, or sald_version_2 content."

/-- Cycle-128 lower obligation for discharging the canonical `barB`
measurability input after the no-boundary trace refiner. -/