AutoSamplingTheory.SALD.cycle128GeneralMovingTargetDiscreteEmCanonicalBarBMeasLowerObligation

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 cycle128GeneralMovingTargetDiscreteEmCanonicalBarBMeasLowerObligation :
    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_canonical_barB_meas_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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated for appendix.tex:1368-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hcanonicalBarBMeas from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated. The theorem derives AEStronglyMeasurable canonicalBarB (hatRhoS s0) from hhatRhoS s0, hXk, the guide/score measurability and integrability inputs, and SALD.generalMovingTargetDiscreteCondDistribCanonicalDriftRegularity. Remaining exact boundary: htestGradMeas, hgradNormBound, hdiffusionSource, 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated
3. SALD.generalMovingTargetDiscreteCondDistribCanonicalDriftRegularity
4. AutoSamplingTheory.condDistribIntegralNamedLawAEStronglyMeasurable
5. AutoSamplingTheory.condDistribIntegralNamedLawIntegrable
6. appendix.tex:1368-1377
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 packet after the no-boundary refiner. It rejects wrapper churn around hcanonicalBarBMeas: the old direct canonical-field measurability continuation is absent from the theorem statement and is reconstructed from the existing condDistrib regularity theorem. The theorem keeps htestGradMeas, 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 cycle128GeneralMovingTargetDiscreteEmCanonicalBarBMeasLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle128_em_canonical_barB_meas_lower"
  statement := "Cycle 128 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated for appendix.tex:1368-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hcanonicalBarBMeas from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated. The theorem derives AEStronglyMeasurable canonicalBarB (hatRhoS s0) from hhatRhoS s0, hXk, the guide/score measurability and integrability inputs, and SALD.generalMovingTargetDiscreteCondDistribCanonicalDriftRegularity. Remaining exact boundary: htestGradMeas, hgradNormBound, hdiffusionSource, and optional law-derivative/partialS uniqueness."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceDominated",
    "SALD.generalMovingTargetDiscreteCondDistribCanonicalDriftRegularity",
    "AutoSamplingTheory.condDistribIntegralNamedLawAEStronglyMeasurable",
    "AutoSamplingTheory.condDistribIntegralNamedLawIntegrable",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower packet after the no-boundary refiner. It rejects wrapper churn around hcanonicalBarBMeas: the old direct canonical-field measurability continuation is absent from the theorem statement and is reconstructed from the existing condDistrib regularity theorem. The theorem keeps htestGradMeas, 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 proof-DAG pane for the canonical `barB` no-boundary trace
refinement inside the EM conditional-drift/weak-Fokker--Planck backend. -/