AutoSamplingTheory.SALD.cycle127GeneralMovingTargetDiscreteEmDriftActionDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle127GeneralMovingTargetDiscreteEmDriftActionDag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

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.

Ordered data items

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle127.lower_packet.canonical_barB_drift_action_from_components
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated derives the canonical hdriftBarBAction continuation from guideAction/scoreAction component pairings for the canonical condDistrib guide and score fields plus weak-pairing congruence/additivity/scalar-linearity, then reuses the cycle-126 path-value theorem.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
5. appendix.tex:1368-1377
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. thm:forward-KL-discrete
3. thm:general-moving-target-SALD-discrete
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle127.lower_packet.canonical_barB_pair_meas_from_fields
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated derives the old hpairMeas continuation from separate AEStronglyMeasurable testGrad phi and canonicalBarB hypotheses using MeasureTheory.AEStronglyMeasurable.inner, then reuses the cycle-127 drift-action theorem.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle127GeneralMovingTargetDiscreteEmPairMeasLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated
4. MeasureTheory.AEStronglyMeasurable.inner
5. appendix.tex:1368-1377
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. thm:forward-KL-discrete
3. thm:general-moving-target-SALD-discrete
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle127.remaining_canonical_source_actions_after_drift_action
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after the canonical drift weak-action identity and raw hpairMeas continuation are discharged: prove the separate weak-test-gradient and canonicalBarB measurability inputs, gradient-bound regularity, the no-boundary divergence identity for hatRhoS * canonicalBarB, the diffusion source action, and optional law-derivative/partialS uniqueness.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated
3. ASTIS.SALD.cycle126.remaining_canonical_source_actions_after_deriv_value
4. appendix.tex:1379-1387
5. appendix.tex:1368-1377
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. thm:general-moving-target-SALD-discrete
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle127.reviewer_em_drift_action_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hdriftBarBAction, the old direct driftAction=weakGradPairing canonicalBarB continuation is absent from the theorem statement, the guide/score component pairings and weak-pairing algebra preserve dotTk and sigmaCoeff signs, and python3 tools/astis.py check passes with no wrapper churn, non-EM fallback, SLT/Lake change, source-index rebaseline, theorem-status promotion, fake closure, or sald_version_2 use.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated
3. appendix.tex:1368-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 127 reviewer
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle127GeneralMovingTargetDiscreteEmDriftActionDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle127.lower_packet.canonical_barB_drift_action_from_components"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated derives the canonical hdriftBarBAction continuation from guideAction/scoreAction component pairings for the canonical condDistrib guide and score fields plus weak-pairing congruence/additivity/scalar-linearity, then reuses the cycle-126 path-value theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
        "appendix.tex:1368-1377",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle127.lower_packet.canonical_barB_pair_meas_from_fields"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated derives the old hpairMeas continuation from separate AEStronglyMeasurable testGrad phi and canonicalBarB hypotheses using MeasureTheory.AEStronglyMeasurable.inner, then reuses the cycle-127 drift-action theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle127GeneralMovingTargetDiscreteEmPairMeasLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated",
        "MeasureTheory.AEStronglyMeasurable.inner",
        "appendix.tex:1368-1377",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle127.remaining_canonical_source_actions_after_drift_action"
      interface := "Remaining exact theorem after the canonical drift weak-action identity and raw hpairMeas continuation are discharged: prove the separate weak-test-gradient and canonicalBarB measurability inputs, gradient-bound regularity, the no-boundary divergence identity for hatRhoS * canonicalBarB, the diffusion source action, and optional law-derivative/partialS uniqueness."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated",
        "ASTIS.SALD.cycle126.remaining_canonical_source_actions_after_deriv_value",
        "appendix.tex:1379-1387",
        "appendix.tex:1368-1377"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle127.reviewer_em_drift_action_check"
      interface := "Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hdriftBarBAction, the old direct driftAction=weakGradPairing canonicalBarB continuation is absent from the theorem statement, the guide/score component pairings and weak-pairing algebra preserve dotTk and sigmaCoeff signs, and python3 tools/astis.py check passes with no wrapper churn, non-EM fallback, SLT/Lake change, source-index rebaseline, theorem-status promotion, fake closure, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated",
        "appendix.tex:1368-1387"
      ]
      reusedBy := ["cycle 127 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 128: Canonical barB no-boundary trace refiner -/

/-- Cycle-128 lower obligation for narrowing the direct canonical `barB`
no-boundary input in the EM weak-FP consumer. -/

Existing module entry · Audited data-reader index · All teaching coverage