AutoSamplingTheory.SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerDag

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 cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerDag :
    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.cycle119.middle_packet.canonical_barB_weak_fp_consumer
interface : String (explicit)
Text describing intended mathematical interface.
Middle packet: keep barB fixed to the canonical condDistrib guide-plus-score representative from appendix.tex:1368-1377 and route it into the weak-FP generator/source-sign consumer at appendix.tex:1379-1387. This rejects reopening hbarBCondExp or a selected-representative equality unless a separate named barB is deliberately retained.
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.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
3. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
4. appendix.tex:1368-1377
5. 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. sald.discrete_forward_kl.em_interpolation_fp
3. thm:forward-KL-discrete
4. 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.cycle119.lower_ready.canonical_barB_weak_fp_consumer_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated consumes the cycle-118 canonical barB witness in the dominated named-law weak-FP route, derives Integrable canonicalBarB (hatRhoS s0), feeds the inner-gradient no-boundary drift-source handoff, and leaves only the EM path-derivative/domination/source-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.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBInnerGradientBound
5. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
6. ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.discrete_forward_kl.em_interpolation_fp
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.cycle119.remaining_em_path_derivative_domination_and_source_actions
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem: for each admissible weak test, prove the EM interpolation pointwise HasDerivAt and local dominated derivative-under-integral package, identify the derivative integral with driftAction + diffusionAction for the canonical condDistrib barB, prove driftAction = weakGradPairing canonicalBarB, prove weakGradPairing canonicalBarB = -driftDiv through the no-boundary divergence theorem for hatRhoS * canonicalBarB, prove diffusionAction = sigmaCoeff • laplacian, and supply the law-derivative/partialS uniqueness step if the normalized source-sign consumer is used.
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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated
2. Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le
3. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated
4. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
5. SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
6. ASTIS.SALD.cycle100.remaining_no_boundary_after_inner_gradient
7. appendix.tex:1379-1387
8. 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.cycle119.reviewer_canonical_barB_weak_fp_consumer_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the target remains the EM conditional-drift/weak-FP backend at appendix.tex:1368-1387, the canonical barB witness is consumed rather than wrapped, and python3 tools/astis.py check passes with no fake closures, non-EM fallback, SLT/Lake change, source-index rebaseline, theorem-status promotion, 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.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
4. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
5. appendix.tex:1368-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 119 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 cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle119.middle_packet.canonical_barB_weak_fp_consumer"
      interface := "Middle packet: keep barB fixed to the canonical condDistrib guide-plus-score representative from appendix.tex:1368-1377 and route it into the weak-FP generator/source-sign consumer at appendix.tex:1379-1387. This rejects reopening hbarBCondExp or a selected-representative equality unless a separate named barB is deliberately retained."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "appendix.tex:1368-1377",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle119.lower_ready.canonical_barB_weak_fp_consumer_boundary"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated consumes the cycle-118 canonical barB witness in the dominated named-law weak-FP route, derives Integrable canonicalBarB (hatRhoS s0), feeds the inner-gradient no-boundary drift-source handoff, and leaves only the EM path-derivative/domination/source-action theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBInnerGradientBound",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "ASTIS.SALD.cycle110.remaining_parametric_generator_boundary_after_dominated_transport"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions"
      interface := "Remaining exact theorem: for each admissible weak test, prove the EM interpolation pointwise HasDerivAt and local dominated derivative-under-integral package, identify the derivative integral with driftAction + diffusionAction for the canonical condDistrib barB, prove driftAction = weakGradPairing canonicalBarB, prove weakGradPairing canonicalBarB = -driftDiv through the no-boundary divergence theorem for hatRhoS * canonicalBarB, prove diffusionAction = sigmaCoeff • laplacian, and supply the law-derivative/partialS uniqueness step if the normalized source-sign consumer is used."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated",
        "Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le",
        "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
        "ASTIS.SALD.cycle100.remaining_no_boundary_after_inner_gradient",
        "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.cycle119.reviewer_canonical_barB_weak_fp_consumer_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the target remains the EM conditional-drift/weak-FP backend at appendix.tex:1368-1387, the canonical barB witness is consumed rather than wrapped, and python3 tools/astis.py check passes with no fake closures, non-EM fallback, SLT/Lake change, source-index rebaseline, theorem-status promotion, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
        "appendix.tex:1368-1387"
      ]
      reusedBy := ["cycle 119 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 120: EM sample-path derivative and domination boundary -/

/-- Cycle-120 middle obligation for the EM sample-path derivative and
domination inputs.

After the cycle-119 canonical `barB` weak-FP consumer compiled, the remaining
source-cited theorem was still a bundle.  This middle packet narrows that
bundle to the seven parametric-integral hypotheses required by
`generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated`.
The derivative-value split and source-action identities remain separate
boundary facts.
-/

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