AutoSamplingTheory.SALD.cycle126GeneralMovingTargetDiscreteEmDerivValueDag

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 cycle126GeneralMovingTargetDiscreteEmDerivValueDag :
    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.cycle126.lower_packet.em_deriv_value_from_concrete_integral_split
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated derives hderivValue from a concrete EM derivative integral split plus interval a.e. equality to sampleDeriv, then reuses the cycle-125 path 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.cycle126GeneralMovingTargetDiscreteEmDerivValueLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated
4. MeasureTheory.integral_congr_ae
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. 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.cycle126.remaining_canonical_source_actions_after_deriv_value
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after hsampleMeas, hsampleInt, hsampleDerivMeas, hsampleDerivBound, hboundInt, hpathDeriv, and hderivValue are discharged: prove the canonical barB drift weak-action/pairing regularity, no-boundary divergence, 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated
2. ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative
3. appendix.tex:1379-1387
4. 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.cycle126.reviewer_em_deriv_value_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hderivValue, the proof uses a concrete derivative integral split and MeasureTheory.integral_congr_ae rather than restating hderivValue, 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.cycle126GeneralMovingTargetDiscreteEmDerivValueLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated
3. appendix.tex:1368-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 126 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 cycle126GeneralMovingTargetDiscreteEmDerivValueDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle126.lower_packet.em_deriv_value_from_concrete_integral_split"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated derives hderivValue from a concrete EM derivative integral split plus interval a.e. equality to sampleDeriv, then reuses the cycle-125 path theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle126GeneralMovingTargetDiscreteEmDerivValueLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated",
        "MeasureTheory.integral_congr_ae",
        "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.cycle126.remaining_canonical_source_actions_after_deriv_value"
      interface := "Remaining exact theorem after hsampleMeas, hsampleInt, hsampleDerivMeas, hsampleDerivBound, hboundInt, hpathDeriv, and hderivValue are discharged: prove the canonical barB drift weak-action/pairing regularity, no-boundary divergence, diffusion source action, and optional law-derivative/partialS uniqueness."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated",
        "ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative",
        "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.cycle126.reviewer_em_deriv_value_check"
      interface := "Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hderivValue, the proof uses a concrete derivative integral split and MeasureTheory.integral_congr_ae rather than restating hderivValue, 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.cycle126GeneralMovingTargetDiscreteEmDerivValueLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated",
        "appendix.tex:1368-1387"
      ]
      reusedBy := ["cycle 126 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 127: Canonical barB drift action from component pairings -/

/-- Cycle-127 lower obligation for discharging the canonical `barB` drift
weak-action input from the EM interval path-value dominated packet.

This packet stays inside the EM conditional-law/Fokker--Planck backend.  It
removes only the supplied `hdriftBarBAction` continuation by requiring the
smaller source-facing guide and score component action pairings for the
canonical `condDistrib` fields, plus weak-pairing congruence, additivity, and
scalar linearity.  Pairing measurability, the gradient bound, no-boundary
divergence, diffusion source action, and optional law-derivative/`partialS`
uniqueness remain explicit.
-/

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