AutoSamplingTheory.SALD.cycle125GeneralMovingTargetDiscreteEmPathDerivDag

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 cycle125GeneralMovingTargetDiscreteEmPathDerivDag :
    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.cycle125.lower_packet.em_path_deriv_from_concrete_differentiability
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated derives hpathDeriv from concrete weak-test path differentiability plus the existing interval a.e. equality to sampleDeriv, then reuses the cycle-124 bound-integrability 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.cycle125GeneralMovingTargetDiscreteEmPathDerivLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated
4. Mathlib.Analysis.Calculus.Deriv.Basic.DifferentiableAt.hasDerivAt
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.cycle125.remaining_source_actions_after_path_deriv
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after hsampleMeas, hsampleInt, hsampleDerivMeas, hsampleDerivBound, hboundInt, and hpathDeriv are discharged: prove hderivValue and 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated
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.cycle125.reviewer_em_path_deriv_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hpathDeriv, the proof uses DifferentiableAt.hasDerivAt and the concrete derivative representative rather than restating hpathDeriv, 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.cycle125GeneralMovingTargetDiscreteEmPathDerivLowerObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated
3. appendix.tex:1368-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 125 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 cycle125GeneralMovingTargetDiscreteEmPathDerivDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle125.lower_packet.em_path_deriv_from_concrete_differentiability"
      interface := "Compiled lower theorem: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated derives hpathDeriv from concrete weak-test path differentiability plus the existing interval a.e. equality to sampleDeriv, then reuses the cycle-124 bound-integrability theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle125GeneralMovingTargetDiscreteEmPathDerivLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated",
        "Mathlib.Analysis.Calculus.Deriv.Basic.DifferentiableAt.hasDerivAt",
        "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.cycle125.remaining_source_actions_after_path_deriv"
      interface := "Remaining exact theorem after hsampleMeas, hsampleInt, hsampleDerivMeas, hsampleDerivBound, hboundInt, and hpathDeriv are discharged: prove hderivValue and 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated",
        "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.cycle125.reviewer_em_path_deriv_check"
      interface := "Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis for hpathDeriv, the proof uses DifferentiableAt.hasDerivAt and the concrete derivative representative rather than restating hpathDeriv, 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.cycle125GeneralMovingTargetDiscreteEmPathDerivLowerObligation",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated",
        "appendix.tex:1368-1387"
      ]
      reusedBy := ["cycle 125 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 126: EM derivative-value split from concrete derivative integral -/

/-- Cycle-126 lower obligation for discharging the derivative-value input from
the EM interval path-derivative dominated packet.

This packet stays inside the EM conditional-law/Fokker--Planck backend.  It
removes only the supplied `hderivValue` hypothesis by requiring the smaller
source-facing concrete derivative integral split for
`deriv (fun t => testEval phi (hatX t omega)) s0`; the existing interval a.e.
equality transports that split to the selected `sampleDeriv` representative.
-/

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