AutoSamplingTheory.SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag

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 cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag :
    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.cycle94.middle_weak_fp_drift_action_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: appendix.tex:1379-1387 invokes the Fokker-Planck equation for hat rho_s with drift source -div(hat rho_s*bar b_{k,s}); after cycle 91 has named barB and cycle 92 has split the generator, replace primitive hdriftSource by the barB weak-pairing plus divergence/no-boundary theorem boundary.
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.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation
2. SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation
3. SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation
4. sald.general_moving_target_discrete.em_interpolation_fp
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.cycle94.lower_barB_drift_action_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing handoff: SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction derives the old hdriftSource shape from two smaller source-cited facts, then SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff feed that derived drift source into the cycle-92 direct mapped-law derivative and normalized source-sign routes.
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.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
3. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff
7. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff
3. sald.general_moving_target_discrete.em_interpolation_fp
4. thm:forward-KL-discrete
5. 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.cycle94.remaining_barB_divergence_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact boundary: prove driftAction phi = integral pairing of barB with grad phi from the condDistrib conditional expectation defining bar b_{k,s}, then prove that this pairing equals -(driftDiv phi) by the divergence/integration-by-parts/no-boundary theorem for hatRhoS*barB.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
4. Mathlib.MeasureTheory.Integral.DivergenceTheorem
5. Mathlib.MeasureTheory.Integral.Bochner.Basic
6. appendix.tex:1368-1377
7. 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
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 cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle94.middle_weak_fp_drift_action_source_map"
      interface := "Middle source map: appendix.tex:1379-1387 invokes the Fokker-Planck equation for hat rho_s with drift source -div(hat rho_s*bar b_{k,s}); after cycle 91 has named barB and cycle 92 has split the generator, replace primitive hdriftSource by the barB weak-pairing plus divergence/no-boundary theorem boundary."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation",
        "SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation",
        "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      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.cycle94.lower_barB_drift_action_handoff"
      interface := "Lower proof-producing handoff: SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction derives the old hdriftSource shape from two smaller source-cited facts, then SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff feed that derived drift source into the cycle-92 direct mapped-law derivative and normalized source-sign routes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary"
      interface := "Remaining exact boundary: prove driftAction phi = integral pairing of barB with grad phi from the condDistrib conditional expectation defining bar b_{k,s}, then prove that this pairing equals -(driftDiv phi) by the divergence/integration-by-parts/no-boundary theorem for hatRhoS*barB."
      source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
        "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic",
        "appendix.tex:1368-1377",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 95: discrete theorem pressure test after the `barB` handoff -/

/-- Cycle-95 upper packet for the discrete forward-KL closure pressure test.

This is an upper-role route record only.  It rechecks
`thm:forward-KL-discrete` after the cycle-94 `barB` weak-action handoff and
selects the next non-wrapper blocker without changing the theorem statement or
promoting any analytic backend.
-/

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