AutoSamplingTheory.SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag

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 cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag :
    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.cycle73.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 73 judgment: cycle 72 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for continued single-backend backfill; the highest-risk packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now the KL-derivative handoff from weak FP.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
3. sald.general_moving_target_discrete.em_interpolation_fp
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
2. thm:general-moving-target-SALD-discrete
3. sald.general_moving_target_discrete.em_interpolation_fp
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.cycle73.middle_kl_derivative_weak_fp_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion window for appendix.tex:1358-1387: select the log-density-ratio weak test, keep admissibility/density hypotheses explicit, and hand the supplied weak FP identity to the KL derivative formula before integration by parts.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
4. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.general_moving_target_discrete.kl_derivative
3. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle73.lower_kl_derivative_weak_fp_substitution
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrappers: from the differentiated KL formula and supplied admissible-test weak FP identity, substitute the source-signed weak FP action at the log-ratio test, including the composition through the cycle-72 admissible source-sign theorem, and preserve the unchanged target-time term.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. thm:forward-KL-discrete
3. thm:general-moving-target-SALD-discrete
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 cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle73.global_phase_judgment"
      interface := "Cycle 73 judgment: cycle 72 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for continued single-backend backfill; the highest-risk packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now the KL-derivative handoff from weak FP."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle73.middle_kl_derivative_weak_fp_handoff"
      interface := "Middle conversion window for appendix.tex:1358-1387: select the log-density-ratio weak test, keep admissibility/density hypotheses explicit, and hand the supplied weak FP identity to the KL derivative formula before integration by parts."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle73.lower_kl_derivative_weak_fp_substitution"
      interface := "Local proof-producing wrappers: from the differentiated KL formula and supplied admissible-test weak FP identity, substitute the source-signed weak FP action at the log-ratio test, including the composition through the cycle-72 admissible source-sign theorem, and preserve the unchanged target-time term."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-74 source-cited Mathlib measure interface for the blocked
conditional-kernel layer.

This is intentionally narrow: it records the Mathlib conditional-expectation
kernel that lower work should audit before attempting another weak-FP proof
step.  It is not imported as a new dependency here and it is not a proof of
the SALD weak Fokker-Planck theorem.
-/

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