AutoSamplingTheory.SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag

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 cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag :
    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.cycle78.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 78 judgment: cycle 77 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining proof risk is still sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now narrowed to connecting cycle-77 generator-level weak FP source signs to the discrete KL derivative handoff.
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.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
4. 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.cycle78.middle_kl_derivative_generator_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion window for appendix.tex:1358-1387: align eq:general_KL_derivative_0_discrete with the cycle-77 generator-piece weak FP source signs at the admissible log-ratio test, so the lower wrappers are only the source-ordered equality substitution before integration by parts, Laplacian splitting, and FI identification.
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.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation
2. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperObligation
3. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. sald.general_moving_target_discrete.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.cycle78.lower_kl_derivative_generator_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrappers: first substitute normalized admissible weak-FP source signs into the differentiated KL formula, then compose that handoff with supplied generator/time-derivative, generator split, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 hypotheses at the admissible log-ratio test.
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.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation
2. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
7. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
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 cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle78.global_phase_judgment"
      interface := "Cycle 78 judgment: cycle 77 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining proof risk is still sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now narrowed to connecting cycle-77 generator-level weak FP source signs to the discrete KL derivative handoff."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
        "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.cycle78.middle_kl_derivative_generator_source_map"
      interface := "Middle conversion window for appendix.tex:1358-1387: align eq:general_KL_derivative_0_discrete with the cycle-77 generator-piece weak FP source signs at the admissible log-ratio test, so the lower wrappers are only the source-ordered equality substitution before integration by parts, Laplacian splitting, and FI identification."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation",
        "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperObligation",
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle78.lower_kl_derivative_generator_handoff"
      interface := "Local proof-producing wrappers: first substitute normalized admissible weak-FP source signs into the differentiated KL formula, then compose that handoff with supplied generator/time-derivative, generator split, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 hypotheses at the admissible log-ratio test."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation",
        "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-79 source-cited measure/calculus interface for the weak generator
time-derivative theorem behind the EM interpolation Fokker-Planck line.

Cycles 77 and 78 compiled the equality packaging after a generator identity is
supplied.  This interface names the remaining theorem boundary: turn the
frozen EM interpolation law into a weak time derivative on admissible tests.
-/

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