AutoSamplingTheory.SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag

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 cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag :
    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.cycle77.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 77 judgment: cycle 76 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 back to the weak conditional FP source-sign theorem at appendix.tex:1379-1387.
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.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
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.cycle77.middle_weak_fp_generator_source_signs
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion window for appendix.tex:1379-1387: split the associated Fokker--Planck invocation into a generator/time-derivative identity and a source expansion with negative drift-divergence and positive sigma_eta^2/2 Laplacian, with the lower path able to split that expansion into separate drift and diffusion actions while keeping conditional-law, density, test, and boundary hypotheses explicit.
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.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
5. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle77.lower_weak_fp_generator_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrapper: compose a supplied generator/time-derivative identity, a supplied generator source expansion or split drift/diffusion source actions, and sigmaCoeff=sigma_eta^2/2 into the source-signed weak FP identity on admissible tests.
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.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
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.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 cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle77.global_phase_judgment"
      interface := "Cycle 77 judgment: cycle 76 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 back to the weak conditional FP source-sign theorem at appendix.tex:1379-1387."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "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.cycle77.middle_weak_fp_generator_source_signs"
      interface := "Middle conversion window for appendix.tex:1379-1387: split the associated Fokker--Planck invocation into a generator/time-derivative identity and a source expansion with negative drift-divergence and positive sigma_eta^2/2 Laplacian, with the lower path able to split that expansion into separate drift and diffusion actions while keeping conditional-law, density, test, and boundary hypotheses explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle77.lower_weak_fp_generator_handoff"
      interface := "Local proof-producing wrapper: compose a supplied generator/time-derivative identity, a supplied generator source expansion or split drift/diffusion source actions, and sigmaCoeff=sigma_eta^2/2 into the source-signed weak FP identity on admissible tests."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-78 upper packet for the generator-to-KL derivative handoff.

Cycle 77 sharpened the weak conditional Fokker--Planck source signs down to
generator pieces.  Cycle 78 keeps the same EM backend and asks lower work to
connect those supplied generator pieces directly to the discrete KL derivative
handoff at the log-density-ratio test.
-/

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