AutoSamplingTheory.SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalDag

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 cycle76GeneralMovingTargetDiscreteEndpointConditionalDag :
    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.cycle76.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 76 judgment: cycle 75 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest shared risk remains endpoint-to-conditional compatibility inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
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.cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperObligation
2. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
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.cycle76.middle_endpoint_conditional_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map for appendix.tex:1358-1387: keep endpoint Measure.map laws, named interior hat rho_s marginal, and swapped condDistrib orientation synchronized before weak FP proof search.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle76GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
2. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
3. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
4. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
5. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
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.cycle76.lower_endpoint_to_swapped_conditional
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrapper: combine endpoint Measure.map law equalities with the swapped first marginal, original second marginal, and swap bridge, yielding original-orientation kernel compatibility for the weak FP interface under supplied kernel hypotheses.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility
3. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
4. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
5. SALD.generalMovingTargetDiscreteHatRhoFirstMarginalOfSwappedJointMap
6. SALD.generalMovingTargetDiscreteHatRhoMarginalOfJointMap
7. AutoSamplingTheory.lawMapProdSwap
8. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
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

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 cycle76GeneralMovingTargetDiscreteEndpointConditionalDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle76.global_phase_judgment"
      interface := "Cycle 76 judgment: cycle 75 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest shared risk remains endpoint-to-conditional compatibility inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperObligation",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
        "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.cycle76.middle_endpoint_conditional_map"
      interface := "Middle source map for appendix.tex:1358-1387: keep endpoint Measure.map laws, named interior hat rho_s marginal, and swapped condDistrib orientation synchronized before weak FP proof search."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation"
      ]
      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.cycle76.lower_endpoint_to_swapped_conditional"
      interface := "Local proof-producing wrapper: combine endpoint Measure.map law equalities with the swapped first marginal, original second marginal, and swap bridge, yielding original-orientation kernel compatibility for the weak FP interface under supplied kernel hypotheses."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
          "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
          "SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility",
          "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
          "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
          "SALD.generalMovingTargetDiscreteHatRhoFirstMarginalOfSwappedJointMap",
          "SALD.generalMovingTargetDiscreteHatRhoMarginalOfJointMap",
          "AutoSamplingTheory.lawMapProdSwap",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface"
      ]
      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
    }
  ]

/-- Cycle-77 middle obligation for the generator-level weak FP source-sign
handoff. -/

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