AutoSamplingTheory.SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalDag

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 cycle71GeneralMovingTargetDiscreteEndpointConditionalDag : 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.cycle71.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 71 judgment: cycle 70 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 endpoint-law-to-conditional-law compatibility layer.
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.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation
2. SALD.cycle70GeneralMovingTargetDiscreteConditionalLawLowerObligation
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.cycle71.middle_endpoint_conditional_compatibility
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion window for appendix.tex:1368-1377: connect the joint Measure.map law of (X_k^eta,hat X_s) and its second marginal to the named hat rho_s marginal required by the conditional-kernel compatibility predicate.
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.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
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.cycle71.lower_endpoint_conditional_wrapper
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrappers: identify the second marginal of the joint pushforward with hat rho_s, then transport a supplied conditional-kernel compatibility predicate to that named marginal by equality.
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.cycle71GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
2. SALD.generalMovingTargetDiscreteHatRhoMarginalOfJointMap
3. SALD.generalMovingTargetDiscreteConditionalKernelCompatibilityOfJointMapMarginal
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityOfJointMap
5. AutoSamplingTheory.lawMapProdSnd
6. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
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 cycle71GeneralMovingTargetDiscreteEndpointConditionalDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle71.global_phase_judgment"
      interface := "Cycle 71 judgment: cycle 70 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 endpoint-law-to-conditional-law compatibility layer."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation",
        "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawLowerObligation",
        "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.cycle71.middle_endpoint_conditional_compatibility"
      interface := "Middle conversion window for appendix.tex:1368-1377: connect the joint Measure.map law of (X_k^eta,hat X_s) and its second marginal to the named hat rho_s marginal required by the conditional-kernel compatibility predicate."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle71.lower_endpoint_conditional_wrapper"
      interface := "Local proof-producing wrappers: identify the second marginal of the joint pushforward with hat rho_s, then transport a supplied conditional-kernel compatibility predicate to that named marginal by equality."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.generalMovingTargetDiscreteHatRhoMarginalOfJointMap",
        "SALD.generalMovingTargetDiscreteConditionalKernelCompatibilityOfJointMapMarginal",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityOfJointMap",
        "AutoSamplingTheory.lawMapProdSnd",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-72 middle obligation for the weak conditional Fokker--Planck
source-sign interface. -/

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