Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag

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 cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag :
    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

  1. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle80.global_phase_judgment
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle 80 judgment: cycle 79 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 the conditional-law/measurability and named drift layer inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
    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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperObligation
    2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
    3. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
    4. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
    5. 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
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle80.middle_conditional_law_source_map
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle source map for appendix.tex:1368-1377: lower must instantiate or cite the regular conditional kernel for X_k^eta | hat X_s=x, align the named hat rho_s marginal with the condDistrib/condExpKernel orientation, provide component conditional-integral fields, and feed the existing named-drift regularity wrappers. Weak FP and KL derivative work remain downstream consumers.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource — 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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation
    2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
    3. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation
    4. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
    5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
    6. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
    7. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
    8. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents
    9. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
    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
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle80.lower_packet.conditional_law_measurability
    interface : String (explicit)

    Text describing intended mathematical interface.

    Selected lower packet: refine the appendix.tex:1368-1377 conditional-law/measurability interface by connecting the joint law, named hat rho_s marginal, condDistrib/condExpKernel orientation, component conditional-integral fields, and measurable/integrable bar b_{k,s}; leave weak FP and KL derivative work as consumers.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource — 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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation
    2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
    3. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation
    4. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
    5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
    6. SALD.generalMovingTargetDiscreteConditionalDriftContract
    7. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
    8. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
    9. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
    10. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
    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
  4. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle80.lower_endpoint_conditional_drift_regularity
    interface : String (explicit)

    Text describing intended mathematical interface.

    Local supplied-hypothesis wrapper: compose endpoint-to-conditional compatibility with component conditional-integral field regularity to return endpoint laws, named hat rho_s marginal views, original-orientation kernel compatibility, and measurable/integrable bar b_{k,s}.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource — 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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
    2. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
    3. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
    4. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
    5. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
    6. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
    7. 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.formalized — 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 cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle80.global_phase_judgment"
      interface := "Cycle 80 judgment: cycle 79 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 the conditional-law/measurability and named drift layer inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperObligation",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "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.cycle80.middle_conditional_law_source_map"
      interface := "Middle source map for appendix.tex:1368-1377: lower must instantiate or cite the regular conditional kernel for X_k^eta | hat X_s=x, align the named hat rho_s marginal with the condDistrib/condExpKernel orientation, provide component conditional-integral fields, and feed the existing named-drift regularity wrappers. Weak FP and KL derivative work remain downstream consumers."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
        "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
        "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface"
      ]
      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.cycle80.lower_packet.conditional_law_measurability"
      interface := "Selected lower packet: refine the appendix.tex:1368-1377 conditional-law/measurability interface by connecting the joint law, named hat rho_s marginal, condDistrib/condExpKernel orientation, component conditional-integral fields, and measurable/integrable bar b_{k,s}; leave weak FP and KL derivative work as consumers."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
        "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff"
      ]
      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.cycle80.lower_endpoint_conditional_drift_regularity"
      interface := "Local supplied-hypothesis wrapper: compose endpoint-to-conditional compatibility with component conditional-integral field regularity to return endpoint laws, named hat rho_s marginal views, original-orientation kernel compatibility, and measurable/integrable bar b_{k,s}."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
        "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.formalized
    }
  ]

/-- Cycle-81 upper packet for the endpoint-law-to-conditional-law bridge.

Cycle 80 compiled only a supplied-hypothesis wrapper around endpoint/orientation
and conditional-drift regularity facts.  This packet keeps the next work on the
same EM interpolation backend, now selecting the endpoint-law bookkeeping that
has to feed the conditional-law interface used by the weak Fokker-Planck
statement.
-/

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