AutoSamplingTheory.SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag

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 cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag :
    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.cycle74.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 74 judgment: cycle 73 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining risk is the conditional-law measure backend 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.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
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.cycle74.middle_conditional_kernel_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion map for appendix.tex:1368-1377: line up the joint law of (X_k^eta,hat X_s), the named marginal hat rho_s, Mathlib condDistrib/condExpKernel candidate facts, and the measurable/integrable conditional drift fields needed 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.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
5. SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation
6. SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
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.cycle74.lower_packet.conditional_kernel_measure_interface
interface : String (explicit)
Text describing intended mathematical interface.
Minimal cited measure interface: audit Mathlib Probability.Kernel.Condexp/CondDistrib/Disintegration.StandardBorel as the regular conditional-kernel backend needed to define bar b_{k,s} from the joint law of (X_k^eta, hat X_s) before weak FP can be proved.
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.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
2. SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
5. SALD.generalMovingTargetDiscreteConditionalDriftContract
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.general_moving_target_discrete.kl_derivative
3. sald.discrete_forward_kl.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.sourceCited — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle74.lower_conditional_kernel_regularity_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Local supplied-kernel wrapper: after Mathlib condDistrib/condExpKernel provides kernel compatibility and component integral measurability/integrability, transport compatibility to hat rho_s and inherit regularity for 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.cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation
2. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
3. SALD.generalMovingTargetDiscreteConditionalKernelCompatibilityOfJointMapMarginal
4. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
5. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
6. SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.general_moving_target_discrete.kl_derivative
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 cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle74.global_phase_judgment"
      interface := "Cycle 74 judgment: cycle 73 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining risk is the conditional-law measure backend inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "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.cycle74.middle_conditional_kernel_source_map"
      interface := "Middle conversion map for appendix.tex:1368-1377: line up the joint law of (X_k^eta,hat X_s), the named marginal hat rho_s, Mathlib condDistrib/condExpKernel candidate facts, and the measurable/integrable conditional drift fields needed before weak FP proof search."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
        "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation",
        "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation"
      ]
      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.cycle74.lower_packet.conditional_kernel_measure_interface"
      interface := "Minimal cited measure interface: audit Mathlib Probability.Kernel.Condexp/CondDistrib/Disintegration.StandardBorel as the regular conditional-kernel backend needed to define bar b_{k,s} from the joint law of (X_k^eta, hat X_s) before weak FP can be proved."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.sourceCited
    },
    {
      id := "ASTIS.SALD.cycle74.lower_conditional_kernel_regularity_handoff"
      interface := "Local supplied-kernel wrapper: after Mathlib condDistrib/condExpKernel provides kernel compatibility and component integral measurability/integrability, transport compatibility to hat rho_s and inherit regularity for bar b_{k,s}."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation",
        "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
        "SALD.generalMovingTargetDiscreteConditionalKernelCompatibilityOfJointMapMarginal",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-75 upper packet returning to the EM conditional-law interface.

Cycle 74 recorded the blocked conditional-kernel theorem as a precise
source-cited interface.  Cycle 75 keeps the same source window and asks lower
work to reduce that blocker by instantiating or sharpening the
condDistrib/condExpKernel construction for the named joint law and marginal,
without advancing to weak Fokker-Planck or KL-derivative proof search.
-/

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