AutoSamplingTheory.SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalDag

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 cycle81GeneralMovingTargetDiscreteEndpointConditionalDag :
    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.cycle81.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 81 judgment: cycle 80 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 endpoint-law-to-conditional-law compatibility inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
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.cycle81GeneralMovingTargetDiscreteEndpointConditionalUpperObligation
2. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
3. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
4. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle81.lower_packet.endpoint_conditional_compatibility
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: connect endpoint Measure.map laws and the named hat rho_s marginal to the conditional-kernel orientation required by the existing conditional-law/measurability interface and cycle-80 drift-regularity handoff; leave weak FP and KL derivative work downstream.
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.cycle81GeneralMovingTargetDiscreteEndpointConditionalUpperObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
3. SALD.generalMovingTargetDiscreteHatRhoMarginalOfJointMap
4. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
5. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
6. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
7. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
8. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
9. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
10. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
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.cycle81.lower_endpoint_measure_map_weak_fp_prereq
interface : String (explicit)
Text describing intended mathematical interface.
Lower handoff: compose the endpoint Measure.map compatibility package with supplied bar b_{k,s} measurability/integrability and a supplied WeakFpPrereq consumer, without rebuilding component conditional expectations.
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.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
2. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
3. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
5. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
6. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-discrete
5. thm:general-moving-target-SALD-discrete
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle81.middle_endpoint_conditional_weak_fp_readiness
interface : String (explicit)
Text describing intended mathematical interface.
Middle handoff: package endpoint Measure.map laws, named hat rho_s marginal views, swapped/original orientation compatibility, original kernel compatibility, and bar b_{k,s} regularity into a supplied WeakFpPrereq predicate for the later weak conditional Fokker-Planck theorem.
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.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
3. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
4. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
6. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-discrete
5. 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 cycle81GeneralMovingTargetDiscreteEndpointConditionalDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle81.global_phase_judgment"
      interface := "Cycle 81 judgment: cycle 80 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 endpoint-law-to-conditional-law compatibility inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalUpperObligation",
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "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.cycle81.lower_packet.endpoint_conditional_compatibility"
      interface := "Selected lower packet: connect endpoint Measure.map laws and the named hat rho_s marginal to the conditional-kernel orientation required by the existing conditional-law/measurability interface and cycle-80 drift-regularity handoff; leave weak FP and KL derivative work downstream."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalUpperObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
        "SALD.generalMovingTargetDiscreteHatRhoMarginalOfJointMap",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation"
      ]
      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.cycle81.lower_endpoint_measure_map_weak_fp_prereq"
      interface := "Lower handoff: compose the endpoint Measure.map compatibility package with supplied bar b_{k,s} measurability/integrability and a supplied WeakFpPrereq consumer, without rebuilding component conditional expectations."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "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
    },
    {
      id := "ASTIS.SALD.cycle81.middle_endpoint_conditional_weak_fp_readiness"
      interface := "Middle handoff: package endpoint Measure.map laws, named hat rho_s marginal views, swapped/original orientation compatibility, original kernel compatibility, and bar b_{k,s} regularity into a supplied WeakFpPrereq predicate for the later weak conditional Fokker-Planck theorem."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "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-82 upper packet for the weak conditional Fokker--Planck source-sign
backend.

Cycle 81 supplied the endpoint/conditional readiness package consumed before
weak FP.  This upper packet returns to the paper's associated FP line and keeps
the next work on the source signs themselves.
-/

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