AutoSamplingTheory.SALD.cycle70GeneralMovingTargetDiscreteConditionalLawDag

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 cycle70GeneralMovingTargetDiscreteConditionalLawDag : 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.cycle70.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 70 judgment: cycle 69 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for one cited-theory/SDE backend backfill; the risk-reducing packet is sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to conditional-law/measurability and named conditional drift interfaces.
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.cycle69MainSkeletonAnalyticMiddleObligation
2. SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation
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.cycle70.middle_conditional_law_interface
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion window for appendix.tex:1368-1377: name the regular conditional kernel, component conditional fields, selected bar b_{k,s}, and regularity side conditions before the weak conditional Fokker-Planck handoff.
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.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
3. SALD.generalMovingTargetDiscreteConditionalDriftContract
4. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
5. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
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.cycle70.lower_named_conditional_drift
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing wrappers: from supplied conditional-expectation linearity and named component fields, rewrite bar b_{k,s} into dot t_k*condC_{k,s}+(sigma_eta^2/2)*condScore_{k,s}; derive the combination regularity from component regularity using add/smul closure, then transfer it to bar b_{k,s} by pointwise 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.cycle70GeneralMovingTargetDiscreteConditionalLawLowerObligation
2. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
3. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityHandoff
4. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
6. 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. 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 cycle70GeneralMovingTargetDiscreteConditionalLawDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle70.global_phase_judgment"
      interface := "Cycle 70 judgment: cycle 69 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for one cited-theory/SDE backend backfill; the risk-reducing packet is sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to conditional-law/measurability and named conditional drift interfaces."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle69MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation",
        "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.cycle70.middle_conditional_law_interface"
      interface := "Middle conversion window for appendix.tex:1368-1377: name the regular conditional kernel, component conditional fields, selected bar b_{k,s}, and regularity side conditions before the weak conditional Fokker-Planck handoff."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle70.lower_named_conditional_drift"
      interface := "Lower proof-producing wrappers: from supplied conditional-expectation linearity and named component fields, rewrite bar b_{k,s} into dot t_k*condC_{k,s}+(sigma_eta^2/2)*condScore_{k,s}; derive the combination regularity from component regularity using add/smul closure, then transfer it to bar b_{k,s} by pointwise equality."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawLowerObligation",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityHandoff",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-69 proof-DAG pane for the post-route analytic-interface ledger. -/

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