AutoSamplingTheory.SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelDag

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 cycle91GeneralMovingTargetDiscreteConditionalKernelDag :
    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.cycle91.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 91 judgment: cycle 90 passed and needs no recovery; Phase 1 theorem skeletons are stable enough for cited-theory backfill; the largest remaining proof risk is the conditional-kernel/named-law field theorem at appendix.tex:1368-1377.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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.cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation
2. SALD.cycle90DiscreteForwardKlMassConservationLowerObligation
3. sald.general_moving_target_discrete.em_interpolation_fp
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle91.middle_conditional_kernel_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: keep the TeX window on hat rho_s=Law(hat X_s), condDistrib X_k^eta hat X_s P, component fields condC/condScore, and the bar b_{k,s} combination; reject wrapper churn around abstract KernelIntegralField regularity.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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.cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation
2. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
3. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
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.cycle91.lower_condDistrib_named_drift_regular
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing theorem: SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions derives AEStronglyMeasurable and Integrable barB under hatRhoS from sample-space component version equalities, ae_map_iff transport, canonical condDistrib component integral regularity, and the pointwise barB component formula.
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.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation
2. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
4. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularity
5. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
6. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
7. Mathlib.Probability.Kernel.CondDistrib
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
2. sald.general_moving_target_discrete.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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary: prove the SALD-specific sample-space conditional-expectation/disintegration equalities for condC/condScore after composing with hatXAtS, the measurable equality-set side conditions needed by ae_map_iff, and the conditional-kernel compatibility theorem; then route endpoint weak-FP readiness through the existing endpoint compatibility wrappers.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
2. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularity
4. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
5. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
6. Mathlib.Probability.Kernel.Condexp
7. Mathlib.Probability.Kernel.CondDistrib
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

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 cycle91GeneralMovingTargetDiscreteConditionalKernelDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle91.global_phase_judgment"
      interface := "Cycle 91 judgment: cycle 90 passed and needs no recovery; Phase 1 theorem skeletons are stable enough for cited-theory backfill; the largest remaining proof risk is the conditional-kernel/named-law field theorem at appendix.tex:1368-1377."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation",
        "SALD.cycle90DiscreteForwardKlMassConservationLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle91.middle_conditional_kernel_source_map"
      interface := "Middle source map: keep the TeX window on hat rho_s=Law(hat X_s), condDistrib X_k^eta hat X_s P, component fields condC/condScore, and the bar b_{k,s} combination; reject wrapper churn around abstract KernelIntegralField regularity."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation",
        "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
        "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle91.lower_condDistrib_named_drift_regular"
      interface := "Lower proof-producing theorem: SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions derives AEStronglyMeasurable and Integrable barB under hatRhoS from sample-space component version equalities, ae_map_iff transport, canonical condDistrib component integral regularity, and the pointwise barB component formula."
      source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation",
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularity",
        "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
        "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
        "Mathlib.Probability.Kernel.CondDistrib"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary"
      interface := "Remaining exact theorem boundary: prove the SALD-specific sample-space conditional-expectation/disintegration equalities for condC/condScore after composing with hatXAtS, the measurable equality-set side conditions needed by ae_map_iff, and the conditional-kernel compatibility theorem; then route endpoint weak-FP readiness through the existing endpoint compatibility wrappers."
      source := saldGeneralMovingTargetDiscreteConditionalDriftSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
        "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularity",
        "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
        "Mathlib.Probability.Kernel.Condexp",
        "Mathlib.Probability.Kernel.CondDistrib"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 92: generator-to-law weak-FP split-generator backfill -/

/-- Cycle-92 middle obligation for the weak generator-to-law boundary.

This keeps the conversion window on `appendix.tex:1379-1387`: the paper invokes
the Fokker--Planck equation for the frozen EM interpolation, and the current
Lean route should remove or narrow one supplied input to the existing
sample-generator law-transport handoff.
-/

Existing module entry · Audited data-reader index · All teaching coverage