AutoSamplingTheory.SALD.cycle72GeneralMovingTargetDiscreteWeakFpDag

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 cycle72GeneralMovingTargetDiscreteWeakFpDag : 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.cycle72.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 72 judgment: cycle 71 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for continued single-backend cited-theory backfill; the highest-risk packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now the weak conditional Fokker--Planck source-sign statement at appendix.tex:1379-1387.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
2. SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
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.cycle72.middle_weak_fp_source_signs
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion window for appendix.tex:1379-1387: state the weak-test conditional Fokker--Planck interface for hat rho_s with -div(hat rho_s*bar b_{k,s}) and +(sigma_eta^2/2)*Delta hat rho_s under explicit conditional-law, measurability, integrability, density, and admissible-test hypotheses.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
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.cycle72.lower_weak_fp_source_signs
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrappers: from a supplied weak conditional Fokker--Planck identity and sigmaCoeff=sigma_eta^2/2, preserve the negative drift-divergence term and positive sigma_eta^2/2 Laplacian term for each admissible test, with an explicit admissible-test predicate variant.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
5. SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff
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 cycle72GeneralMovingTargetDiscreteWeakFpDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle72.global_phase_judgment"
      interface := "Cycle 72 judgment: cycle 71 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for continued single-backend cited-theory backfill; the highest-risk packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now the weak conditional Fokker--Planck source-sign statement at appendix.tex:1379-1387."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
        "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "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.cycle72.middle_weak_fp_source_signs"
      interface := "Middle conversion window for appendix.tex:1379-1387: state the weak-test conditional Fokker--Planck interface for hat rho_s with -div(hat rho_s*bar b_{k,s}) and +(sigma_eta^2/2)*Delta hat rho_s under explicit conditional-law, measurability, integrability, density, and admissible-test hypotheses."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
        "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle72.lower_weak_fp_source_signs"
      interface := "Local proof-producing wrappers: from a supplied weak conditional Fokker--Planck identity and sigmaCoeff=sigma_eta^2/2, preserve the negative drift-divergence term and positive sigma_eta^2/2 Laplacian term for each admissible test, with an explicit admissible-test predicate variant."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-73 upper packet for the KL-derivative handoff from weak FP.

This is the fourth single-backend backfill packet after the post-route cycle-69
ledger.  It keeps the active backend fixed at
`sald.general_moving_target_discrete.em_interpolation_fp` and narrows the next
handoff to substituting the supplied weak conditional Fokker--Planck identity
into `eq:general_KL_derivative_0_discrete`.
-/

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