AutoSamplingTheory.SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

id : String (explicit)

Stable obligation identifier.

sald.general_moving_target_discrete.cycle72_weak_fp_source_signs_lower

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 72 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff for appendix.tex lines 1379-1387: for every admissible weak test phi, if the supplied weak conditional Fokker--Planck identity has partial_s hat rho_s paired with phi equal to -(drift-divergence action on phi) plus sigmaCoeff times the Laplacian action on phi, and sigmaCoeff=sigma_eta^2/2, then the source-signed weak form has the negative drift-divergence term and positive +(sigma_eta^2/2) Laplacian term.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
5. SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff
6. SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
7. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Proof-producing wrappers only. The new admissible-test variant keeps the weak-test predicate explicit but still consumes a supplied weak-FP identity. The actual weak conditional Fokker--Planck theorem, common-space construction, regular conditional drift, density/absolute-continuity, admissible test class, boundary/integration-by-parts conditions, KL derivative, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations.

def cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle72_weak_fp_source_signs_lower"
  statement := "Cycle 72 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff for appendix.tex lines 1379-1387: for every admissible weak test phi, if the supplied weak conditional Fokker--Planck identity has partial_s hat rho_s paired with phi equal to -(drift-divergence action on phi) plus sigmaCoeff times the Laplacian action on phi, and sigmaCoeff=sigma_eta^2/2, then the source-signed weak form has the negative drift-divergence term and positive +(sigma_eta^2/2) Laplacian term."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
    "SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing wrappers only. The new admissible-test variant keeps the weak-test predicate explicit but still consumes a supplied weak-FP identity. The actual weak conditional Fokker--Planck theorem, common-space construction, regular conditional drift, density/absolute-continuity, admissible test class, boundary/integration-by-parts conditions, KL derivative, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations."

/-- Cycle-72 proof-DAG pane for weak conditional Fokker--Planck source signs. -/