AutoSamplingTheory.SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation

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 cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation :
    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.cycle77_weak_fp_generator_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 77 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff for appendix.tex lines 1379-1387: if the frozen EM interpolation generator represents partial_s hat rho_s on admissible weak tests under explicit common-space, regular conditional kernel, drift regularity, density/time-regularity, test-regularity, and boundary hypotheses, if that generator has the paper source expansion or separate drift/diffusion source actions, and if sigmaCoeff=sigma_eta^2/2, then the resulting weak FP statement has exactly the source signs -div(hat rho_s*bar b_{k,s}) and +(sigma_eta^2/2)*Delta hat rho_s.

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.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
6. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
7. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
8. SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation
9. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
10. 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 wrapper only. The actual generator theorem, Brownian/EM construction, regular conditional law, density/absolute-continuity, admissible-test approximation, boundary/integration-by-parts, KL differentiation, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations.

def cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle77_weak_fp_generator_lower"
  statement := "Cycle 77 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff for appendix.tex lines 1379-1387: if the frozen EM interpolation generator represents partial_s hat rho_s on admissible weak tests under explicit common-space, regular conditional kernel, drift regularity, density/time-regularity, test-regularity, and boundary hypotheses, if that generator has the paper source expansion or separate drift/diffusion source actions, and if sigmaCoeff=sigma_eta^2/2, then the resulting weak FP statement has exactly the source signs -div(hat rho_s*bar b_{k,s}) and +(sigma_eta^2/2)*Delta hat rho_s."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation",
    "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing wrapper only. The actual generator theorem, Brownian/EM construction, regular conditional law, density/absolute-continuity, admissible-test approximation, boundary/integration-by-parts, KL differentiation, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations."

/-- Cycle-77 proof-DAG pane for the generator-level weak conditional
Fokker--Planck source-sign handoff. -/