AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation

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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation :
    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.cycle82_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 82 lower compiles SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff for appendix.tex lines 1379-1387. The wrapper first uses the cycle-81 endpoint/conditional readiness package to build WeakFpPrereq for the named interpolation law hat rho_s, kernel, and bar b_{k,s}; then it composes the cycle-82 readiness-to-generator-piece bridge with supplied density/time regularity, admissible tests, boundary behavior, generator/time derivative, drift source action, diffusion source action, and fpCoeff=sigma_eta^2/2 to obtain the source-signed weak form partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi. It proves no analytic weak-FP theorem.

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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
4. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
5. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
8. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
9. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
10. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
11. 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.

Lower proof-producing wrapper under explicit supplied hypotheses only. It composes existing local wrappers and preserves the paper signs; regular conditional laws, density/AC, generator-to-law calculus, weak Fokker-Planck, KL differentiation, theorem status, SLT imports, and Lake dependencies remain unpromoted.

def cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle82_weak_fp_source_signs_lower"
  statement := "Cycle 82 lower compiles SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff for appendix.tex lines 1379-1387. The wrapper first uses the cycle-81 endpoint/conditional readiness package to build WeakFpPrereq for the named interpolation law hat rho_s, kernel, and bar b_{k,s}; then it composes the cycle-82 readiness-to-generator-piece bridge with supplied density/time regularity, admissible tests, boundary behavior, generator/time derivative, drift source action, diffusion source action, and fpCoeff=sigma_eta^2/2 to obtain the source-signed weak form partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi. It proves no analytic weak-FP theorem."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Lower proof-producing wrapper under explicit supplied hypotheses only. It composes existing local wrappers and preserves the paper signs; regular conditional laws, density/AC, generator-to-law calculus, weak Fokker-Planck, KL differentiation, theorem status, SLT imports, and Lake dependencies remain unpromoted."

/-- Cycle-82 proof-DAG pane for the weak conditional FP source-sign packet. -/