AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation

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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation :
    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_middle

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 middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff for appendix.tex lines 1379-1387. The wrapper consumes the cycle-81 WeakFpPrereq readiness output for the named interpolation law hat rho_s, kernel, and bar b_{k,s}, derives the common-space, conditional-kernel, and drift-regularity hypotheses required by the cycle-77 generator-piece source-sign handoff, and keeps density/time regularity, admissible tests, boundary behavior, generator/time derivative, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 as explicit supplied hypotheses. It preserves the exact source signs partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi and 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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
3. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
4. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
6. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
7. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
8. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
9. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
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.

Middle proof-producing local wrapper under supplied hypotheses only. It does not construct conditional kernels, density/AC, generator-to-law calculus, weak Fokker-Planck, KL differentiation, or theorem closure, and it does not promote SLT or Lake dependencies.

def cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle82_weak_fp_source_signs_middle"
  statement := "Cycle 82 middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff for appendix.tex lines 1379-1387. The wrapper consumes the cycle-81 WeakFpPrereq readiness output for the named interpolation law hat rho_s, kernel, and bar b_{k,s}, derives the common-space, conditional-kernel, and drift-regularity hypotheses required by the cycle-77 generator-piece source-sign handoff, and keeps density/time regularity, admissible tests, boundary behavior, generator/time derivative, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 as explicit supplied hypotheses. It preserves the exact source signs partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi and proves no analytic weak-FP theorem."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation",
    "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 := "Middle proof-producing local wrapper under supplied hypotheses only. It does not construct conditional kernels, density/AC, generator-to-law calculus, weak Fokker-Planck, KL differentiation, or theorem closure, and it does not promote SLT or Lake dependencies."

/-- Cycle-82 lower obligation for the endpoint-readiness-to-source-sign bridge. -/