AutoSamplingTheory.SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation

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 cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation :
    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_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 77 middle keeps the active backend at sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and returns to appendix.tex:1379-1387 after the accepted endpoint-to-conditional cycle 76. The weak conditional Fokker--Planck source-sign interface is sharpened by splitting the supplied analytic theorem into (i) a generator/time-derivative identity for the frozen EM interpolation law on admissible tests and (ii) a source expansion of that generator as -div(hat rho_s*bar b_{k,s}) plus sigmaCoeff*Delta hat rho_s, with the lower wrapper now allowing the source expansion itself to be split into separate drift and diffusion actions under explicit common-space, regular conditional kernel, drift regularity, density/time-regularity, admissible-test, and boundary hypotheses.

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.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
6. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
7. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
8. 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 synchronization only. It records the cycle-77 global judgment: cycle 76 passed and needs no recovery; Phase 1 skeleton translation is stable enough for cited-theory backfill; the best risk-reducing packet is the generator-level weak FP source-sign handoff, not theorem-route audit, KL derivative work, display algebra, or broad API migration.

def cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle77_weak_fp_generator_middle"
  statement := "Cycle 77 middle keeps the active backend at sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and returns to appendix.tex:1379-1387 after the accepted endpoint-to-conditional cycle 76. The weak conditional Fokker--Planck source-sign interface is sharpened by splitting the supplied analytic theorem into (i) a generator/time-derivative identity for the frozen EM interpolation law on admissible tests and (ii) a source expansion of that generator as -div(hat rho_s*bar b_{k,s}) plus sigmaCoeff*Delta hat rho_s, with the lower wrapper now allowing the source expansion itself to be split into separate drift and diffusion actions under explicit common-space, regular conditional kernel, drift regularity, density/time-regularity, admissible-test, and boundary hypotheses."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle synchronization only. It records the cycle-77 global judgment: cycle 76 passed and needs no recovery; Phase 1 skeleton translation is stable enough for cited-theory backfill; the best risk-reducing packet is the generator-level weak FP source-sign handoff, not theorem-route audit, KL derivative work, display algebra, or broad API migration."

/-- Cycle-77 lower obligation for the generator-level weak FP source-sign
wrapper. -/