AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation

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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation :
    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_upper

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 upper records that cycle 81 passed reviewer/build and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower packet is the weak conditional Fokker-Planck source-sign statement at appendix.tex:1379-1387: after the cycle-81 endpoint/conditional WeakFpPrereq readiness package, sharpen or prove a supplied-hypothesis bridge whose weak-test form has the exact paper signs partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + (sigma_eta^2/2)*Delta hat rho_s under explicit common-space, conditional-kernel, bar b regularity, density/time-regularity, admissible-test, boundary, generator/time-derivative, and drift/diffusion source-action 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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket
2. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
3. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
4. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
5. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
7. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
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.

Upper workflow obligation only. It selects the weak-FP source-sign packet and status discipline; it proves no conditional law, density/AC, generator theorem, weak Fokker-Planck theorem, KL derivative, or theorem closure.

def cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle82_weak_fp_source_signs_upper"
  statement := "Cycle 82 upper records that cycle 81 passed reviewer/build and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower packet is the weak conditional Fokker-Planck source-sign statement at appendix.tex:1379-1387: after the cycle-81 endpoint/conditional WeakFpPrereq readiness package, sharpen or prove a supplied-hypothesis bridge whose weak-test form has the exact paper signs partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + (sigma_eta^2/2)*Delta hat rho_s under explicit common-space, conditional-kernel, bar b regularity, density/time-regularity, admissible-test, boundary, generator/time-derivative, and drift/diffusion source-action hypotheses."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Upper workflow obligation only. It selects the weak-FP source-sign packet and status discipline; it proves no conditional law, density/AC, generator theorem, weak Fokker-Planck theorem, KL derivative, or theorem closure."

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