AutoSamplingTheory.SALD.cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryMiddleObligation

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 cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryMiddleObligation :
    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.cycle98_barB_divergence_no_boundary_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 98 middle keeps the active backend on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1358-1387, narrowed to the generator-to-law weak-FP drift source signs at appendix.tex lines 1379-1387. The selected lower packet is the barB divergence/no-boundary half of ASTIS.SALD.cycle94.remaining_barB_divergence_boundary: replace the primitive hbarBWeakDivergence input by two smaller source-cited facts, namely weakGradPairing barB phi is the hatRhoS-law integral of the test-gradient contraction with barB, and driftDiv phi is the negative of that same integral by the divergence/integration-by-parts/no-boundary theorem for hatRhoS * barB. Classification: narrows-source-cited-boundary.

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.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBNoBoundaryIntegral
3. SALD.generalMovingTargetDiscreteBarBWeakDivergenceOfNoBoundaryIntegral
4. SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation
5. SALD.cycle95DiscreteForwardKlClosurePressureLowerObligation
6. SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation
7. Mathlib.MeasureTheory.Integral.DivergenceTheorem
8. Mathlib.MeasureTheory.Integral.Bochner.Basic
9. appendix.tex:1379-1387
10. sald.general_moving_target_discrete.em_interpolation_fp
11. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Middle source-map record plus lower-ready target. It adds no theorem-status promotion and does not prove the analytic divergence theorem, boundary decay/no-flux hypotheses, admissible-test closure, density regularity, or weak Fokker-Planck equation.

def cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle98_barB_divergence_no_boundary_middle"
  statement := "Cycle 98 middle keeps the active backend on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1358-1387, narrowed to the generator-to-law weak-FP drift source signs at appendix.tex lines 1379-1387. The selected lower packet is the barB divergence/no-boundary half of ASTIS.SALD.cycle94.remaining_barB_divergence_boundary: replace the primitive hbarBWeakDivergence input by two smaller source-cited facts, namely weakGradPairing barB phi is the hatRhoS-law integral of the test-gradient contraction with barB, and driftDiv phi is the negative of that same integral by the divergence/integration-by-parts/no-boundary theorem for hatRhoS * barB. Classification: narrows-source-cited-boundary."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBNoBoundaryIntegral",
    "SALD.generalMovingTargetDiscreteBarBWeakDivergenceOfNoBoundaryIntegral",
    "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation",
    "SALD.cycle95DiscreteForwardKlClosurePressureLowerObligation",
    "SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Middle source-map record plus lower-ready target. It adds no theorem-status promotion and does not prove the analytic divergence theorem, boundary decay/no-flux hypotheses, admissible-test closure, density regularity, or weak Fokker-Planck equation."

/-- Cycle-98 lower-ready obligation for the compiled integral no-boundary
handoff. -/