AutoSamplingTheory.SALD.cycle100GeneralMovingTargetDiscreteBarBWeakGradDefMiddleObligation

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 cycle100GeneralMovingTargetDiscreteBarBWeakGradDefMiddleObligation :
    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.cycle100_barB_weakGrad_def_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 100 middle keeps the active backend on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1379-1387. Classification: narrows-source-cited-boundary. The selected supplied hypothesis is hweakGradIntegral in the cycle-98 bounded no-boundary route. The lower packet should remove that premise by specializing weakGradPairing to the law-integral definition fun f phi => int x, fieldPairing phi f x d hatRhoS, so weakGradPairing barB phi is definitionally the hatRhoS integral of the barB test-gradient contraction. The concrete contraction bound and the no-boundary driftDiv identity remain the exact source-cited analytic 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.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBBoundedNoBoundaryIntegral
2. SALD.generalMovingTargetDiscreteBarBWeakDivergenceOfNoBoundaryBoundedPairing
3. SALD.generalMovingTargetDiscreteBarBPairIntegrableOfNormBound
4. ASTIS.SALD.cycle98.remaining_exact_no_boundary_theorem
5. Mathlib.MeasureTheory.Integral.DivergenceTheorem
6. Mathlib.MeasureTheory.Integral.Bochner.Basic
7. appendix.tex:1379-1387
8. appendix.tex:1368-1377

note : String (explicit)

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

Middle source synchronization only. This rejects a new wrapper around hbarBWeakDivergence and targets one definition-alignment premise inside the existing no-boundary theorem boundary.

def cycle100GeneralMovingTargetDiscreteBarBWeakGradDefMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle100_barB_weakGrad_def_middle"
  statement := "Cycle 100 middle keeps the active backend on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1379-1387. Classification: narrows-source-cited-boundary. The selected supplied hypothesis is hweakGradIntegral in the cycle-98 bounded no-boundary route. The lower packet should remove that premise by specializing weakGradPairing to the law-integral definition fun f phi => int x, fieldPairing phi f x d hatRhoS, so weakGradPairing barB phi is definitionally the hatRhoS integral of the barB test-gradient contraction. The concrete contraction bound and the no-boundary driftDiv identity remain the exact source-cited analytic hypotheses."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBBoundedNoBoundaryIntegral",
    "SALD.generalMovingTargetDiscreteBarBWeakDivergenceOfNoBoundaryBoundedPairing",
    "SALD.generalMovingTargetDiscreteBarBPairIntegrableOfNormBound",
    "ASTIS.SALD.cycle98.remaining_exact_no_boundary_theorem",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "appendix.tex:1379-1387",
    "appendix.tex:1368-1377"
  ]
  note := "Middle source synchronization only. This rejects a new wrapper around hbarBWeakDivergence and targets one definition-alignment premise inside the existing no-boundary theorem boundary."

/-- Cycle-100 lower-ready obligation for the compiled weak-pairing definition
alignment handoff. -/