AutoSamplingTheory.SALD.cycle131GeneralMovingTargetDiscreteEmSecondGreenTraceBoundaryLowerObligation

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 cycle131GeneralMovingTargetDiscreteEmSecondGreenTraceBoundaryLowerObligation :
    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.cycle131_em_second_green_trace_boundary_lower

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 131 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hsecondGreenZeroBoundary premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux is replaced by hsecondGreenBoundaryFluxIntegral and hsecondGreenTraceProductZero. The second-Green residual/divergence facts, hdiffusionAction, hdiffusionLaplacianTerm, first-Green subfacts, and htestLaplacian remain separate.

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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux
3. MeasureTheory.integral_congr_ae
4. appendix.tex:1392-1427
5. 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.

Proof-producing lower_1 handoff plus scout route. It does not prove the analytic boundary-flux integral representation, trace/compact-support theorem, second-Green residual, second-Green divergence, test-Laplacian normalization, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content.

def cycle131GeneralMovingTargetDiscreteEmSecondGreenTraceBoundaryLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle131_em_second_green_trace_boundary_lower"
  statement := "Cycle 131 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hsecondGreenZeroBoundary premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux is replaced by hsecondGreenBoundaryFluxIntegral and hsecondGreenTraceProductZero. The second-Green residual/divergence facts, hdiffusionAction, hdiffusionLaplacianTerm, first-Green subfacts, and htestLaplacian remain separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux",
    "MeasureTheory.integral_congr_ae",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing lower_1 handoff plus scout route. It does not prove the analytic boundary-flux integral representation, trace/compact-support theorem, second-Green residual, second-Green divergence, test-Laplacian normalization, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content."

/-- Cycle-131 lower_2 obligation narrowing the second-Green boundary-flux
integral input to the existing Mathlib box-divergence interface. -/