AutoSamplingTheory.SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenTraceEqTestTraceZeroScoutObligation

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 cycle132GeneralMovingTargetDiscreteEmSecondGreenTraceEqTestTraceZeroScoutObligation :
    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.cycle132_em_second_green_trace_eq_test_trace_zero_lower_1

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 132 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hsecondGreenTestTraceZero premise exposed by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero is replaced by hsecondGreenTestTraceEq, identifying the second-Green test trace with the standard admissible-test boundary trace a.e., and htestTraceZero, the existing zero boundary trace condition for admissible weak tests. The theorem keeps box-divergence regularity/face-trace facts, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit.

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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero
3. SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero
4. ASTIS.SALD.forward_KL_discrete.cycle102_test_trace_zero_lower
5. appendix.tex:1392-1427
6. appendix.tex:1379-1387
7. 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 scout packet. It does not prove the analytic compact-support/zero-trace theorem, the second-Green trace-identification theorem, weighted-field regularity, divergence integrability, face-to-trace identification, second-Green residual/divergence facts, 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 cycle132GeneralMovingTargetDiscreteEmSecondGreenTraceEqTestTraceZeroScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle132_em_second_green_trace_eq_test_trace_zero_lower_1"
  statement := "Cycle 132 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hsecondGreenTestTraceZero premise exposed by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero is replaced by hsecondGreenTestTraceEq, identifying the second-Green test trace with the standard admissible-test boundary trace a.e., and htestTraceZero, the existing zero boundary trace condition for admissible weak tests. The theorem keeps box-divergence regularity/face-trace facts, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero",
    "SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero",
    "ASTIS.SALD.forward_KL_discrete.cycle102_test_trace_zero_lower",
    "appendix.tex:1392-1427",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing lower_1 scout packet. It does not prove the analytic compact-support/zero-trace theorem, the second-Green trace-identification theorem, weighted-field regularity, divergence integrability, face-to-trace identification, second-Green residual/divergence facts, 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-132 lower_2 continuation narrowing second-Green trace identification
from an a.e. statement to pointwise selected-trace equality. -/