AutoSamplingTheory.SALD.cycle130GeneralMovingTargetDiscreteEmFirstGreenNoBoundaryFluxLowerObligation

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 cycle130GeneralMovingTargetDiscreteEmFirstGreenNoBoundaryFluxLowerObligation :
    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.cycle130_em_first_green_no_boundary_flux_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 130 lower_2 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hfirstGreen premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP is replaced by hfirstGreenResidual, hfirstGreenDivergence, and hfirstGreenZeroBoundary, exposing the first Green residual, divergence-theorem boundary-flux identity, and zero boundary-flux condition. The EM/Brownian hdiffusionAction fact, hdiffusionLaplacianTerm, hsecondGreen, 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP
3. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
4. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
5. appendix.tex:1379-1387
6. appendix.tex:1368-1377
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.

Illness-area lower_2 packet. It rejects wrapper churn around hweakLaplacianIbP and targets only the first-Green leaf selected by lower_1. The theorem does not prove second Green, test-Laplacian normalization, Brownian diffusion construction, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, or sald_version_2 content.

def cycle130GeneralMovingTargetDiscreteEmFirstGreenNoBoundaryFluxLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle130_em_first_green_no_boundary_flux_lower"
  statement := "Cycle 130 lower_2 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux for appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hfirstGreen premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP is replaced by hfirstGreenResidual, hfirstGreenDivergence, and hfirstGreenZeroBoundary, exposing the first Green residual, divergence-theorem boundary-flux identity, and zero boundary-flux condition. The EM/Brownian hdiffusionAction fact, hdiffusionLaplacianTerm, hsecondGreen, and htestLaplacian remain separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP",
    "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
    "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
    "appendix.tex:1379-1387",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area lower_2 packet. It rejects wrapper churn around hweakLaplacianIbP and targets only the first-Green leaf selected by lower_1. The theorem does not prove second Green, test-Laplacian normalization, Brownian diffusion construction, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, or sald_version_2 content."

/-! ### Cycle 131: EM second Green no-boundary flux boundary -/

/-- Cycle-131 middle/lower-ready obligation narrowing the second Green identity
to no-boundary flux algebra. -/