AutoSamplingTheory.SALD.cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation

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 cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation :
    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.cycle138_em_first_green_pointwise_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 138 middle compiles SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hfirstGreenPointwise leaf from SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux is no longer primitive; it follows from hfirstGreenResidual, hfirstGreenDivergence, and hfirstGreenZeroBoundary, exposing the first-Green residual, divergence/boundary-flux identity, and zero-boundary fact. The theorem keeps htestLaplacianPointwise, hdensityLaplacianActionDef, hsourceDensityLaplacianEqLaplacian, htestLaplacianStdBasisDef, diffusion leaves, and the second-Green box-divergence/trace leaves 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.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero
2. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux
3. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux
4. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity
5. SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity
6. appendix.tex:1392-1427
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.

Dynamic-leaf worker packet. It narrows only the first-Green pointwise leaf under the cycle-137 pointwise Green split, replacing direct hfirstGreenPointwise by residual/divergence/zero-boundary facts. It does not prove test-Laplacian pointwise normalization, density-Laplacian source definitions, second-Green residual/divergence, box-divergence, trace, diffusion-source closure, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle138_em_first_green_pointwise_boundary_flux_lower"
  statement := "Cycle 138 middle compiles SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux for appendix.tex:1392-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct hfirstGreenPointwise leaf from SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux is no longer primitive; it follows from hfirstGreenResidual, hfirstGreenDivergence, and hfirstGreenZeroBoundary, exposing the first-Green residual, divergence/boundary-flux identity, and zero-boundary fact. The theorem keeps htestLaplacianPointwise, hdensityLaplacianActionDef, hsourceDensityLaplacianEqLaplacian, htestLaplacianStdBasisDef, diffusion leaves, and the second-Green box-divergence/trace leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity",
    "SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It narrows only the first-Green pointwise leaf under the cycle-137 pointwise Green split, replacing direct hfirstGreenPointwise by residual/divergence/zero-boundary facts. It does not prove test-Laplacian pointwise normalization, density-Laplacian source definitions, second-Green residual/divergence, box-divergence, trace, diffusion-source closure, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-138 lower_1 scout bridge narrowing pointwise test-Laplacian
normalization to shared source-pullback definitions. -/