Samplinglib
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AutoSamplingTheory.SALD.cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxDag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

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.

Ordered data items

  1. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle138.middle_packet.first_green_pointwise_boundary_flux
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled dynamic-leaf theorem: SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero derives hfirstGreenPointwise from hfirstGreenResidual, hfirstGreenDivergence, and hfirstGreenZeroBoundary. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux feeds this derived first-Green leaf into the existing cycle-137 second-Green box-boundary standard-basis consumer.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation
    2. SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero
    3. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux
    4. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux
    5. appendix.tex:1392-1427
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    3. thm:forward-KL-discrete
    4. thm:general-moving-target-SALD-discrete
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle138.lower_1_packet.test_laplacian_pointwise_source_pullback
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_1 scout theorem: SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback derives the pointwise test-Laplacian normalization testLaplacianAction phi = laplacian phi from htestLaplacianActionDef and hweakFpLaplacianDef, both identifying the two abstract actions with the same selected source-Laplacian pullback. The source-definition leaves themselves remain explicit.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation
    2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback
    3. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
    4. SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity
    5. appendix.tex:1379-1427
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    3. thm:forward-KL-discrete
    4. thm:general-moving-target-SALD-discrete
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle138.lower_2_packet.test_laplacian_pointwise_std_basis
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula derives the pointwise test-Laplacian normalization testLaplacianAction phi = laplacian phi from htestLaplacianStdBasisDef plus the still-explicit hweakFpLaplacianDef. This removes htestLaplacianActionDef from the pointwise Green route while avoiding the circular use of hweakFpStdBasisDef.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation
    2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula
    3. SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula
    4. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback
    5. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
    6. Mathlib.Analysis.InnerProductSpace.Laplacian
    7. appendix.tex:1379-1427
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    3. thm:forward-KL-discrete
    4. thm:general-moving-target-SALD-discrete
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
  4. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle138.remaining_pointwise_green_after_first_green
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary after cycle 138 lower_2: prove the source-facing htestLaplacianStdBasisDef for the local test-calculus action and prove hweakFpLaplacianDef from a non-circular weak-FP source-Laplacian definition, then use SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula to obtain the pointwise test-Laplacian normalization. The density-Laplacian source-action/source-field facts and the explicit second-Green residual/divergence, box-divergence, signed-face trace, pointwise trace equality, and pointwise zero-trace leaves remain separate. The first-Green pointwise leaf is narrowed to residual/divergence/zero-boundary facts, and htestLaplacianActionDef is no longer primitive for the pointwise route.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula
    2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback
    3. SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula
    4. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux
    5. SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero
    6. SALD.generalMovingTargetDiscreteSecondGreenPointwiseOfBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
    7. SALD.generalMovingTargetDiscreteDensityLaplacianStdBasisDefOfPointwiseSourceFormula
    8. SALD.generalMovingTargetDiscreteSourceDensityLaplacianStdBasisOfLaplacianSourceField
    9. appendix.tex:1379-1427
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
  5. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle138.reviewer_first_green_pointwise_boundary_flux_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hfirstGreenPointwise is narrowed to first-Green residual/divergence/zero-boundary facts through SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero, htestLaplacianPointwise is narrowed first to source-pullback definitions through SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback and then on the test side to htestLaplacianStdBasisDef through SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula, hweakFpLaplacianDef remains explicit rather than being derived from hweakFpStdBasisDef, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, or sald_version_2 use.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
    targetLean : String (explicit)

    Textual planned implementation destination.

    AutoSamplingTheory/SALD.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. SALD.cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation
    2. SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation
    3. SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation
    4. SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero
    5. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback
    6. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula
    7. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux
    8. appendix.tex:1392-1427
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 138 reviewer
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle138.middle_packet.first_green_pointwise_boundary_flux"
      interface := "Compiled dynamic-leaf theorem: SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero derives hfirstGreenPointwise from hfirstGreenResidual, hfirstGreenDivergence, and hfirstGreenZeroBoundary. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux feeds this derived first-Green leaf into the existing cycle-137 second-Green box-boundary standard-basis consumer."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation",
        "SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero",
        "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenSecondGreenBoxBoundaryFlux",
        "appendix.tex:1392-1427"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle138.lower_1_packet.test_laplacian_pointwise_source_pullback"
      interface := "Compiled lower_1 scout theorem: SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback derives the pointwise test-Laplacian normalization testLaplacianAction phi = laplacian phi from htestLaplacianActionDef and hweakFpLaplacianDef, both identifying the two abstract actions with the same selected source-Laplacian pullback. The source-definition leaves themselves remain explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback",
        "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
        "SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity",
        "appendix.tex:1379-1427"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle138.lower_2_packet.test_laplacian_pointwise_std_basis"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula derives the pointwise test-Laplacian normalization testLaplacianAction phi = laplacian phi from htestLaplacianStdBasisDef plus the still-explicit hweakFpLaplacianDef. This removes htestLaplacianActionDef from the pointwise Green route while avoiding the circular use of hweakFpStdBasisDef."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:1379-1427"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle138.remaining_pointwise_green_after_first_green"
      interface := "Remaining exact theorem boundary after cycle 138 lower_2: prove the source-facing htestLaplacianStdBasisDef for the local test-calculus action and prove hweakFpLaplacianDef from a non-circular weak-FP source-Laplacian definition, then use SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula to obtain the pointwise test-Laplacian normalization. The density-Laplacian source-action/source-field facts and the explicit second-Green residual/divergence, box-divergence, signed-face trace, pointwise trace equality, and pointwise zero-trace leaves remain separate. The first-Green pointwise leaf is narrowed to residual/divergence/zero-boundary facts, and htestLaplacianActionDef is no longer primitive for the pointwise route."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback",
        "SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux",
        "SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero",
        "SALD.generalMovingTargetDiscreteSecondGreenPointwiseOfBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
        "SALD.generalMovingTargetDiscreteDensityLaplacianStdBasisDefOfPointwiseSourceFormula",
        "SALD.generalMovingTargetDiscreteSourceDensityLaplacianStdBasisOfLaplacianSourceField",
        "appendix.tex:1379-1427"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle138.reviewer_first_green_pointwise_boundary_flux_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hfirstGreenPointwise is narrowed to first-Green residual/divergence/zero-boundary facts through SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero, htestLaplacianPointwise is narrowed first to source-pullback definitions through SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback and then on the test side to htestLaplacianStdBasisDef through SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula, hweakFpLaplacianDef remains explicit rather than being derived from hweakFpStdBasisDef, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle138GeneralMovingTargetDiscreteEmFirstGreenPointwiseBoundaryFluxLowerObligation",
        "SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation",
        "SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteFirstGreenPointwiseOfBoundaryFluxZero",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfFirstGreenBoundaryFluxAndSecondGreenBoxBoundaryFlux",
        "appendix.tex:1392-1427"
      ]
      reusedBy := ["cycle 138 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-139 weak-FP source-Laplacian field split for the pointwise
test-Laplacian route. -/

Existing module entry · Audited data-reader index · All teaching coverage