Samplinglib
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AutoSamplingTheory.SALD.cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroDag

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 cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroDag :
    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.cycle133.middle_packet.second_green_pointwise_test_trace_zero
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled illness-area refiner: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero removes the direct a.e. htestTraceZero premise by deriving it from htestTracePointwiseZero via Filter.Eventually.of_forall. It keeps hsecondGreenTestTracePointwiseEq, the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian 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.cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
    3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero
    4. Filter.Eventually.of_forall
    5. appendix.tex:1392-1427
    6. appendix.tex:1379-1387
    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.cycle133.lower_1_packet.test_laplacian_normalization
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_1 scout continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization removes the broad htestLaplacian premise by deriving it from the test-local htestLaplacianLocal premise, depending only on Admissible phi and testRegular. It keeps hsecondGreenTestTracePointwiseEq, htestTracePointwiseZero, the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, and hdiffusionLaplacianTerm 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.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation
    2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
    3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
    4. appendix.tex:1379-1387
    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
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle133.lower_2_packet.test_laplacian_operator_normalization
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization narrows htestLaplacianLocal to the operator-level source identity htestLaplacianOperator : testRegular → testLaplacianAction = laplacian. It removes admissibility from the analytic normalization boundary while leaving the selected regular test calculus identity 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.cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation
    2. SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
    3. SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation
    4. appendix.tex:1379-1387
    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
  4. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle133.remaining_laplacian_ibp_analysis
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary after cycle 133: prove the density-Laplacian weak term for the EM/Brownian diffusion contribution, instantiate the first-Green residual/divergence/zero-flux facts, instantiate the second-Green residual/divergence facts, prove the box-divergence regularity/face-trace facts behind the second-Green boundary flux, prove the pointwise source trace-definition equality identifying the second-Green test trace with the admissible-test boundary trace, prove pointwise zero boundary trace for source admissible tests, and prove the operator-level test-Laplacian normalization htestLaplacianOperator.
    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. appendix.tex:1379-1387
    2. appendix.tex:1392-1427
    3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
    4. SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
    5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
    6. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero
    7. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
    8. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
    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.cycle133.reviewer_pointwise_test_trace_zero_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks direct a.e. htestTraceZero, the lower_1 theorem statement lacks broad htestLaplacian and replaces it only with test-local htestLaplacianLocal, the lower_2 theorem narrows htestLaplacianLocal to htestLaplacianOperator, hsecondGreenTestTracePointwiseEq remains explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, broad audit, 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.cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation
    2. SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation
    3. SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation
    4. SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
    5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
    6. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
    7. appendix.tex:1392-1427
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 133 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 cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle133.middle_packet.second_green_pointwise_test_trace_zero"
      interface := "Compiled illness-area refiner: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero removes the direct a.e. htestTraceZero premise by deriving it from htestTracePointwiseZero via Filter.Eventually.of_forall. It keeps hsecondGreenTestTracePointwiseEq, the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero",
        "Filter.Eventually.of_forall",
        "appendix.tex:1392-1427",
        "appendix.tex:1379-1387"
      ]
      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.cycle133.lower_1_packet.test_laplacian_normalization"
      interface := "Compiled lower_1 scout continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization removes the broad htestLaplacian premise by deriving it from the test-local htestLaplacianLocal premise, depending only on Admissible phi and testRegular. It keeps hsecondGreenTestTracePointwiseEq, htestTracePointwiseZero, the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, and hdiffusionLaplacianTerm explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
        "appendix.tex:1379-1387",
        "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.cycle133.lower_2_packet.test_laplacian_operator_normalization"
      interface := "Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization narrows htestLaplacianLocal to the operator-level source identity htestLaplacianOperator : testRegular → testLaplacianAction = laplacian. It removes admissibility from the analytic normalization boundary while leaving the selected regular test calculus identity explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation",
        "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
        "SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation",
        "appendix.tex:1379-1387",
        "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.cycle133.remaining_laplacian_ibp_analysis"
      interface := "Remaining exact theorem boundary after cycle 133: prove the density-Laplacian weak term for the EM/Brownian diffusion contribution, instantiate the first-Green residual/divergence/zero-flux facts, instantiate the second-Green residual/divergence facts, prove the box-divergence regularity/face-trace facts behind the second-Green boundary flux, prove the pointwise source trace-definition equality identifying the second-Green test trace with the admissible-test boundary trace, prove pointwise zero boundary trace for source admissible tests, and prove the operator-level test-Laplacian normalization htestLaplacianOperator."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "appendix.tex:1379-1387",
        "appendix.tex:1392-1427",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
        "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero",
        "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle133.reviewer_pointwise_test_trace_zero_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks direct a.e. htestTraceZero, the lower_1 theorem statement lacks broad htestLaplacian and replaces it only with test-local htestLaplacianLocal, the lower_2 theorem narrows htestLaplacianLocal to htestLaplacianOperator, hsecondGreenTestTracePointwiseEq remains explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, broad audit, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle133GeneralMovingTargetDiscreteEmSecondGreenPointwiseTestTraceZeroLowerObligation",
        "SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation",
        "SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianOperatorNormalizationLowerObligation",
        "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
        "appendix.tex:1392-1427"
      ]
      reusedBy := ["cycle 133 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 134: EM test-Laplacian source pullback boundary -/

/-- Cycle-134 dynamic-leaf packet narrowing the operator-level
test-Laplacian normalization to shared source-pullback definitions. -/

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