AutoSamplingTheory.SALD.cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackDag

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 cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackDag :
    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

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle134.middle_packet.test_laplacian_source_pullback
interface : String (explicit)
Text describing intended mathematical interface.
Compiled dynamic-leaf worker packet: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback removes the direct htestLaplacianOperator premise by deriving it from SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback. The new source-facing leaves are htestLaplacianActionDef and hweakFpLaplacianDef, both identifying their abstract actions with the same selected weak-test source Laplacian pullback over appendix.tex:1379-1427.
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.cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation
2. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback
4. SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle134.lower_1_packet.source_laplacian_std_basis_formula
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 proof-scout theorem: SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv identifies Mathlib's source Laplacian for a selected real-valued finite-dimensional test function with the standard-basis sum of second iterated Frechet derivatives. This narrows htestLaplacianActionDef and hweakFpLaplacianDef to action-definition equalities against Mathlib's Laplacian, instead of an unspecified sourceLaplacianAction.
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.cycle134GeneralMovingTargetDiscreteEmSourceLaplacianStdBasisScoutObligation
2. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
3. InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis
4. Mathlib.Analysis.InnerProductSpace.Laplacian
5. appendix.tex:1379-1427
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle134.lower_2_packet.weak_fp_laplacian_std_basis_definition
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula narrows hweakFpLaplacianDef to hweakFpStdBasisDef, a source formula saying the weak-FP abstract laplacian action is the standard-basis second-derivative action on the selected weak test. The theorem uses the lower_1 Mathlib Laplacian formula and leaves htestLaplacianActionDef plus all second-Green, box-divergence, trace, diffusion, and first-Green leaves separate.
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.cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. appendix.tex:1379-1427
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.discrete_forward_kl.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle134.remaining_source_laplacian_definitions
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 134 lower_2: instantiate the selected weak-test representation and prove htestLaplacianActionDef for the test-calculus action, and prove hweakFpStdBasisDef for the weak-FP action's standard-basis second-derivative source formula; all second-Green, box-divergence, trace, diffusion, and first-Green leaves remain separate.
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.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback
6. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle134.reviewer_test_laplacian_source_pullback_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the weak-FP source-definition leaf is narrowed from hweakFpLaplacianDef to hweakFpStdBasisDef through SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula, htestLaplacianActionDef remains explicit, hsecondGreenTestTracePointwiseEq and htestTracePointwiseZero remain 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.cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula
3. SALD.cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback
5. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
6. appendix.tex:1379-1427
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 134 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 cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle134.middle_packet.test_laplacian_source_pullback"
      interface := "Compiled dynamic-leaf worker packet: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback removes the direct htestLaplacianOperator premise by deriving it from SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback. The new source-facing leaves are htestLaplacianActionDef and hweakFpLaplacianDef, both identifying their abstract actions with the same selected weak-test source Laplacian pullback over appendix.tex:1379-1427."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation",
        "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback",
        "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
        "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.cycle134.lower_1_packet.source_laplacian_std_basis_formula"
      interface := "Compiled lower_1 proof-scout theorem: SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv identifies Mathlib's source Laplacian for a selected real-valued finite-dimensional test function with the standard-basis sum of second iterated Frechet derivatives. This narrows htestLaplacianActionDef and hweakFpLaplacianDef to action-definition equalities against Mathlib's Laplacian, instead of an unspecified sourceLaplacianAction."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle134GeneralMovingTargetDiscreteEmSourceLaplacianStdBasisScoutObligation",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:1379-1427"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle134.lower_2_packet.weak_fp_laplacian_std_basis_definition"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula narrows hweakFpLaplacianDef to hweakFpStdBasisDef, a source formula saying the weak-FP abstract laplacian action is the standard-basis second-derivative action on the selected weak test. The theorem uses the lower_1 Mathlib Laplacian formula and leaves htestLaplacianActionDef plus all second-Green, box-divergence, trace, diffusion, and first-Green leaves separate."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:1379-1427"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle134.remaining_source_laplacian_definitions"
      interface := "Remaining exact theorem boundary after cycle 134 lower_2: instantiate the selected weak-test representation and prove htestLaplacianActionDef for the test-calculus action, and prove hweakFpStdBasisDef for the weak-FP action's standard-basis second-derivative source formula; all second-Green, box-divergence, trace, diffusion, and first-Green leaves remain separate."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "appendix.tex:1379-1387",
        "appendix.tex:1392-1427",
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback",
        "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
        "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.cycle134.reviewer_test_laplacian_source_pullback_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the weak-FP source-definition leaf is narrowed from hweakFpLaplacianDef to hweakFpStdBasisDef through SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula, htestLaplacianActionDef remains explicit, hsecondGreenTestTracePointwiseEq and htestTracePointwiseZero remain 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.cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula",
        "SALD.cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback",
        "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
        "appendix.tex:1379-1427"
      ]
      reusedBy := ["cycle 134 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 135: EM test-Laplacian action standard-basis definition -/

/-- Cycle-135 lower obligation narrowing the test-calculus Laplacian action
definition leaf to the standard-basis source formula. -/

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