Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffDag

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 cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffDag :
    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.cycle177.middle_packet.source_hessian_gap_decision
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle confirms the upper decision: hSourceHasHessian and hSourceHessianBound are not supplied by the original SALD source anchors and remain source-contract gaps. Reject testRegular projection, sourceHessian-by-conclusion, unsourced bounded-Hessian predicates, VP score-Hessian substitution, SLT import, and wrapper churn.
    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.selectedWeakTestHessianOpNormOfSourceHessianField
    2. hSourceHasHessian
    3. hSourceHessianBound
    4. appendix.tex:984-995
    5. appendix.tex:1026-1072
    6. appendix.tex:1379-1387
    7. main_body.tex:273-305
    8. iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. reviewer source-contract check
    2. future source-backed selected weak-test Hessian interface
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

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

    Stable plan-node identifier.

    ASTIS.SALD.cycle177.middle_packet.scalar_line_second_coeff_bridge
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled bridge: SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef derives hSecondTaylorCoeffDef from source-facing hScalarLineSecondCoeffDef plus ambient selected-test ContDiffOn Real 2 regularity, by reusing the affine scalar-line second-derivative chain rule at q = 0.
    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.cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffMiddleObligation
    2. SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef
    3. SALD.gaussianRealSelectedTestLineSecondDerivEqDirectionalFDeriv
    4. hSecondTaylorCoeffDef
    5. hScalarLineSecondCoeffDef
    6. hSource
    7. appendix.tex:984-995
    8. appendix.tex:1170-1176
    9. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef
    2. SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef
    3. hFrozenScalarBrownianItoQuadraticVariationNormalization
    4. sald.general_moving_target_discrete.em_interpolation_fp
    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.cycle177.remaining_scalar_line_second_coeff_boundary
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact source boundary: prove hScalarLineSecondCoeffDef from the paper's scalar Brownian Taylor expansion after drift separation and before the external sigma_eta^2/2 diffusion coefficient. Keep hNormalizedVarianceDef, hSourceHasHessian/hSourceHessianBound, hSecondCoeff, Taylor moment decomposition, DCT data, and coordinate-sum 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. hScalarLineSecondCoeffDef
    2. hNormalizedVarianceDef
    3. hSourceHasHessian
    4. hSourceHessianBound
    5. hSecondCoeff
    6. hFrozenScalarBrownianItoTaylorMomentDecomposition
    7. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
    8. hFrozenScalarBrownianItoEventFieldCoordinateSum
    9. appendix.tex:958-970
    10. appendix.tex:984-995
    11. appendix.tex:1170-1176
    12. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. hSecondTaylorCoeffDef
    2. hFrozenScalarBrownianItoQuadraticVariationNormalization
    3. Brownian/Ito scalar generator bookkeeping
    4. sald.general_moving_target_discrete.em_interpolation_fp
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

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

    Stable plan-node identifier.

    ASTIS.SALD.cycle177.reviewer_second_taylor_coeff_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer accepts only if the packet is narrows-source-cited-boundary, hSecondTaylorCoeffDef is narrowed to hScalarLineSecondCoeffDef plus hSource rather than restated, the selected weak-test Hessian fields remain source gaps, sibling Brownian/Ito leaves remain explicit, no sigma_eta^2/2 is moved into the event field, and python3 tools/astis.py check passes.
    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.cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffMiddleObligation
    2. SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef
    3. hSecondTaylorCoeffDef
    4. hScalarLineSecondCoeffDef
    5. hSource
    6. hSourceHasHessian
    7. hSourceHessianBound
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 177 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 cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle177.middle_packet.source_hessian_gap_decision"
      interface := "Middle confirms the upper decision: hSourceHasHessian and hSourceHessianBound are not supplied by the original SALD source anchors and remain source-contract gaps. Reject testRegular projection, sourceHessian-by-conclusion, unsourced bounded-Hessian predicates, VP score-Hessian substitution, SLT import, and wrapper churn."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestHessianOpNormOfSourceHessianField",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305",
        "iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest"
      ]
      reusedBy := [
        "reviewer source-contract check",
        "future source-backed selected weak-test Hessian interface"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle177.middle_packet.scalar_line_second_coeff_bridge"
      interface := "Compiled bridge: SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef derives hSecondTaylorCoeffDef from source-facing hScalarLineSecondCoeffDef plus ambient selected-test ContDiffOn Real 2 regularity, by reusing the affine scalar-line second-derivative chain rule at q = 0."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffMiddleObligation",
        "SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef",
        "SALD.gaussianRealSelectedTestLineSecondDerivEqDirectionalFDeriv",
        "hSecondTaylorCoeffDef",
        "hScalarLineSecondCoeffDef",
        "hSource",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle177.remaining_scalar_line_second_coeff_boundary"
      interface := "Remaining exact source boundary: prove hScalarLineSecondCoeffDef from the paper's scalar Brownian Taylor expansion after drift separation and before the external sigma_eta^2/2 diffusion coefficient. Keep hNormalizedVarianceDef, hSourceHasHessian/hSourceHessianBound, hSecondCoeff, Taylor moment decomposition, DCT data, and coordinate-sum explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hScalarLineSecondCoeffDef",
        "hNormalizedVarianceDef",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "hSecondCoeff",
        "hFrozenScalarBrownianItoTaylorMomentDecomposition",
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "hFrozenScalarBrownianItoEventFieldCoordinateSum",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hSecondTaylorCoeffDef",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "Brownian/Ito scalar generator bookkeeping",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle177.reviewer_second_taylor_coeff_check"
      interface := "Reviewer accepts only if the packet is narrows-source-cited-boundary, hSecondTaylorCoeffDef is narrowed to hScalarLineSecondCoeffDef plus hSource rather than restated, the selected weak-test Hessian fields remain source gaps, sibling Brownian/Ito leaves remain explicit, no sigma_eta^2/2 is moved into the event field, and python3 tools/astis.py check passes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle177GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSecondTaylorCoeffMiddleObligation",
        "SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef",
        "hSecondTaylorCoeffDef",
        "hScalarLineSecondCoeffDef",
        "hSource",
        "hSourceHasHessian",
        "hSourceHessianBound"
      ]
      reusedBy := ["cycle 177 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 178 middle: normalized Brownian coordinate variance law -/

/-- Cycle-178 middle packet for the normalized Brownian variance source field.

This packet follows the accepted source-Hessian decision: the Hessian fields
remain source-contract gaps, so the connected Brownian/Ito variance leaf is
reduced instead.  The older `hNormalizedVarianceDef` source field is narrowed to
an explicit normalized-coordinate law equality and a variance-field definition.
-/

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