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

AutoSamplingTheory.SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffDag

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 cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffDag :
    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.cycle179.middle_packet.source_hessian_audit_closed
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle records the source-dependency decision: hSourceHasHessian and hSourceHessianBound are not derivable from the checked original SALD source anchors and remain source-contract gaps. Reject testRegular projection, sourceHessian-by-conclusion, unsourced C2_b wrappers, 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. sourceHessian
    5. appendix.tex:984-995
    6. appendix.tex:1026-1072
    7. appendix.tex:1170-1176
    8. appendix.tex:1379-1387
    9. main_body.tex:273-305
    10. iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest
    11. paper-wide original-source search excluding sald_version_2.tex
    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.cycle179.middle_packet.scalar_line_second_coeff_lower_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower_1 route assignment: narrow hScalarLineSecondCoeffDef to the scalar Brownian Taylor coefficient read from the frozen interpolation and normalized coordinate law, keeping sigma_eta^2/2 outside the event field.
    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. SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef
    3. appendix.tex:984-995
    4. appendix.tex:1170-1176
    5. appendix.tex:1379-1387
    6. sald.general_moving_target_discrete.em_interpolation_fp
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

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

    Recorded workflow status, default planned.

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

    Stable plan-node identifier.

    ASTIS.SALD.cycle179.middle_packet.lower_2_exact_target
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower_2 target discipline: implement exactly one compiled theorem or record one strictly smaller source-cited obligation narrowing hScalarLineSecondCoeffDef. Keep hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSecondCoeff, Taylor moment decomposition, DCT domination, coordinate-sum, and the source-Hessian gaps 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. hNormalizedVectorLaw
    3. hCoordinateLawDef
    4. hVarianceDef
    5. hSecondCoeff
    6. hFrozenScalarBrownianItoTaylorMomentDecomposition
    7. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
    8. hFrozenScalarBrownianItoEventFieldCoordinateSum
    9. hSourceHasHessian
    10. hSourceHessianBound
    11. appendix.tex:958-970
    12. appendix.tex:984-995
    13. appendix.tex:1170-1176
    14. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. future lower_2 hScalarLineSecondCoeffDef packet
    2. 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.cycle179.lower_1_packet.scalar_line_taylor_coeff_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower_1 route: narrow hScalarLineSecondCoeffDef to the paper's scalar-line Taylor coefficient convention hScalarLineTaylorCoeffDef, where quadraticCoeff is twice the order-two taylorCoeffWithin term and sigma_eta^2/2 remains outside the Brownian event field.
    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.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoScalarLineCoeffLower1Obligation
    2. hScalarLineTaylorCoeffDef
    3. hScalarLineSecondCoeffDef
    4. taylorCoeffWithin
    5. iteratedDerivWithin_univ
    6. appendix.tex:984-995
    7. appendix.tex:1170-1176
    8. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.selectedWeakTestScalarLineSecondCoeffDefOfTaylorCoeffWithin
    2. SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef
    3. hFrozenScalarBrownianItoQuadraticVariationNormalization
    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.cycle179.lower_2_packet.scalar_line_second_coeff_from_taylor_coeff
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_2 bridge: SALD.selectedWeakTestScalarLineSecondCoeffDefOfTaylorCoeffWithin derives hScalarLineSecondCoeffDef from hScalarLineTaylorCoeffDef by unfolding Mathlib's taylorCoeffWithin over Set.univ and simplifying the order-two factorial normalization.
    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.selectedWeakTestScalarLineSecondCoeffDefOfTaylorCoeffWithin
    2. SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoScalarLineCoeffLower2Obligation
    3. hScalarLineTaylorCoeffDef
    4. hScalarLineSecondCoeffDef
    5. taylorCoeffWithin
    6. iteratedDerivWithin_univ
    7. Nat.factorial
    8. appendix.tex:984-995
    9. appendix.tex:1170-1176
    10. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef
    2. SALD.selectedWeakTestQuadraticVariationNormalizationOfScalarLineSecondCoeffAndNormalizedVarianceDef
    3. 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
  6. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle179.reviewer_hessian_audit_scalar_coeff_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer accepts only if the packet is narrows-source-cited-boundary, the Hessian fields remain honest source-contract gaps after the source audit, lower work is assigned to hScalarLineSecondCoeffDef rather than wrapper churn, no VP score-Hessian substitution or sald_version_2.tex use occurs, 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.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffMiddleObligation
    2. SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffDag
    3. hSourceHasHessian
    4. hSourceHessianBound
    5. hScalarLineSecondCoeffDef
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 179 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 cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle179.middle_packet.source_hessian_audit_closed"
      interface := "Middle records the source-dependency decision: hSourceHasHessian and hSourceHessianBound are not derivable from the checked original SALD source anchors and remain source-contract gaps. Reject testRegular projection, sourceHessian-by-conclusion, unsourced C2_b wrappers, VP score-Hessian substitution, SLT import, and wrapper churn."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestHessianOpNormOfSourceHessianField",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "sourceHessian",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305",
        "iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest",
        "paper-wide original-source search excluding sald_version_2.tex"
      ]
      reusedBy := [
        "reviewer source-contract check",
        "future source-backed selected weak-test Hessian interface"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle179.middle_packet.scalar_line_second_coeff_lower_route"
      interface := "Lower_1 route assignment: narrow hScalarLineSecondCoeffDef to the scalar Brownian Taylor coefficient read from the frozen interpolation and normalized coordinate law, keeping sigma_eta^2/2 outside the event field."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hScalarLineSecondCoeffDef",
        "SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "hSecondTaylorCoeffDef",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "Brownian/Ito scalar generator bookkeeping"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle179.middle_packet.lower_2_exact_target"
      interface := "Lower_2 target discipline: implement exactly one compiled theorem or record one strictly smaller source-cited obligation narrowing hScalarLineSecondCoeffDef. Keep hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSecondCoeff, Taylor moment decomposition, DCT domination, coordinate-sum, and the source-Hessian gaps explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hScalarLineSecondCoeffDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "hSecondCoeff",
        "hFrozenScalarBrownianItoTaylorMomentDecomposition",
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "hFrozenScalarBrownianItoEventFieldCoordinateSum",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "future lower_2 hScalarLineSecondCoeffDef packet",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle179.lower_1_packet.scalar_line_taylor_coeff_route"
      interface := "Lower_1 route: narrow hScalarLineSecondCoeffDef to the paper's scalar-line Taylor coefficient convention hScalarLineTaylorCoeffDef, where quadraticCoeff is twice the order-two taylorCoeffWithin term and sigma_eta^2/2 remains outside the Brownian event field."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoScalarLineCoeffLower1Obligation",
        "hScalarLineTaylorCoeffDef",
        "hScalarLineSecondCoeffDef",
        "taylorCoeffWithin",
        "iteratedDerivWithin_univ",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestScalarLineSecondCoeffDefOfTaylorCoeffWithin",
        "SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle179.lower_2_packet.scalar_line_second_coeff_from_taylor_coeff"
      interface := "Compiled lower_2 bridge: SALD.selectedWeakTestScalarLineSecondCoeffDefOfTaylorCoeffWithin derives hScalarLineSecondCoeffDef from hScalarLineTaylorCoeffDef by unfolding Mathlib's taylorCoeffWithin over Set.univ and simplifying the order-two factorial normalization."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestScalarLineSecondCoeffDefOfTaylorCoeffWithin",
        "SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoScalarLineCoeffLower2Obligation",
        "hScalarLineTaylorCoeffDef",
        "hScalarLineSecondCoeffDef",
        "taylorCoeffWithin",
        "iteratedDerivWithin_univ",
        "Nat.factorial",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestSecondTaylorCoeffDefOfScalarLineSecondCoeffDef",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfScalarLineSecondCoeffAndNormalizedVarianceDef",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle179.reviewer_hessian_audit_scalar_coeff_check"
      interface := "Reviewer accepts only if the packet is narrows-source-cited-boundary, the Hessian fields remain honest source-contract gaps after the source audit, lower work is assigned to hScalarLineSecondCoeffDef rather than wrapper churn, no VP score-Hessian substitution or sald_version_2.tex use occurs, and python3 tools/astis.py check passes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffMiddleObligation",
        "SALD.cycle179GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianAuditScalarLineCoeffDag",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "hScalarLineSecondCoeffDef"
      ]
      reusedBy := ["cycle 179 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 179 lower_1: scalar-line coefficient proof scout -/

/-- Cycle-179 lower_1 route for the remaining scalar-line coefficient boundary.

This is a proof-scout packet, not a theorem-status promotion.  It keeps the
selected weak-test Hessian fields as source-contract gaps and narrows the next
connected Brownian/Ito coefficient leaf to the paper's scalar Taylor
coefficient convention.
-/

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