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

AutoSamplingTheory.SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationDag

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 cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationDag :
    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.cycle174.middle_refiner.source_hessian_gap_decision
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle records the upper decision: hSourceHasHessian and hSourceHessianBound are not supplied by the original SALD source anchors and remain a source-contract gap, so no lower packet may derive them from testRegular, sourceHessian-by-definition, an unsourced bounded-Hessian predicate, or VP score-Hessian regularity.
    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.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation
    2. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
    3. hSourceHasHessian
    4. hSourceHessianBound
    5. appendix.tex:984-995
    6. appendix.tex:1026-1072
    7. appendix.tex:1379-1387
    8. main_body.tex:273-305
    9. 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.cycle174.middle_packet.quadratic_variation_normalization_lower_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower-ready route: narrow hFrozenScalarBrownianItoQuadraticVariationNormalization to source-backed hQuadraticCoeffDef plus hVarianceOne for the normalized scalar Brownian coordinate from eq:general_moving_target_SALD_frozen_interp, with sigma_eta^2/2 kept 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. SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    3. SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator
    4. hFrozenScalarBrownianItoQuadraticVariationNormalization
    5. hQuadraticCoeffDef
    6. hVarianceOne
    7. eq:general_moving_target_SALD_frozen_interp
    8. appendix.tex:984-995
    9. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    3. 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
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle174.lower_1_packet.quadratic_variation_coeff_variance_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower_1 proof-scout route: hFrozenScalarBrownianItoQuadraticVariationNormalization should be reduced to source-backed hQuadraticCoeffDef plus hVarianceOne. The normalized scalar Brownian coordinate from eq:general_moving_target_SALD_frozen_interp has variance one, and the sigma_eta^2/2 factor remains outside the event field, so the quadratic coefficient is the diagonal Hessian generator SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator.
    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.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower1Obligation
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    3. SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator
    4. hFrozenScalarBrownianItoQuadraticVariationNormalization
    5. hQuadraticCoeffDef
    6. hVarianceOne
    7. appendix.tex:984-995
    8. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
    2. hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor
    3. 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.cycle174.lower_2_packet.quadratic_variation_coeff_variance_bridge
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_2 bridge: SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne derives hFrozenScalarBrownianItoQuadraticVariationNormalization from source-backed hQuadraticCoeffDef and hVarianceOne by rewriting and simplifying multiplication by one.
    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.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
    2. SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower2Obligation
    3. SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower1Obligation
    4. hFrozenScalarBrownianItoQuadraticVariationNormalization
    5. hQuadraticCoeffDef
    6. hVarianceOne
    7. SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator
    8. appendix.tex:984-995
    9. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    2. hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor
    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
  5. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle174.reviewer_quadratic_variation_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer accepts only if the packet is narrows-source-cited-boundary, the Hessian source fields are kept as a source-contract gap, the lower_2 theorem targets hFrozenScalarBrownianItoQuadraticVariationNormalization through hQuadraticCoeffDef and hVarianceOne, sibling Taylor/remainder/coordinate-sum leaves remain explicit, 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.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation
    2. ASTIS.SALD.cycle174.middle_refiner.source_hessian_gap_decision
    3. ASTIS.SALD.cycle174.middle_packet.quadratic_variation_normalization_lower_route
    4. ASTIS.SALD.cycle174.lower_1_packet.quadratic_variation_coeff_variance_route
    5. ASTIS.SALD.cycle174.lower_2_packet.quadratic_variation_coeff_variance_bridge
    6. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
    7. hFrozenScalarBrownianItoQuadraticVariationNormalization
    8. hQuadraticCoeffDef
    9. hVarianceOne
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 174 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 cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle174.middle_refiner.source_hessian_gap_decision"
      interface := "Middle records the upper decision: hSourceHasHessian and hSourceHessianBound are not supplied by the original SALD source anchors and remain a source-contract gap, so no lower packet may derive them from testRegular, sourceHessian-by-definition, an unsourced bounded-Hessian predicate, or VP score-Hessian regularity."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation",
        "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
        "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.cycle174.middle_packet.quadratic_variation_normalization_lower_route"
      interface := "Lower-ready route: narrow hFrozenScalarBrownianItoQuadraticVariationNormalization to source-backed hQuadraticCoeffDef plus hVarianceOne for the normalized scalar Brownian coordinate from eq:general_moving_target_SALD_frozen_interp, with sigma_eta^2/2 kept outside the event field."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
        "SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "hQuadraticCoeffDef",
        "hVarianceOne",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle174.lower_1_packet.quadratic_variation_coeff_variance_route"
      interface := "Lower_1 proof-scout route: hFrozenScalarBrownianItoQuadraticVariationNormalization should be reduced to source-backed hQuadraticCoeffDef plus hVarianceOne. The normalized scalar Brownian coordinate from eq:general_moving_target_SALD_frozen_interp has variance one, and the sigma_eta^2/2 factor remains outside the event field, so the quadratic coefficient is the diagonal Hessian generator SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower1Obligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
        "SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "hQuadraticCoeffDef",
        "hVarianceOne",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
        "hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle174.lower_2_packet.quadratic_variation_coeff_variance_bridge"
      interface := "Compiled lower_2 bridge: SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne derives hFrozenScalarBrownianItoQuadraticVariationNormalization from source-backed hQuadraticCoeffDef and hVarianceOne by rewriting and simplifying multiplication by one."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
        "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower2Obligation",
        "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower1Obligation",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "hQuadraticCoeffDef",
        "hVarianceOne",
        "SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
        "hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle174.reviewer_quadratic_variation_check"
      interface := "Reviewer accepts only if the packet is narrows-source-cited-boundary, the Hessian source fields are kept as a source-contract gap, the lower_2 theorem targets hFrozenScalarBrownianItoQuadraticVariationNormalization through hQuadraticCoeffDef and hVarianceOne, sibling Taylor/remainder/coordinate-sum leaves remain explicit, and python3 tools/astis.py check passes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation",
        "ASTIS.SALD.cycle174.middle_refiner.source_hessian_gap_decision",
        "ASTIS.SALD.cycle174.middle_packet.quadratic_variation_normalization_lower_route",
        "ASTIS.SALD.cycle174.lower_1_packet.quadratic_variation_coeff_variance_route",
        "ASTIS.SALD.cycle174.lower_2_packet.quadratic_variation_coeff_variance_bridge",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "hQuadraticCoeffDef",
        "hVarianceOne"
      ]
      reusedBy := ["cycle 174 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 175: selected-line Taylor domination from source Hessian fields -/

/-- Cycle-175 dynamic-leaf worker packet for the standard-basis selected-line
Taylor-domination leaf.

The cycle-174 reviewer accepted the Brownian quadratic-variation algebraic
bridge.  This packet returns to the connected normalized-remainder domination
chain and narrows the first-order selected-line Taylor remainder for the
standard Brownian coordinate.  The source-facing Hessian fields are not closed
or hidden; they remain the exact source-contract gap identified by cycle 173.
-/

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