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

AutoSamplingTheory.SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorDag

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 cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorDag :
    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.cycle163.lower_packet.selected_test_line_taylor_hpoint
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled theorem: SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE supplies the a.e. Gaussian pointwise Tendsto hPoint for the scaled selected-test line r |-> sourceTest (x + r • e), using ContDiffOn Real 2 and Mathlib Real.taylor_tendsto.
    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.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorLowerObligation
    2. SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE
    3. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT
    4. Real.taylor_tendsto
    5. Mathlib.Analysis.Calculus.Taylor
    6. eq:general_moving_target_SALD_frozen_interp
    7. appendix.tex:984-995
    8. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    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
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle163.lower_1_packet.normalized_remainder_source_eq_to_dct
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_1 scout bridge: SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq consumes an eventual Gaussian-a.e. source equality hSourceEq between normalizedRemainder and the scaled selected-test line Taylor remainder, then derives the DCT integral limit from the compiled pointwise Taylor theorem and SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT.
    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.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq
    2. SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE
    3. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT
    4. Filter.Tendsto.congr'
    5. hSourceEq
    6. hMeas
    7. hBound
    8. hBoundInt
    9. eq:general_moving_target_SALD_frozen_interp
    10. appendix.tex:984-995
    11. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    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.cycle163.lower_2_packet.normalized_remainder_source_eq
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_2 bridge: SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq supplies the hSourceEq input by definitional equality for the concrete source-shaped selected-test normalized remainder, and SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero derives the DCT integral limit without an hSourceEq premise.
    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.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation
    2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder
    3. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq
    4. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
    5. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq
    6. taylorWithinEval
    7. Filter.Eventually.of_forall
    8. hMeas
    9. hBound
    10. hBoundInt
    11. eq:general_moving_target_SALD_frozen_interp
    12. appendix.tex:984-995
    13. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    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.cycle163.remaining_normalized_remainder_source_identification
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem after the lower_2 source-shaped remainder bridge: provide eventual AEStronglyMeasurable and domination/integrability for the concrete selected-test normalized remainder, and separately prove the Taylor moment decomposition plus Brownian quadratic-variation 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.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE
    2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
    3. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT
    4. hMeas
    5. hBound
    6. hBoundInt
    7. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
    8. hFrozenScalarBrownianItoTaylorMomentDecomposition
    9. hFrozenScalarBrownianItoQuadraticVariationNormalization
    10. hFrozenScalarBrownianItoEventFieldCoordinateSum
    11. eq:general_moving_target_SALD_frozen_interp
    12. appendix.tex:984-995
    13. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
    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.cycle163.reviewer_pointwise_taylor_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the compiled theorem targets the source Taylor hPoint or the concrete normalized-remainder source equality below the normalized remainder DCT theorem, the Taylor moment and quadratic-variation hypotheses 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.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorLowerObligation
    2. SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation
    3. SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE
    4. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq
    5. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
    6. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT
    7. appendix.tex:984-995
    8. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 163 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 cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle163.lower_packet.selected_test_line_taylor_hpoint"
      interface := "Compiled theorem: SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE supplies the a.e. Gaussian pointwise Tendsto hPoint for the scaled selected-test line r |-> sourceTest (x + r • e), using ContDiffOn Real 2 and Mathlib Real.taylor_tendsto."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorLowerObligation",
        "SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE",
        "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT",
        "Real.taylor_tendsto",
        "Mathlib.Analysis.Calculus.Taylor",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle163.lower_1_packet.normalized_remainder_source_eq_to_dct"
      interface := "Compiled lower_1 scout bridge: SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq consumes an eventual Gaussian-a.e. source equality hSourceEq between normalizedRemainder and the scaled selected-test line Taylor remainder, then derives the DCT integral limit from the compiled pointwise Taylor theorem and SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq",
        "SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE",
        "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT",
        "Filter.Tendsto.congr'",
        "hSourceEq",
        "hMeas",
        "hBound",
        "hBoundInt",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle163.lower_2_packet.normalized_remainder_source_eq"
      interface := "Compiled lower_2 bridge: SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq supplies the hSourceEq input by definitional equality for the concrete source-shaped selected-test normalized remainder, and SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero derives the DCT integral limit without an hSourceEq premise."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq",
        "taylorWithinEval",
        "Filter.Eventually.of_forall",
        "hMeas",
        "hBound",
        "hBoundInt",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle163.remaining_normalized_remainder_source_identification"
      interface := "Remaining exact theorem after the lower_2 source-shaped remainder bridge: provide eventual AEStronglyMeasurable and domination/integrability for the concrete selected-test normalized remainder, and separately prove the Taylor moment decomposition plus Brownian quadratic-variation normalization."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT",
        "hMeas",
        "hBound",
        "hBoundInt",
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "hFrozenScalarBrownianItoTaylorMomentDecomposition",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "hFrozenScalarBrownianItoEventFieldCoordinateSum",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle163.reviewer_pointwise_taylor_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the compiled theorem targets the source Taylor hPoint or the concrete normalized-remainder source equality below the normalized remainder DCT theorem, the Taylor moment and quadratic-variation hypotheses remain explicit, and python3 tools/astis.py check passes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseTaylorLowerObligation",
        "SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation",
        "SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 163 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 164: measurability for the concrete normalized remainder -/

/-- Cycle-164 lower packet for the concrete selected-test remainder `hMeas`.

The refreshed blueprint and upper handoff select only the eventual
`AEStronglyMeasurable` input below the concrete DCT theorem.  This packet
discharges that supplied hypothesis from the selected one-dimensional line
regularity; domination and integrability remain separate source-cited inputs.
-/

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