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

AutoSamplingTheory.SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneDag

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 cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneDag :
    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.cycle176.lower_1_packet.variance_one_normalized_source_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower_1 proof-scout route: narrow hVarianceOne to the source-facing normalized Brownian variance definition hNormalizedVarianceDef, then lower_2 can recover the downstream Real equality by NNReal-to-Real coercion simplification.
    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.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneLower1Obligation
    2. SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef
    3. hVarianceOne
    4. hNormalizedVarianceDef
    5. eq:SALD_general_EM
    6. eq:general_moving_target_SALD_frozen_interp
    7. eq:increment_basic_bound_revised
    8. appendix.tex:958-970
    9. appendix.tex:984-995
    10. appendix.tex:1170-1176
    11. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef
    2. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
    3. hFrozenScalarBrownianItoQuadraticVariationNormalization
    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
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle176.middle_packet.variance_one_from_normalized_brownian_field
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled theorem: SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef derives the downstream real-valued hVarianceOne field from the smaller source-facing normalized Brownian variance definition hNormalizedVarianceDef : variance phi x i = (1 : NNReal).
    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.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneMiddleObligation
    2. SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef
    3. hVarianceOne
    4. hNormalizedVarianceDef
    5. eq:SALD_general_EM
    6. eq:general_moving_target_SALD_frozen_interp
    7. eq:increment_basic_bound_revised
    8. appendix.tex:958-970
    9. appendix.tex:984-995
    10. appendix.tex:1170-1176
    11. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
    2. hFrozenScalarBrownianItoQuadraticVariationNormalization
    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
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle176.lower_2_packet.quadratic_variation_from_second_taylor_and_normalized_variance
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled lower_2 bridge: SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef derives the quadratic-variation normalization directly from the source-facing hSecondTaylorCoeffDef and hNormalizedVarianceDef fields, composing the cycle-175 coefficient bridge with the normalized-variance bridge.
    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.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneLower2Obligation
    2. SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef
    3. SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef
    4. SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef
    5. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
    6. hSecondTaylorCoeffDef
    7. hNormalizedVarianceDef
    8. hQuadraticCoeffDef
    9. hVarianceOne
    10. appendix.tex:958-970
    11. appendix.tex:984-995
    12. appendix.tex:1170-1176
    13. appendix.tex:1379-1387
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. hFrozenScalarBrownianItoQuadraticVariationNormalization
    2. Brownian/Ito scalar generator bookkeeping
    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
  4. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle176.remaining_variance_source_boundary
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact boundary after the cycle-176 bridges: source hSecondTaylorCoeffDef and hNormalizedVarianceDef from the standard Gaussian coordinate normalization xi ~ N(0,I) and the selected-line second Taylor coefficient correspondence. Keep 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. hNormalizedVarianceDef
    2. hSecondTaylorCoeffDef
    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. hFrozenScalarBrownianItoQuadraticVariationNormalization
    2. Brownian/Ito scalar generator bookkeeping
    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
  5. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle176.reviewer_variance_one_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer accepts only if the packet is narrows-source-cited-boundary, hVarianceOne is narrowed to hNormalizedVarianceDef rather than restated, hSecondTaylorCoeffDef and source-Hessian fields remain source-facing gaps, sibling Brownian/Ito 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.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneMiddleObligation
    2. SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneLower2Obligation
    3. SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef
    4. SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef
    5. ASTIS.SALD.cycle176.remaining_variance_source_boundary
    6. hVarianceOne
    7. hNormalizedVarianceDef
    8. hSecondTaylorCoeffDef
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. cycle 176 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 cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle176.lower_1_packet.variance_one_normalized_source_route"
      interface := "Lower_1 proof-scout route: narrow hVarianceOne to the source-facing normalized Brownian variance definition hNormalizedVarianceDef, then lower_2 can recover the downstream Real equality by NNReal-to-Real coercion simplification."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneLower1Obligation",
        "SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef",
        "hVarianceOne",
        "hNormalizedVarianceDef",
        "eq:SALD_general_EM",
        "eq:general_moving_target_SALD_frozen_interp",
        "eq:increment_basic_bound_revised",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle176.middle_packet.variance_one_from_normalized_brownian_field"
      interface := "Compiled theorem: SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef derives the downstream real-valued hVarianceOne field from the smaller source-facing normalized Brownian variance definition hNormalizedVarianceDef : variance phi x i = (1 : NNReal)."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneMiddleObligation",
        "SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef",
        "hVarianceOne",
        "hNormalizedVarianceDef",
        "eq:SALD_general_EM",
        "eq:general_moving_target_SALD_frozen_interp",
        "eq:increment_basic_bound_revised",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle176.lower_2_packet.quadratic_variation_from_second_taylor_and_normalized_variance"
      interface := "Compiled lower_2 bridge: SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef derives the quadratic-variation normalization directly from the source-facing hSecondTaylorCoeffDef and hNormalizedVarianceDef fields, composing the cycle-175 coefficient bridge with the normalized-variance bridge."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneLower2Obligation",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef",
        "SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef",
        "SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
        "hSecondTaylorCoeffDef",
        "hNormalizedVarianceDef",
        "hQuadraticCoeffDef",
        "hVarianceOne",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "Brownian/Ito scalar generator bookkeeping",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle176.remaining_variance_source_boundary"
      interface := "Remaining exact boundary after the cycle-176 bridges: source hSecondTaylorCoeffDef and hNormalizedVarianceDef from the standard Gaussian coordinate normalization xi ~ N(0,I) and the selected-line second Taylor coefficient correspondence. Keep hSourceHasHessian/hSourceHessianBound, hSecondCoeff, Taylor moment decomposition, DCT data, and coordinate-sum explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hNormalizedVarianceDef",
        "hSecondTaylorCoeffDef",
        "hSourceHasHessian",
        "hSourceHessianBound",
        "hSecondCoeff",
        "hFrozenScalarBrownianItoTaylorMomentDecomposition",
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "hFrozenScalarBrownianItoEventFieldCoordinateSum",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFrozenScalarBrownianItoQuadraticVariationNormalization",
        "Brownian/Ito scalar generator bookkeeping",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle176.reviewer_variance_one_check"
      interface := "Reviewer accepts only if the packet is narrows-source-cited-boundary, hVarianceOne is narrowed to hNormalizedVarianceDef rather than restated, hSecondTaylorCoeffDef and source-Hessian fields remain source-facing gaps, sibling Brownian/Ito leaves remain explicit, and python3 tools/astis.py check passes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneMiddleObligation",
        "SALD.cycle176GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoVarianceOneLower2Obligation",
        "SALD.selectedWeakTestVarianceOneOfNormalizedBrownianVarianceDef",
        "SALD.selectedWeakTestQuadraticVariationNormalizationOfSecondTaylorCoeffAndNormalizedVarianceDef",
        "ASTIS.SALD.cycle176.remaining_variance_source_boundary",
        "hVarianceOne",
        "hNormalizedVarianceDef",
        "hSecondTaylorCoeffDef"
      ]
      reusedBy := ["cycle 176 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 177 middle: scalar-line second Taylor coefficient packet -/

/-- Cycle-177 middle packet for the remaining Brownian/Ito coefficient side.

The selected weak-test Hessian fields are kept as source-contract gaps after
the source audit.  This packet narrows the connected coefficient leaf
`hSecondTaylorCoeffDef` to a scalar-line second Taylor coefficient definition
plus the already explicit ambient selected-test regularity needed by the local
chain-rule bridge.
-/

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