AutoSamplingTheory.SALD.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasDag

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 cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasDag :
    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

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle164.lower_packet.normalized_remainder_hmeas
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable supplies the eventual AEStronglyMeasurable hMeas input for the concrete selected-test normalized Taylor remainder from ContDiffOn Real 2 line 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.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasLowerObligation
2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable
3. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder
4. ContDiffOn.continuousOn
5. hasDerivAt_taylorWithinEval_succ
6. Continuous.comp_aestronglyMeasurable
7. MeasureTheory.AEStronglyMeasurable.div₀
8. eq:general_moving_target_SALD_frozen_interp
9. appendix.tex:984-995
10. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
2. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle164.lower_2_packet.normalized_remainder_quadratic_bound_integrable
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable supplies the DCT hBoundInt input for the quadratic Gaussian bound fun z => C * z ^ 2, using Mathlib Gaussian exponential moments and integrable powers. The remaining domination leaf is hBound for the concrete selected-test normalized remainder against that bound.
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.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderQuadraticBoundIntLowerObligation
2. SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable
3. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
4. ProbabilityTheory.integrable_exp_mul_gaussianReal
5. ProbabilityTheory.integrable_pow_of_integrable_exp_mul
6. MeasureTheory.Integrable.const_mul
7. Mathlib.Probability.Distributions.Gaussian.Real
8. Mathlib.Probability.Moments.IntegrableExpMul
9. appendix.tex:984-995
10. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
2. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle164.remaining_normalized_remainder_domination
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem after the hMeas and quadratic hBoundInt discharge: provide hBound for the concrete selected-test normalized remainder against the quadratic Gaussian bound fun z => C * z ^ 2, and separately prove the Taylor moment decomposition, Brownian quadratic-variation normalization, and coordinate-sum leaves.
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.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable
2. SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable
3. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
4. hBound
5. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
6. hFrozenScalarBrownianItoTaylorMomentDecomposition
7. hFrozenScalarBrownianItoQuadraticVariationNormalization
8. hFrozenScalarBrownianItoEventFieldCoordinateSum
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. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle164.reviewer_hmeas_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis, the concrete hMeas premise is eliminated by a compiled theorem rather than renamed, hBound/hBoundInt and the moment/normalization/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.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasLowerObligation
2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable
3. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
4. appendix.tex:984-995
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 164 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 cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle164.lower_packet.normalized_remainder_hmeas"
      interface := "Compiled theorem: SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable supplies the eventual AEStronglyMeasurable hMeas input for the concrete selected-test normalized Taylor remainder from ContDiffOn Real 2 line regularity."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasLowerObligation",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder",
        "ContDiffOn.continuousOn",
        "hasDerivAt_taylorWithinEval_succ",
        "Continuous.comp_aestronglyMeasurable",
        "MeasureTheory.AEStronglyMeasurable.div₀",
        "eq:general_moving_target_SALD_frozen_interp",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle164.lower_2_packet.normalized_remainder_quadratic_bound_integrable"
      interface := "Compiled theorem: SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable supplies the DCT hBoundInt input for the quadratic Gaussian bound fun z => C * z ^ 2, using Mathlib Gaussian exponential moments and integrable powers. The remaining domination leaf is hBound for the concrete selected-test normalized remainder against that bound."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderQuadraticBoundIntLowerObligation",
        "SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "ProbabilityTheory.integrable_exp_mul_gaussianReal",
        "ProbabilityTheory.integrable_pow_of_integrable_exp_mul",
        "MeasureTheory.Integrable.const_mul",
        "Mathlib.Probability.Distributions.Gaussian.Real",
        "Mathlib.Probability.Moments.IntegrableExpMul",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle164.remaining_normalized_remainder_domination"
      interface := "Remaining exact theorem after the hMeas and quadratic hBoundInt discharge: provide hBound for the concrete selected-test normalized remainder against the quadratic Gaussian bound fun z => C * z ^ 2, and separately prove the Taylor moment decomposition, Brownian quadratic-variation normalization, and coordinate-sum leaves."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable",
        "SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "hBound",
        "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.cycle164.reviewer_hmeas_check"
      interface := "Reviewer check: accept only if the packet classification is discharges-supplied-hypothesis, the concrete hMeas premise is eliminated by a compiled theorem rather than renamed, hBound/hBoundInt and the moment/normalization/coordinate-sum leaves remain explicit, and python3 tools/astis.py check passes."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderMeasLowerObligation",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderEventuallyAEStronglyMeasurable",
        "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 164 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 165: quadratic domination for the concrete normalized remainder -/

/-- Cycle-165 lower packet for the concrete selected-test remainder `hBound`.

The refreshed blueprint after cycle 164 leaves the pointwise domination input
as the next dynamic leaf.  This packet compiles the local algebraic bridge from
a deterministic scalar Taylor quotient bound to the exact eventual a.e.
quadratic domination shape consumed by the DCT theorem.
-/

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