AutoSamplingTheory.SALD.cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormDag

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 cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormDag :
    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.cycle170.lower_2_packet.hsecond_fderiv_from_hessian_op_norm
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm converts a uniform operator-norm bound on fderiv Real (fderiv Real sourceTest) into the hSecondFDerivOpNorm shape consumed by the cycle-169/170 selected-test directional-Hessian 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.cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormLower2Obligation
2. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
3. norm_iteratedFDeriv_fderiv
4. norm_iteratedFDeriv_one
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
2. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSourceContDiffOnAndDirectionalSecondBound
3. hDirectionalSecond
4. hSecondFDerivOpNorm
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.cycle170.remaining_selected_test_hessian_operator_norm_source_contract
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact source-contract gap after cycle 170 lower_2: expose the selected weak-test C2_b/bounded-Hessian field forall z, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 from the paper/testRegular interface. Do not replace this by an opaque testRegular-to-hSecondFDerivOpNorm wrapper.
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.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
2. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
3. hHessianOpNorm
4. selected weak-test C2_b/bounded-Hessian source interface
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSecondFDerivOpNorm
2. hDirectionalSecond
3. selected-line Taylor domination
4. scalar Ito Brownian coordinate generator leaves
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 cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle170.lower_2_packet.hsecond_fderiv_from_hessian_op_norm"
      interface := "Compiled theorem: SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm converts a uniform operator-norm bound on fderiv Real (fderiv Real sourceTest) into the hSecondFDerivOpNorm shape consumed by the cycle-169/170 selected-test directional-Hessian bridge."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormLower2Obligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "norm_iteratedFDeriv_fderiv",
        "norm_iteratedFDeriv_one",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
        "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSourceContDiffOnAndDirectionalSecondBound",
        "hDirectionalSecond",
        "hSecondFDerivOpNorm"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle170.remaining_selected_test_hessian_operator_norm_source_contract"
      interface := "Remaining exact source-contract gap after cycle 170 lower_2: expose the selected weak-test C2_b/bounded-Hessian field forall z, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 from the paper/testRegular interface. Do not replace this by an opaque testRegular-to-hSecondFDerivOpNorm wrapper."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
        "hHessianOpNorm",
        "selected weak-test C2_b/bounded-Hessian source interface",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hSecondFDerivOpNorm",
        "hDirectionalSecond",
        "selected-line Taylor domination",
        "scalar Ito Brownian coordinate generator leaves"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 171 middle: selected-test Hessian source-contract refiner -/

/-- Cycle-171 middle refiner rejecting an opaque `testRegular` wrapper for the
remaining selected-test Hessian source contract. -/

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