AutoSamplingTheory.SALD.cycle193GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleDag

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 cycle193GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleDag :
    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.cycle193.middle_packet.taylor_moment_scalar_pushforward_remainder_discharge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive the Taylor moment decomposition without primitive hBrownianCoordinateGeneratorTaylorIntegralDef or hRemainderGeneratorLimitDef by composing the cycle-192 Taylor-integral scalar-pushforward/raw-terms bridge, the cycle-190 remainder-limit scalar-pushforward bridge, and the dominated remainder integrability bridge.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfScalarPushforwardRawTaylorAndDominatedRemainder
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle193GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation
2. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfScalarPushforwardRawTaylorAndDominatedRemainder
3. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsDominatedRemainderAndRemainderLimitScalarPushforward
4. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs
5. SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw
6. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder
7. hBrownianCoordinateGeneratorTaylorIntegralDef
8. hRemainderGeneratorLimitDef
9. appendix.tex:958-970
10. appendix.tex:983-996
11. appendix.tex:1161-1170
12. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. Taylor moment split
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.general_moving_target_discrete.kl_derivative
4. divergence/FI/IBP handoff
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.cycle193.remaining_taylor_moment_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito backend after the cycle-193 composition bridge: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedRemainderMeas, hRemainderPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, hRemainderMeas, hRemainderBound, and hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — 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. hScalarMeas
2. hNormalizedCoordinateLawDef
3. hSourceTaylorIntegrandMeas
4. hGeneratorPullbackDef
5. hNormalizedRemainderMeas
6. hRemainderPullbackDef
7. hNormalizedVectorLaw
8. hCoordinateLawDef
9. hVarianceDef
10. hSourceTaylorIntegrandRawDef
11. hSelectedLineTaylorRawSplitDef
12. hSourceLinearTermTaylorDef
13. hScalarLineFirstCoeffDef
14. hSourceQuadraticTermTaylorDef
15. hScalarLineTaylorCoeffDef
16. hRemainderMeas
17. hRemainderBound
18. hRemainderBoundInt
19. source-contract-gap for selected weak-test Hessian fields
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.general_moving_target_discrete.kl_derivative
3. divergence/FI/IBP handoff
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 cycle193GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle193.middle_packet.taylor_moment_scalar_pushforward_remainder_discharge"
      interface := "Compiled bridge: derive the Taylor moment decomposition without primitive hBrownianCoordinateGeneratorTaylorIntegralDef or hRemainderGeneratorLimitDef by composing the cycle-192 Taylor-integral scalar-pushforward/raw-terms bridge, the cycle-190 remainder-limit scalar-pushforward bridge, and the dominated remainder integrability bridge."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfScalarPushforwardRawTaylorAndDominatedRemainder"
      dependsOn := [
        "SALD.cycle193GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfScalarPushforwardRawTaylorAndDominatedRemainder",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsDominatedRemainderAndRemainderLimitScalarPushforward",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs",
        "SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder",
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "hRemainderGeneratorLimitDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "Taylor moment split",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle193.remaining_taylor_moment_backend"
      interface := "Remaining exact Brownian/Ito backend after the cycle-193 composition bridge: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedRemainderMeas, hRemainderPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, hRemainderMeas, hRemainderBound, and hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "hRemainderMeas",
        "hRemainderBound",
        "hRemainderBoundInt",
        "source-contract-gap for selected weak-test Hessian fields"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 197 lower_2: normalized-remainder bound-definition source gap -/

/-- Cycle-197 lower_2 packet for the normalized remainder bound definition.

The existing Lean declarations treat `remainderBound` and `remainderBoundC`
as parameters.  Therefore the source-facing equality
`remainderBound phi x i z = remainderBoundC phi x i * z ^ 2` is not a
definitional unfolding available to Lean.  This obligation records the smaller
source-cited blocker instead of adding a wrapper that assumes the same
equality under another name.
-/

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