AutoSamplingTheory.SALD.cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralRawTermsDag

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 cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralRawTermsDag :
    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.cycle189.middle_packet.coordinate_taylor_integral_raw_terms_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hBrownianCoordinateGeneratorTaylorIntegralDef from hBrownianCoordinateGeneratorSourceIntegralDef plus hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, and hScalarLineTaylorCoeffDef by SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs.
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. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
2. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralAndAE
3. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
4. SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs
5. SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef
6. SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef
7. hBrownianCoordinateGeneratorSourceIntegralDef
8. hSourceTaylorIntegrandRawDef
9. hSelectedLineTaylorRawSplitDef
10. hSourceLinearTermTaylorDef
11. hScalarLineFirstCoeffDef
12. hSourceQuadraticTermTaylorDef
13. hScalarLineTaylorCoeffDef
14. appendix.tex:958-970
15. appendix.tex:984-995
16. appendix.tex:1170-1176
17. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hBrownianCoordinateGeneratorTaylorIntegralDef
2. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.general_moving_target_discrete.kl_derivative
5. 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.cycle189.remaining_coordinate_taylor_integral_raw_terms_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the raw-term coordinate Taylor integral bridge: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar pushforward/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, and hRemainderMeas/hRemainderBound/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. hBrownianCoordinateGeneratorSourceIntegralDef
2. hSourceTaylorIntegrandRawDef
3. hSelectedLineTaylorRawSplitDef
4. hSourceLinearTermTaylorDef
5. hScalarLineFirstCoeffDef
6. hSourceQuadraticTermTaylorDef
7. hScalarLineTaylorCoeffDef
8. hScalarMeas
9. hNormalizedCoordinateLawDef
10. hSourceTaylorIntegrandMeas
11. hGeneratorPullbackDef
12. hNormalizedRemainderMeas
13. hRemainderPullbackDef
14. hRemainderGeneratorLimitDef
15. hRemainderMeas
16. hRemainderBound
17. hRemainderBoundInt
18. 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 cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralRawTermsDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle189.middle_packet.coordinate_taylor_integral_raw_terms_bridge"
      interface := "Compiled bridge: derive hBrownianCoordinateGeneratorTaylorIntegralDef from hBrownianCoordinateGeneratorSourceIntegralDef plus hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, and hScalarLineTaylorCoeffDef by SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralAndAE",
        "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
        "SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs",
        "SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef",
        "SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef",
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder",
        "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.cycle189.remaining_coordinate_taylor_integral_raw_terms_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the raw-term coordinate Taylor integral bridge: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar pushforward/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "hRemainderGeneratorLimitDef",
        "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 189 lower_2: source Taylor integrand raw selected-increment bridge -/

/-- Cycle-189 lower_2 packet for the raw source Taylor integrand leaf.

This narrows `hSourceTaylorIntegrandRawDef` to two smaller source-cited
definition fields.  The compiled theorem only composes those fields: the
paper's source Taylor integrand is named as the selected weak-test increment,
and that selected increment is then identified with the normalized scalar
Brownian coordinate line.
-/

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