AutoSamplingTheory.SALD.cycle192GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralLower2Dag

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 cycle192GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralLower2Dag :
    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.cycle192.lower_1_packet.taylor_integral_source_integral_discharge_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: remove hBrownianCoordinateGeneratorSourceIntegralDef from the hBrownianCoordinateGeneratorTaylorIntegralDef backend by deriving the source-integral generator identity from scalar Brownian coordinate pushforward plus standard-Gaussian vector coordinate-law fields, then reuse the raw selected-line Taylor 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.
runs/20260612-050646-484742-ASTIS-SALD-001-cycle192/lower_1_taylor_integral_source_integral_discharge_route.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hBrownianCoordinateGeneratorTaylorIntegralDef
2. hBrownianCoordinateGeneratorSourceIntegralDef
3. hScalarMeas
4. hNormalizedCoordinateLawDef
5. hSourceTaylorIntegrandMeas
6. hGeneratorPullbackDef
7. hNormalizedVectorLaw
8. hCoordinateLawDef
9. hVarianceDef
10. hSourceTaylorIntegrandRawDef
11. hSelectedLineTaylorRawSplitDef
12. hSourceLinearTermTaylorDef
13. hScalarLineFirstCoeffDef
14. hSourceQuadraticTermTaylorDef
15. hScalarLineTaylorCoeffDef
16. appendix.tex:958-970
17. appendix.tex:983-996
18. appendix.tex:1161-1170
19. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs
2. hBrownianCoordinateGeneratorTaylorIntegralDef
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle192.lower_2_packet.taylor_integral_scalar_pushforward_raw_terms_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hBrownianCoordinateGeneratorTaylorIntegralDef directly from scalar pushforward/pullback fields, standard-Gaussian vector coordinate-law fields, and raw selected-line Taylor fields by SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs.
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.cycle192GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralLower2Obligation
2. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs
3. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw
4. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
5. hScalarMeas
6. hNormalizedCoordinateLawDef
7. hSourceTaylorIntegrandMeas
8. hGeneratorPullbackDef
9. hNormalizedVectorLaw
10. hCoordinateLawDef
11. hVarianceDef
12. hSourceTaylorIntegrandRawDef
13. hSelectedLineTaylorRawSplitDef
14. hSourceLinearTermTaylorDef
15. hScalarLineFirstCoeffDef
16. hSourceQuadraticTermTaylorDef
17. hScalarLineTaylorCoeffDef
18. appendix.tex:958-970
19. appendix.tex:983-996
20. appendix.tex:1161-1170
21. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hBrownianCoordinateGeneratorTaylorIntegralDef
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.cycle192.remaining_taylor_integral_scalar_pushforward_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the Taylor-integral scalar-pushforward/raw-terms bridge: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, hRemainderGeneratorLimitDef, 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. hNormalizedVectorLaw
6. hCoordinateLawDef
7. hVarianceDef
8. hSourceTaylorIntegrandRawDef
9. hSelectedLineTaylorRawSplitDef
10. hSourceLinearTermTaylorDef
11. hScalarLineFirstCoeffDef
12. hSourceQuadraticTermTaylorDef
13. hScalarLineTaylorCoeffDef
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 cycle192GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle192.lower_1_packet.taylor_integral_source_integral_discharge_route"
      interface := "Natural-language route: remove hBrownianCoordinateGeneratorSourceIntegralDef from the hBrownianCoordinateGeneratorTaylorIntegralDef backend by deriving the source-integral generator identity from scalar Brownian coordinate pushforward plus standard-Gaussian vector coordinate-law fields, then reuse the raw selected-line Taylor bridge."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-050646-484742-ASTIS-SALD-001-cycle192/lower_1_taylor_integral_source_integral_discharge_route.md"
      dependsOn := [
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs",
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle192.lower_2_packet.taylor_integral_scalar_pushforward_raw_terms_bridge"
      interface := "Compiled bridge: derive hBrownianCoordinateGeneratorTaylorIntegralDef directly from scalar pushforward/pullback fields, standard-Gaussian vector coordinate-law fields, and raw selected-line Taylor fields by SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle192GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralLower2Obligation",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "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.cycle192.remaining_taylor_integral_scalar_pushforward_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the Taylor-integral scalar-pushforward/raw-terms bridge: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, hRemainderGeneratorLimitDef, hRemainderMeas, hRemainderBound, and hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "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 193 middle: Taylor-moment scalar-pushforward/remainder discharge -/

/-- Cycle-193 middle packet for the Taylor moment split consumer.

The compiled theorem discharges the primitive
`hBrownianCoordinateGeneratorTaylorIntegralDef` and
`hRemainderGeneratorLimitDef` supplied hypotheses inside the dominated
remainder Taylor moment decomposition, by composing the cycle-192
Taylor-integral bridge with the cycle-190 remainder-limit bridge.
-/

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