AutoSamplingTheory.SALD.cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Dag

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 cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Dag :
    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.cycle191.lower_1_packet.source_integral_scalar_pushforward_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: remove hBrownianCoordinateGeneratorNormalizedLawDef from the hBrownianCoordinateGeneratorSourceIntegralDef backend by deriving it from scalar Brownian coordinate pushforward and sourceTaylorIntegrand sample-space pullback fields, then reuse the standard-Gaussian vector coordinate-law and variance bridges.
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/20260612-044238-334925-ASTIS-SALD-001-cycle191/lower_1_source_integral_scalar_pushforward_route.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hBrownianCoordinateGeneratorSourceIntegralDef
2. hBrownianCoordinateGeneratorNormalizedLawDef
3. hScalarMeas
4. hNormalizedCoordinateLawDef
5. hSourceTaylorIntegrandMeas
6. hGeneratorPullbackDef
7. hNormalizedVectorLaw
8. hCoordinateLawDef
9. hVarianceDef
10. appendix.tex:958-970
11. appendix.tex:983-996
12. appendix.tex:1161-1170
13. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw
2. hBrownianCoordinateGeneratorSourceIntegralDef
3. hBrownianCoordinateGeneratorTaylorIntegralDef
4. 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.cycle191.lower_2_packet.source_integral_scalar_pushforward_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hBrownianCoordinateGeneratorSourceIntegralDef directly from scalar pushforward/pullback fields and standard-Gaussian vector coordinate-law fields by SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw.
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.cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Obligation
2. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw
3. SALD.selectedWeakTestBrownianCoordinateGeneratorNormalizedLawDefOfScalarPushforward
4. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfStdGaussianVectorLaw
5. hScalarMeas
6. hNormalizedCoordinateLawDef
7. hSourceTaylorIntegrandMeas
8. hGeneratorPullbackDef
9. hNormalizedVectorLaw
10. hCoordinateLawDef
11. hVarianceDef
12. appendix.tex:958-970
13. appendix.tex:983-996
14. appendix.tex:1161-1170
15. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hBrownianCoordinateGeneratorSourceIntegralDef
2. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
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.cycle191.remaining_source_integral_scalar_pushforward_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the source-integral scalar-pushforward bridge: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, 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. hSourceTaylorIntegrandSelectedIncrementDef
9. hSelectedIncrementEndpointDef
10. hSelectedEndpointCoordinateLineDef
11. hSelectedLineTaylorRawSplitDef
12. hSourceLinearTermTaylorDef
13. hScalarLineFirstCoeffDef
14. hSourceQuadraticTermTaylorDef
15. hScalarLineTaylorCoeffDef
16. hRemainderGeneratorLimitDef
17. hRemainderMeas
18. hRemainderBound
19. hRemainderBoundInt
20. 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 cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle191.lower_1_packet.source_integral_scalar_pushforward_route"
      interface := "Natural-language route: remove hBrownianCoordinateGeneratorNormalizedLawDef from the hBrownianCoordinateGeneratorSourceIntegralDef backend by deriving it from scalar Brownian coordinate pushforward and sourceTaylorIntegrand sample-space pullback fields, then reuse the standard-Gaussian vector coordinate-law and variance bridges."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-044238-334925-ASTIS-SALD-001-cycle191/lower_1_source_integral_scalar_pushforward_route.md"
      dependsOn := [
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hBrownianCoordinateGeneratorNormalizedLawDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle191.lower_2_packet.source_integral_scalar_pushforward_bridge"
      interface := "Compiled bridge: derive hBrownianCoordinateGeneratorSourceIntegralDef directly from scalar pushforward/pullback fields and standard-Gaussian vector coordinate-law fields by SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Obligation",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorNormalizedLawDefOfScalarPushforward",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfStdGaussianVectorLaw",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "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.cycle191.remaining_source_integral_scalar_pushforward_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the source-integral scalar-pushforward bridge: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, 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",
        "hSourceTaylorIntegrandSelectedIncrementDef",
        "hSelectedIncrementEndpointDef",
        "hSelectedEndpointCoordinateLineDef",
        "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 192 lower_2: Taylor-integral scalar-pushforward/raw-term bridge -/

/-- Cycle-192 lower_2 packet for the Brownian Taylor-integral leaf.

The compiled theorem discharges `hBrownianCoordinateGeneratorSourceIntegralDef`
as a primitive supplied hypothesis in the
`hBrownianCoordinateGeneratorTaylorIntegralDef` route.  It composes the
cycle-191 scalar-pushforward source-integral bridge with the cycle-189 raw
selected-line Taylor bridge.
-/

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