AutoSamplingTheory.SALD.cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandRawLower2Dag

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 cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandRawLower2Dag :
    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.lower_2_packet.source_taylor_integrand_raw_selected_increment_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSourceTaylorIntegrandRawDef from hSourceTaylorIntegrandSelectedIncrementDef and hSelectedIncrementCoordinateLineDef by SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef.
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.cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandRawLower2Obligation
2. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
3. hSourceTaylorIntegrandSelectedIncrementDef
4. hSelectedIncrementCoordinateLineDef
5. appendix.tex:958-970
6. appendix.tex:983-996
7. appendix.tex:1161-1170
8. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSourceTaylorIntegrandRawDef
2. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
3. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
4. sald.general_moving_target_discrete.em_interpolation_fp
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_source_taylor_integrand_raw_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the raw selected-increment bridge: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementCoordinateLineDef, 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. hSourceTaylorIntegrandSelectedIncrementDef
3. hSelectedIncrementCoordinateLineDef
4. hSelectedLineTaylorRawSplitDef
5. hSourceLinearTermTaylorDef
6. hScalarLineFirstCoeffDef
7. hSourceQuadraticTermTaylorDef
8. hScalarLineTaylorCoeffDef
9. hScalarMeas
10. hNormalizedCoordinateLawDef
11. hSourceTaylorIntegrandMeas
12. hGeneratorPullbackDef
13. hNormalizedRemainderMeas
14. hRemainderPullbackDef
15. hRemainderGeneratorLimitDef
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 cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandRawLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle189.lower_2_packet.source_taylor_integrand_raw_selected_increment_bridge"
      interface := "Compiled bridge: derive hSourceTaylorIntegrandRawDef from hSourceTaylorIntegrandSelectedIncrementDef and hSelectedIncrementCoordinateLineDef by SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandRawLower2Obligation",
        "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
        "hSourceTaylorIntegrandSelectedIncrementDef",
        "hSelectedIncrementCoordinateLineDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hSourceTaylorIntegrandRawDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle189.remaining_source_taylor_integrand_raw_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the raw selected-increment bridge: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementCoordinateLineDef, 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",
        "hSourceTaylorIntegrandSelectedIncrementDef",
        "hSelectedIncrementCoordinateLineDef",
        "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 190 middle: selected-increment endpoint/coordinate-line bridge -/

/-- Cycle-190 middle packet for the selected-increment coordinate-line leaf.

This narrows `hSelectedIncrementCoordinateLineDef` to two smaller source-cited
definition fields: the selected increment is the selected weak-test value at a
named normalized frozen endpoint minus its base value, and that endpoint is the
standard-basis coordinate line from the normalized Brownian increment.
-/

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