AutoSamplingTheory.SALD.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorSplitLower2Dag

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 cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorSplitLower2Dag :
    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.cycle188.lower_2_packet.selected_line_taylor_raw_term_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSelectedLineTaylorSplitDef from hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, and hSourceQuadraticTermTaylorDef by SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs.
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.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorSplitLower2Obligation
2. SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs
3. hSelectedLineTaylorRawSplitDef
4. hSourceLinearTermTaylorDef
5. hSourceQuadraticTermTaylorDef
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSelectedLineTaylorSplitDef
2. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
3. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
4. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise
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.cycle188.remaining_selected_line_taylor_split_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the selected-line Taylor split bridge: hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar pushforward/measurability fields, normalized-remainder pullback fields, 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. hSourceTaylorIntegrandRawDef
2. hSelectedLineTaylorRawSplitDef
3. hSourceLinearTermTaylorDef
4. hScalarLineFirstCoeffDef
5. hSourceQuadraticTermTaylorDef
6. hScalarLineTaylorCoeffDef
7. hScalarMeas
8. hNormalizedCoordinateLawDef
9. hSourceTaylorIntegrandMeas
10. hGeneratorPullbackDef
11. hNormalizedRemainderMeas
12. hRemainderPullbackDef
13. hRemainderMeas
14. hRemainderBound
15. hRemainderBoundInt
16. 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 cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorSplitLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle188.lower_2_packet.selected_line_taylor_raw_term_bridge"
      interface := "Compiled bridge: derive hSelectedLineTaylorSplitDef from hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, and hSourceQuadraticTermTaylorDef by SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorSplitLower2Obligation",
        "SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hSourceQuadraticTermTaylorDef"
      ]
      reusedBy := [
        "hSelectedLineTaylorSplitDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle188.remaining_selected_line_taylor_split_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the selected-line Taylor split bridge: hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar pushforward/measurability fields, normalized-remainder pullback fields, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "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 middle: coordinate Taylor integral from raw selected-line data -/

/-- Cycle-189 packet for the Brownian coordinate Taylor integral leaf.

This composes the cycle-183 source-integral/a.e. bridge with the cycle-186,
cycle-187, and cycle-188 source Taylor bridges.  The older top-level
`hBrownianCoordinateGeneratorTaylorIntegralDef` no longer needs
`hBrownianCoordinateGeneratorTaylorIntegrandAE` or
`hSourceTaylorIntegrandPointwise` as primitive supplied hypotheses.
-/

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