AutoSamplingTheory.SALD.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefDag

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 cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefDag :
    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_1_packet.source_taylor_integrand_def_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: narrow hSourceTaylorIntegrandDef to hSourceTaylorIntegrandRawDef plus hSelectedLineTaylorSplitDef. The raw field says the paper sourceTaylorIntegrand is the selected weak-test increment along the normalized scalar Brownian coordinate line; the split field is the source scalar Taylor decomposition into sourceLinearTerm, sourceQuadraticTerm, and normalizedRemainder.
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/20260612-025449-004585-ASTIS-SALD-001-cycle188/lower_1_source_taylor_integrand_def_route.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hSourceTaylorIntegrandDef
2. hSourceTaylorIntegrandRawDef
3. hSelectedLineTaylorSplitDef
4. appendix.tex:958-970
5. appendix.tex:984-995
6. appendix.tex:1170-1176
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
2. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
3. hBrownianCoordinateGeneratorTaylorIntegralDef
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.cycle188.lower_2_packet.source_taylor_integrand_raw_split_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSourceTaylorIntegrandDef from hSourceTaylorIntegrandRawDef and hSelectedLineTaylorSplitDef by SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit.
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.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefMiddleObligation
2. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
3. hSourceTaylorIntegrandRawDef
4. hSelectedLineTaylorSplitDef
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSourceTaylorIntegrandDef
2. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
3. 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_source_taylor_integrand_def_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the source-integrand definition bridge: hSourceTaylorIntegrandRawDef, hSelectedLineTaylorSplitDef, 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. hSelectedLineTaylorSplitDef
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 cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle188.lower_1_packet.source_taylor_integrand_def_route"
      interface := "Natural-language route: narrow hSourceTaylorIntegrandDef to hSourceTaylorIntegrandRawDef plus hSelectedLineTaylorSplitDef. The raw field says the paper sourceTaylorIntegrand is the selected weak-test increment along the normalized scalar Brownian coordinate line; the split field is the source scalar Taylor decomposition into sourceLinearTerm, sourceQuadraticTerm, and normalizedRemainder."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-025449-004585-ASTIS-SALD-001-cycle188/lower_1_source_taylor_integrand_def_route.md"
      dependsOn := [
        "hSourceTaylorIntegrandDef",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorSplitDef",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "hBrownianCoordinateGeneratorTaylorIntegralDef"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle188.lower_2_packet.source_taylor_integrand_raw_split_bridge"
      interface := "Compiled bridge: derive hSourceTaylorIntegrandDef from hSourceTaylorIntegrandRawDef and hSelectedLineTaylorSplitDef by SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefMiddleObligation",
        "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
        "hSourceTaylorIntegrandRawDef",
        "hSelectedLineTaylorSplitDef"
      ]
      reusedBy := [
        "hSourceTaylorIntegrandDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle188.remaining_source_taylor_integrand_def_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the source-integrand definition bridge: hSourceTaylorIntegrandRawDef, hSelectedLineTaylorSplitDef, 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",
        "hSelectedLineTaylorSplitDef",
        "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 188 lower_2: selected-line Taylor split raw-term bridge -/

/-- Cycle-188 lower_2 packet for the selected-line Taylor split leaf.

This narrows `hSelectedLineTaylorSplitDef` one step further.  The source-facing
Taylor expansion itself remains explicit as `hSelectedLineTaylorRawSplitDef`;
the compiled theorem only substitutes the already tracked source linear and
quadratic Taylor term names into that raw scalar expansion.
-/

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