AutoSamplingTheory.SALD.cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandPointwiseDag

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 cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandPointwiseDag :
    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.cycle186.lower_1_packet.source_taylor_integrand_pointwise_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: prove hSourceTaylorIntegrandPointwise by first identifying the paper sourceTaylorIntegrand as the sum of the source scalar linear term, source scalar quadratic term, and normalizedRemainder for the frozen Brownian coordinate, then identify the two source terms with linearCoeff*z and quadraticCoeff*z^2. Keep the scalar-law pushforward fields, normalized-remainder measurability/domination, and source-Hessian contract gaps separate.
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/20260612-015813-121084-ASTIS-SALD-001-cycle186/middle_source_taylor_integrand_pointwise_packet.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hSourceTaylorIntegrandPointwise
2. hSourceTaylorIntegrandDef
3. hSourceLinearTermDef
4. hSourceQuadraticTermDef
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.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
2. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise
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.cycle186.lower_2_packet.source_taylor_integrand_line_term_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSourceTaylorIntegrandPointwise from hSourceTaylorIntegrandDef, hSourceLinearTermDef, and hSourceQuadraticTermDef by SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs.
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.cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandPointwiseMiddleObligation
2. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
3. hSourceTaylorIntegrandDef
4. hSourceLinearTermDef
5. hSourceQuadraticTermDef
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSourceTaylorIntegrandPointwise
2. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise
3. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralAndAE
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.cycle186.remaining_source_taylor_integrand_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the pointwise source-term split: hSourceTaylorIntegrandDef, hSourceLinearTermDef, hSourceQuadraticTermDef, hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedRemainderMeas, hRemainderPullbackDef, 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. hSourceTaylorIntegrandDef
2. hSourceLinearTermDef
3. hSourceQuadraticTermDef
4. hScalarMeas
5. hNormalizedCoordinateLawDef
6. hSourceTaylorIntegrandMeas
7. hGeneratorPullbackDef
8. hNormalizedRemainderMeas
9. hRemainderPullbackDef
10. hRemainderMeas
11. hRemainderBound
12. hRemainderBoundInt
13. 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 cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandPointwiseDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle186.lower_1_packet.source_taylor_integrand_pointwise_route"
      interface := "Natural-language route: prove hSourceTaylorIntegrandPointwise by first identifying the paper sourceTaylorIntegrand as the sum of the source scalar linear term, source scalar quadratic term, and normalizedRemainder for the frozen Brownian coordinate, then identify the two source terms with linearCoeff*z and quadraticCoeff*z^2. Keep the scalar-law pushforward fields, normalized-remainder measurability/domination, and source-Hessian contract gaps separate."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-015813-121084-ASTIS-SALD-001-cycle186/middle_source_taylor_integrand_pointwise_packet.md"
      dependsOn := [
        "hSourceTaylorIntegrandPointwise",
        "hSourceTaylorIntegrandDef",
        "hSourceLinearTermDef",
        "hSourceQuadraticTermDef",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise",
        "hBrownianCoordinateGeneratorTaylorIntegralDef"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle186.lower_2_packet.source_taylor_integrand_line_term_bridge"
      interface := "Compiled bridge: derive hSourceTaylorIntegrandPointwise from hSourceTaylorIntegrandDef, hSourceLinearTermDef, and hSourceQuadraticTermDef by SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandPointwiseMiddleObligation",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "hSourceTaylorIntegrandDef",
        "hSourceLinearTermDef",
        "hSourceQuadraticTermDef"
      ]
      reusedBy := [
        "hSourceTaylorIntegrandPointwise",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralAndAE"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle186.remaining_source_taylor_integrand_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the pointwise source-term split: hSourceTaylorIntegrandDef, hSourceLinearTermDef, hSourceQuadraticTermDef, hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedRemainderMeas, hRemainderPullbackDef, hRemainderMeas, hRemainderBound, and hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hSourceTaylorIntegrandDef",
        "hSourceLinearTermDef",
        "hSourceQuadraticTermDef",
        "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 186 lower_2: source linear term first-coefficient bridge -/

/-- Cycle-186 lower_2 packet for the source linear term leaf.

This narrows `hSourceLinearTermDef` to the two smaller source-cited fields
identified by the lower_1 proof scout: the first-order Taylor source term along
the selected scalar Brownian line, and the convention identifying
`linearCoeff` with that first directional derivative.
-/

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