AutoSamplingTheory.SALD.cycle187GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceQuadraticTermDag

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 cycle187GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceQuadraticTermDag :
    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.cycle187.lower_1_packet.source_quadratic_term_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: narrow hSourceQuadraticTermDef to hSourceQuadraticTermTaylorDef plus hScalarLineTaylorCoeffDef. The source quadratic term is the order-two scalar Taylor term of q |-> selectedTest phi (x + q • e_i), multiplied by z^2, for the normalized scalar Brownian coordinate; sigma_eta^2/2 remains outside this event-field identity.
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/20260612-023148-576665-ASTIS-SALD-001-cycle187/lower_1_source_quadratic_term_route.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hSourceQuadraticTermDef
2. hSourceQuadraticTermTaylorDef
3. hScalarLineTaylorCoeffDef
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.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef
2. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
3. hSourceTaylorIntegrandPointwise
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.cycle187.lower_2_packet.source_quadratic_term_taylor_coeff_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSourceQuadraticTermDef from hSourceQuadraticTermTaylorDef and hScalarLineTaylorCoeffDef by SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef.
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.cycle187GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceQuadraticTermMiddleObligation
2. SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef
3. hSourceQuadraticTermTaylorDef
4. hScalarLineTaylorCoeffDef
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSourceQuadraticTermDef
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.cycle187.remaining_source_quadratic_term_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the source-quadratic bridge: hSourceTaylorIntegrandDef, 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. hSourceTaylorIntegrandDef
2. hSourceLinearTermTaylorDef
3. hScalarLineFirstCoeffDef
4. hSourceQuadraticTermTaylorDef
5. hScalarLineTaylorCoeffDef
6. hScalarMeas
7. hNormalizedCoordinateLawDef
8. hSourceTaylorIntegrandMeas
9. hGeneratorPullbackDef
10. hNormalizedRemainderMeas
11. hRemainderPullbackDef
12. hRemainderMeas
13. hRemainderBound
14. hRemainderBoundInt
15. 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 cycle187GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceQuadraticTermDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle187.lower_1_packet.source_quadratic_term_route"
      interface := "Natural-language route: narrow hSourceQuadraticTermDef to hSourceQuadraticTermTaylorDef plus hScalarLineTaylorCoeffDef. The source quadratic term is the order-two scalar Taylor term of q |-> selectedTest phi (x + q • e_i), multiplied by z^2, for the normalized scalar Brownian coordinate; sigma_eta^2/2 remains outside this event-field identity."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-023148-576665-ASTIS-SALD-001-cycle187/lower_1_source_quadratic_term_route.md"
      dependsOn := [
        "hSourceQuadraticTermDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "hSourceTaylorIntegrandPointwise"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle187.lower_2_packet.source_quadratic_term_taylor_coeff_bridge"
      interface := "Compiled bridge: derive hSourceQuadraticTermDef from hSourceQuadraticTermTaylorDef and hScalarLineTaylorCoeffDef by SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle187GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceQuadraticTermMiddleObligation",
        "SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef"
      ]
      reusedBy := [
        "hSourceQuadraticTermDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle187.remaining_source_quadratic_term_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the source-quadratic bridge: hSourceTaylorIntegrandDef, 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 := [
        "hSourceTaylorIntegrandDef",
        "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 middle/lower_2: source Taylor integrand definition bridge -/

/-- Cycle-188 packet for the source Taylor integrand definition leaf.

This narrows `hSourceTaylorIntegrandDef` to the raw selected-line increment
definition and the selected-line Taylor split into source linear term, source
quadratic term, and normalized remainder.  It stays inside the Brownian/Ito
frozen-interpolation backend and does not reopen the selected weak-test Hessian
source-contract gap.
-/

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