AutoSamplingTheory.SALD.cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceLinearTermLower2Dag

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 cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceLinearTermLower2Dag :
    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_linear_term_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: narrow hSourceLinearTermDef to hSourceLinearTermTaylorDef and hScalarLineFirstCoeffDef using the first-order Taylor term of q |-> selectedTest phi (x + q • e_i) for the normalized scalar Brownian coordinate.
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/lower_1_source_linear_term_route.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hSourceLinearTermDef
2. hSourceLinearTermTaylorDef
3. hScalarLineFirstCoeffDef
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.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef
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.cycle186.lower_2_packet.source_linear_term_first_coeff_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSourceLinearTermDef from hSourceLinearTermTaylorDef and hScalarLineFirstCoeffDef by SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef.
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.cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceLinearTermLower2Obligation
2. SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef
3. hSourceLinearTermTaylorDef
4. hScalarLineFirstCoeffDef
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSourceLinearTermDef
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.cycle186.remaining_source_linear_term_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the source-linear bridge: hSourceTaylorIntegrandDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermDef, 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. hSourceQuadraticTermDef
5. hScalarMeas
6. hNormalizedCoordinateLawDef
7. hSourceTaylorIntegrandMeas
8. hGeneratorPullbackDef
9. hNormalizedRemainderMeas
10. hRemainderPullbackDef
11. hRemainderMeas
12. hRemainderBound
13. hRemainderBoundInt
14. 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 cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceLinearTermLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle186.lower_1_packet.source_linear_term_route"
      interface := "Natural-language route: narrow hSourceLinearTermDef to hSourceLinearTermTaylorDef and hScalarLineFirstCoeffDef using the first-order Taylor term of q |-> selectedTest phi (x + q • e_i) for the normalized scalar Brownian coordinate."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-015813-121084-ASTIS-SALD-001-cycle186/lower_1_source_linear_term_route.md"
      dependsOn := [
        "hSourceLinearTermDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "appendix.tex:958-970",
        "appendix.tex:984-995",
        "appendix.tex:1170-1176",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "hSourceTaylorIntegrandPointwise"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle186.lower_2_packet.source_linear_term_first_coeff_bridge"
      interface := "Compiled bridge: derive hSourceLinearTermDef from hSourceLinearTermTaylorDef and hScalarLineFirstCoeffDef by SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle186GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceLinearTermLower2Obligation",
        "SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef"
      ]
      reusedBy := [
        "hSourceLinearTermDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle186.remaining_source_linear_term_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the source-linear bridge: hSourceTaylorIntegrandDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermDef, 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",
        "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 187 middle/lower_2: source quadratic term bridge -/

/-- Cycle-187 packet for the source quadratic term leaf.

This narrows the remaining quadratic side of the cycle-186 source Taylor
integrand split.  The compiled theorem reduces `hSourceQuadraticTermDef` to
the paper-facing scalar Taylor quadratic term and the already tracked scalar
coefficient convention.  It is not a source-Hessian proof and does not move the
weak-FP diffusion coefficient into the Brownian event field.
-/

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