AutoSamplingTheory.SALD.cycle198GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoCoordinateSumLower2Dag

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 cycle198GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoCoordinateSumLower2Dag :
    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.cycle198.lower_2_packet.event_field_coordinate_sum_source_gap
interface : String (explicit)
Text describing intended mathematical interface.
Typed source-cited boundary: hFrozenScalarBrownianItoEventFieldCoordinateSum is blocked on a paper definition or source-backed theorem identifying the abstract EM Brownian Laplacian event field with the finite sum of one-coordinate Brownian generator contributions. The existing cycle-160 coordinate-generator assembly theorem is not repeated because it already assumes this equality.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.cycle198GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoCoordinateSumLower2Obligation
2. hFrozenScalarBrownianItoEventFieldCoordinateSum
3. emGeneratorLaplacianEventField
4. brownianCoordinateGenerator
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator
6. SALD.emFrozenScalarBrownianItoGeneratorEventField
7. appendix.tex:983-996
8. appendix.tex:1379-1387
9. source_contract_gap_missing_event_field_coordinate_sum_definition
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator
2. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.general_moving_target_discrete.kl_derivative
4. 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 cycle198GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoCoordinateSumLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle198.lower_2_packet.event_field_coordinate_sum_source_gap"
      interface := "Typed source-cited boundary: hFrozenScalarBrownianItoEventFieldCoordinateSum is blocked on a paper definition or source-backed theorem identifying the abstract EM Brownian Laplacian event field with the finite sum of one-coordinate Brownian generator contributions. The existing cycle-160 coordinate-generator assembly theorem is not repeated because it already assumes this equality."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle198GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoCoordinateSumLower2Obligation",
        "hFrozenScalarBrownianItoEventFieldCoordinateSum",
        "emGeneratorLaplacianEventField",
        "brownianCoordinateGenerator",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator",
        "SALD.emFrozenScalarBrownianItoGeneratorEventField",
        "appendix.tex:983-996",
        "appendix.tex:1379-1387",
        "source_contract_gap_missing_event_field_coordinate_sum_definition"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 201 lower_2: selected-test Laplacian continuity source gap -/

/-- Cycle-201 lower_2 packet for selected-test Laplacian regularity.

The cycle-199 local bridge already reduces the law-dependent
`hsourceLaplacianFieldMeas` premise to ordinary measurability of
`Laplacian.laplacian (selectedTest phi)`, and then to continuity if the source
test class provides it.  The original SALD source lines audited for this packet
do not state that selected-test Laplacian continuity or measurability field, so
this obligation records the smaller source contract instead of adding a
same-shape measurability wrapper.
-/

Existing module entry · Audited data-reader index · All teaching coverage