AutoSamplingTheory.SALD.cycle205GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorRawSplitLower2Dag

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 cycle205GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorRawSplitLower2Dag :
    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.cycle205.lower_2_packet.selected_line_taylor_raw_split_source_gap
interface : String (explicit)
Text describing intended mathematical interface.
Typed source-cited boundary: hSelectedLineTaylorRawSplitDef is not closed by a same-shape wrapper; the existing cycle-188/189/192/193 bridges already show that this raw scalar Taylor identity is the smaller source contract needed for hSelectedLineTaylorSplitDef, hBrownianCoordinateGeneratorTaylorIntegralDef, and the Brownian/Ito Taylor moment consumer.
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.cycle205GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorRawSplitLower2Obligation
2. SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs
3. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
4. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs
5. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfScalarPushforwardRawTaylorAndDominatedRemainder
6. runs/20260613-050236-675526-ASTIS-SALD-001-cycle205/lower_1_selected_line_taylor_raw_split_route.md
7. runs/20260613-050236-675526-ASTIS-SALD-001-cycle205/lower_3_selected_line_taylor_api_churn_rejection.md
8. hSelectedLineTaylorRawSplitDef
9. selectedTest
10. normalizedRemainder
11. deriv
12. taylorCoeffWithin
13. Set.univ
14. appendix.tex:958-970
15. appendix.tex:983-996
16. appendix.tex:1161-1176
17. appendix.tex:1379-1387
18. source_contract_gap_missing_selected_line_taylor_raw_split_definition
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSelectedLineTaylorSplitDef
2. hBrownianCoordinateGeneratorTaylorIntegralDef
3. hRemainderGeneratorLimitDef
4. sald.general_moving_target_discrete.em_interpolation_fp
5. sald.general_moving_target_discrete.kl_derivative
6. 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 cycle205GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorRawSplitLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle205.lower_2_packet.selected_line_taylor_raw_split_source_gap"
      interface := "Typed source-cited boundary: hSelectedLineTaylorRawSplitDef is not closed by a same-shape wrapper; the existing cycle-188/189/192/193 bridges already show that this raw scalar Taylor identity is the smaller source contract needed for hSelectedLineTaylorSplitDef, hBrownianCoordinateGeneratorTaylorIntegralDef, and the Brownian/Ito Taylor moment consumer."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle205GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedLineTaylorRawSplitLower2Obligation",
        "SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfScalarPushforwardRawTaylorAndDominatedRemainder",
        "runs/20260613-050236-675526-ASTIS-SALD-001-cycle205/lower_1_selected_line_taylor_raw_split_route.md",
        "runs/20260613-050236-675526-ASTIS-SALD-001-cycle205/lower_3_selected_line_taylor_api_churn_rejection.md",
        "hSelectedLineTaylorRawSplitDef",
        "selectedTest",
        "normalizedRemainder",
        "deriv",
        "taylorCoeffWithin",
        "Set.univ",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1176",
        "appendix.tex:1379-1387",
        "source_contract_gap_missing_selected_line_taylor_raw_split_definition"
      ]
      reusedBy := [
        "hSelectedLineTaylorSplitDef",
        "hBrownianCoordinateGeneratorTaylorIntegralDef",
        "hRemainderGeneratorLimitDef",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 206 middle: normalized-remainder pullback source boundary -/

/-- Cycle-206 middle packet for the normalized-remainder pullback field.

The cycle-185 scalar-pushforward bridge already consumes
`hRemainderPullbackDef` to derive the normalized-law remainder generator
identity.  This packet therefore does not add another consumer wrapper; it
records the smaller source contract that lower agents must either discharge
from a reducible source definition or preserve as a typed source gap.
-/

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