AutoSamplingTheory.SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Dag

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 cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Dag :
    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.cycle206.lower_2_packet.remainder_pullback_source_gap
interface : String (explicit)
Text describing intended mathematical interface.
Typed source-cited boundary: hRemainderPullbackDef remains the exact sample-space definition of remainderGeneratorLimit as the expectation of normalizedRemainder evaluated at scalarBrownianCoordinate. Local Lean inspection found no reducible definition for the three names, and the existing scalar-pushforward bridge already consumes this field to derive hRemainderGeneratorNormalizedLawDef and hRemainderGeneratorLimitDef.
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.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Obligation
2. SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation
3. SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward
4. SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw
5. hRemainderPullbackDef
6. hScalarMeas
7. hNormalizedCoordinateLawDef
8. hNormalizedRemainderMeas
9. scalarBrownianCoordinate
10. normalizedRemainder
11. remainderGeneratorLimit
12. appendix.tex:958-970
13. appendix.tex:983-996
14. appendix.tex:1161-1170
15. appendix.tex:1379-1387
16. source_contract_gap_missing_remainder_pullback_definition
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hRemainderGeneratorNormalizedLawDef
2. hRemainderGeneratorLimitDef
3. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsDominatedRemainderAndRemainderLimitScalarPushforward
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 cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle206.lower_2_packet.remainder_pullback_source_gap"
      interface := "Typed source-cited boundary: hRemainderPullbackDef remains the exact sample-space definition of remainderGeneratorLimit as the expectation of normalizedRemainder evaluated at scalarBrownianCoordinate. Local Lean inspection found no reducible definition for the three names, and the existing scalar-pushforward bridge already consumes this field to derive hRemainderGeneratorNormalizedLawDef and hRemainderGeneratorLimitDef."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Obligation",
        "SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation",
        "SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward",
        "SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "hRemainderPullbackDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hNormalizedRemainderMeas",
        "scalarBrownianCoordinate",
        "normalizedRemainder",
        "remainderGeneratorLimit",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387",
        "source_contract_gap_missing_remainder_pullback_definition"
      ]
      reusedBy := [
        "hRemainderGeneratorNormalizedLawDef",
        "hRemainderGeneratorLimitDef",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsDominatedRemainderAndRemainderLimitScalarPushforward",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-130 proof-DAG pane for the weak Laplacian integration-by-parts
sub-boundary inside the EM diffusion source action. -/

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