AutoSamplingTheory.SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleDag

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.

def cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleDag :
    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

1. id : String (explicit)

   Stable plan-node identifier.

   ASTIS.SALD.cycle206.middle_packet.remainder_pullback_source_gap

   interface : String (explicit)

   Text describing intended mathematical interface.

   Typed source-cited boundary: hRemainderPullbackDef is the sample-space definition of remainderGeneratorLimit as the expectation of normalizedRemainder evaluated at the normalized scalar Brownian coordinate. This is strictly below hRemainderGeneratorLimitDef because the compiled scalar-pushforward and Gaussian-law bridges already consume hRemainderPullbackDef.

   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.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation
   2. SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward
   3. SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw
   4. hRemainderPullbackDef
   5. hScalarMeas
   6. hNormalizedCoordinateLawDef
   7. hNormalizedRemainderMeas
   8. scalarBrownianCoordinate
   9. normalizedRemainder
   10. remainderGeneratorLimit
   11. appendix.tex:958-970
   12. appendix.tex:983-996
   13. appendix.tex:1161-1170
   14. appendix.tex:1379-1387
   15. 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

def cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle206.middle_packet.remainder_pullback_source_gap"
      interface := "Typed source-cited boundary: hRemainderPullbackDef is the sample-space definition of remainderGeneratorLimit as the expectation of normalizedRemainder evaluated at the normalized scalar Brownian coordinate. This is strictly below hRemainderGeneratorLimitDef because the compiled scalar-pushforward and Gaussian-law bridges already consume hRemainderPullbackDef."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "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 206 lower_2: normalized-remainder pullback source gap -/

/-- Cycle-206 lower_2 packet for the normalized-remainder pullback field.

Lower_2 inspected the local Lean interfaces and found
`remainderGeneratorLimit`, `normalizedRemainder`, and
`scalarBrownianCoordinate` only as parameters of the scalar-pushforward
remainder bridges, not as reducible definitions.  This records the exact
source contract still needed below `hRemainderGeneratorLimitDef` without
adding another consumer wrapper around the existing compiled bridge.
-/