AutoSamplingTheory.SALD.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineDag

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 cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineDag :
    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.cycle190.middle_packet.selected_increment_endpoint_coordinate_line_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hSelectedIncrementCoordinateLineDef from hSelectedIncrementEndpointDef and hSelectedEndpointCoordinateLineDef by SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef.
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.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineMiddleObligation
2. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
3. hSelectedIncrementEndpointDef
4. hSelectedEndpointCoordinateLineDef
5. appendix.tex:958-970
6. appendix.tex:983-996
7. appendix.tex:1161-1170
8. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSelectedIncrementCoordinateLineDef
2. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
3. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
4. sald.general_moving_target_discrete.em_interpolation_fp
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.cycle190.middle_packet.source_taylor_integrand_raw_endpoint_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled direct bridge: derive hSourceTaylorIntegrandRawDef from hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, and hSelectedEndpointCoordinateLineDef by SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef, removing the older hSelectedIncrementCoordinateLineDef supplied hypothesis from this route.
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.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef
2. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
3. hSourceTaylorIntegrandSelectedIncrementDef
4. hSelectedIncrementEndpointDef
5. hSelectedEndpointCoordinateLineDef
6. appendix.tex:958-970
7. appendix.tex:983-996
8. appendix.tex:1161-1170
9. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSourceTaylorIntegrandRawDef
2. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
3. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
4. sald.general_moving_target_discrete.em_interpolation_fp
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.cycle190.remaining_selected_increment_coordinate_line_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the selected-increment endpoint bridge: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar pushforward/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, 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. hBrownianCoordinateGeneratorSourceIntegralDef
2. hSourceTaylorIntegrandSelectedIncrementDef
3. hSelectedIncrementEndpointDef
4. hSelectedEndpointCoordinateLineDef
5. hSelectedLineTaylorRawSplitDef
6. hSourceLinearTermTaylorDef
7. hScalarLineFirstCoeffDef
8. hSourceQuadraticTermTaylorDef
9. hScalarLineTaylorCoeffDef
10. hScalarMeas
11. hNormalizedCoordinateLawDef
12. hSourceTaylorIntegrandMeas
13. hGeneratorPullbackDef
14. hNormalizedRemainderMeas
15. hRemainderPullbackDef
16. hRemainderGeneratorLimitDef
17. hRemainderMeas
18. hRemainderBound
19. hRemainderBoundInt
20. 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 cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle190.middle_packet.selected_increment_endpoint_coordinate_line_bridge"
      interface := "Compiled bridge: derive hSelectedIncrementCoordinateLineDef from hSelectedIncrementEndpointDef and hSelectedEndpointCoordinateLineDef by SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineMiddleObligation",
        "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
        "hSelectedIncrementEndpointDef",
        "hSelectedEndpointCoordinateLineDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hSelectedIncrementCoordinateLineDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle190.middle_packet.source_taylor_integrand_raw_endpoint_bridge"
      interface := "Compiled direct bridge: derive hSourceTaylorIntegrandRawDef from hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, and hSelectedEndpointCoordinateLineDef by SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef, removing the older hSelectedIncrementCoordinateLineDef supplied hypothesis from this route."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef",
        "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
        "hSourceTaylorIntegrandSelectedIncrementDef",
        "hSelectedIncrementEndpointDef",
        "hSelectedEndpointCoordinateLineDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hSourceTaylorIntegrandRawDef",
        "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
        "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle190.remaining_selected_increment_coordinate_line_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the selected-increment endpoint bridge: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar pushforward/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hSourceTaylorIntegrandSelectedIncrementDef",
        "hSelectedIncrementEndpointDef",
        "hSelectedEndpointCoordinateLineDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hSourceTaylorIntegrandMeas",
        "hGeneratorPullbackDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "hRemainderGeneratorLimitDef",
        "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 190 lower_2: remainder-limit scalar-pushforward bridge -/

/-- Cycle-190 lower_2 packet for the normalized-remainder law leaf.

The compiled theorem discharges `hRemainderGeneratorNormalizedLawDef` as a
primitive supplied hypothesis in the `hRemainderGeneratorLimitDef` route.  It
first derives that normalized-law definition from the scalar-coordinate
pushforward fields, then reuses the existing standard-Gaussian coordinate-law
and variance bridges.
-/

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