AutoSamplingTheory.SALD.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Dag

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 cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Dag :
    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.lower_1_packet.remainder_limit_scalar_pushforward_route
interface : String (explicit)
Text describing intended mathematical interface.
Natural-language route: remove hRemainderGeneratorNormalizedLawDef from the hRemainderGeneratorLimitDef backend by deriving it from the scalar Brownian coordinate pushforward and normalized-remainder pullback definition, then reuse the standard-Gaussian vector coordinate-law and variance bridges.
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.
runs/20260612-041014-095507-ASTIS-SALD-001-cycle190/lower_1_remainder_limit_scalar_pushforward_route.md
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. hRemainderGeneratorLimitDef
2. hRemainderGeneratorNormalizedLawDef
3. hScalarMeas
4. hNormalizedCoordinateLawDef
5. hNormalizedRemainderMeas
6. hRemainderPullbackDef
7. hNormalizedVectorLaw
8. hCoordinateLawDef
9. hVarianceDef
10. appendix.tex:958-970
11. appendix.tex:983-996
12. appendix.tex:1161-1170
13. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw
2. hRemainderGeneratorLimitDef
3. sald.general_moving_target_discrete.em_interpolation_fp
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle190.lower_2_packet.remainder_limit_scalar_pushforward_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: derive hRemainderGeneratorLimitDef directly from scalar pushforward/pullback fields and standard-Gaussian vector coordinate-law fields by SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw.
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.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Obligation
2. SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw
3. SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward
4. SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw
5. hScalarMeas
6. hNormalizedCoordinateLawDef
7. hNormalizedRemainderMeas
8. hRemainderPullbackDef
9. hNormalizedVectorLaw
10. hCoordinateLawDef
11. hVarianceDef
12. appendix.tex:958-970
13. appendix.tex:983-996
14. appendix.tex:1161-1170
15. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hRemainderGeneratorLimitDef
2. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.general_moving_target_discrete.kl_derivative
5. divergence/FI/IBP handoff
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_remainder_limit_scalar_pushforward_backend
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact Brownian/Ito frozen backend after the remainder-limit scalar-pushforward bridge: hScalarMeas, hNormalizedCoordinateLawDef, hNormalizedRemainderMeas, hRemainderPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hRemainderMeas, hRemainderBound, hRemainderBoundInt, plus the active coordinate-generator source leaves. 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. hScalarMeas
2. hNormalizedCoordinateLawDef
3. hNormalizedRemainderMeas
4. hRemainderPullbackDef
5. hNormalizedVectorLaw
6. hCoordinateLawDef
7. hVarianceDef
8. hRemainderMeas
9. hRemainderBound
10. hRemainderBoundInt
11. hBrownianCoordinateGeneratorSourceIntegralDef
12. hSourceTaylorIntegrandSelectedIncrementDef
13. hSelectedIncrementEndpointDef
14. hSelectedEndpointCoordinateLineDef
15. hSelectedLineTaylorRawSplitDef
16. hSourceLinearTermTaylorDef
17. hScalarLineFirstCoeffDef
18. hSourceQuadraticTermTaylorDef
19. hScalarLineTaylorCoeffDef
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 cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle190.lower_1_packet.remainder_limit_scalar_pushforward_route"
      interface := "Natural-language route: remove hRemainderGeneratorNormalizedLawDef from the hRemainderGeneratorLimitDef backend by deriving it from the scalar Brownian coordinate pushforward and normalized-remainder pullback definition, then reuse the standard-Gaussian vector coordinate-law and variance bridges."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "runs/20260612-041014-095507-ASTIS-SALD-001-cycle190/lower_1_remainder_limit_scalar_pushforward_route.md"
      dependsOn := [
        "hRemainderGeneratorLimitDef",
        "hRemainderGeneratorNormalizedLawDef",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "hRemainderGeneratorLimitDef",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle190.lower_2_packet.remainder_limit_scalar_pushforward_bridge"
      interface := "Compiled bridge: derive hRemainderGeneratorLimitDef directly from scalar pushforward/pullback fields and standard-Gaussian vector coordinate-law fields by SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Obligation",
        "SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw",
        "SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward",
        "SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw",
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "appendix.tex:958-970",
        "appendix.tex:983-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hRemainderGeneratorLimitDef",
        "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefsAndDominatedRemainder",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle190.remaining_remainder_limit_scalar_pushforward_backend"
      interface := "Remaining exact Brownian/Ito frozen backend after the remainder-limit scalar-pushforward bridge: hScalarMeas, hNormalizedCoordinateLawDef, hNormalizedRemainderMeas, hRemainderPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hRemainderMeas, hRemainderBound, hRemainderBoundInt, plus the active coordinate-generator source leaves. hSourceHasHessian and hSourceHessianBound stay source-contract gaps."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "hScalarMeas",
        "hNormalizedCoordinateLawDef",
        "hNormalizedRemainderMeas",
        "hRemainderPullbackDef",
        "hNormalizedVectorLaw",
        "hCoordinateLawDef",
        "hVarianceDef",
        "hRemainderMeas",
        "hRemainderBound",
        "hRemainderBoundInt",
        "hBrownianCoordinateGeneratorSourceIntegralDef",
        "hSourceTaylorIntegrandSelectedIncrementDef",
        "hSelectedIncrementEndpointDef",
        "hSelectedEndpointCoordinateLineDef",
        "hSelectedLineTaylorRawSplitDef",
        "hSourceLinearTermTaylorDef",
        "hScalarLineFirstCoeffDef",
        "hSourceQuadraticTermTaylorDef",
        "hScalarLineTaylorCoeffDef",
        "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 191 middle: source-integral scalar-pushforward bridge -/

/-- Cycle-191 middle packet for the Brownian source-integral law leaf.

The compiled theorem discharges `hBrownianCoordinateGeneratorNormalizedLawDef`
as a primitive supplied hypothesis in the
`hBrownianCoordinateGeneratorSourceIntegralDef` route.  It mirrors the accepted
cycle-190 remainder-law composition: first derive the normalized coordinate law
integral from scalar pushforward data, then reuse the standard-Gaussian vector
coordinate-law and variance bridges.
-/

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