Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. 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 cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

id : String (explicit)

Stable obligation identifier.

sald.general_moving_target_discrete.cycle206_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_remainder_pullback_middle
statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 206 middle_formalizer dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hRemainderPullbackDef, the source-facing sample-space pullback definition required by SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward before hRemainderGeneratorLimitDef can be derived from scalar Brownian coordinate law transport. Existing compiled bridges SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward, SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw, and SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw already consume this field, so lower_2 must not add a same-shape consumer wrapper. The lower_2-ready shape is testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP. Source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 identify the EM increment, frozen interpolation, normalized Brownian coordinate, and weak-FP consumer while keeping sigma_eta^2 / 2 outside the scalar remainder pullback. Targeted source search excluding sald_version_2.tex found no named normalized-remainder or pullback definition in the original source, so if the local definitions do not reduce then lower_2 should record typed feedback leaf=hRemainderPullbackDef error_class=source_contract_gap_missing_remainder_pullback_definition. No source-Hessian work, selected-line raw Taylor replay, endpoint/naming replay, direct SLT dependency, project-article work, or wrapper churn is introduced.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — audited data reference, not expanded and not a compiled dependency edge
status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

  1. hRemainderPullbackDef
  2. hRemainderGeneratorLimitDef
  3. hRemainderGeneratorNormalizedLawDef
  4. hScalarMeas
  5. hNormalizedCoordinateLawDef
  6. hNormalizedRemainderMeas
  7. hNormalizedVectorLaw
  8. hCoordinateLawDef
  9. hVarianceDef
  10. scalarBrownianCoordinate
  11. normalizedCoordinateLaw
  12. normalizedRemainder
  13. remainderGeneratorLimit
  14. MeasureTheory.integral_map
  15. SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward
  16. SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw
  17. SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw
  18. AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw
  19. AutoSamplingTheory.TechnicalLemmas.Gaussian.nnrealVarianceOneOfGaussianRealUnitLaw
  20. runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/middle_remainder_pullback_packet.md
  21. needed_shape=testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP
  22. leaf=hRemainderPullbackDef
  23. error_class=source_contract_gap_missing_remainder_pullback_definition
  24. blocked_by=remainderGeneratorLimit and normalizedRemainder are source-facing abstract fields in the compiled scalar-pushforward remainder bridge unless lower_2 finds a reducible local definition
  25. eq:SALD_general_EM
  26. eq:general_moving_target_SALD_frozen_interp
  27. appendix.tex:958-970
  28. appendix.tex:983-996
  29. appendix.tex:1161-1170
  30. appendix.tex:1379-1387
  31. source_contract_gap_missing_remainder_pullback_definition
  32. sald.general_moving_target_discrete.em_interpolation_fp
  33. sald.general_moving_target_discrete.kl_derivative
  34. divergence/FI/IBP handoff
  35. thm:general-moving-target-SALD-discrete
note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

typed_verifier_feedback: leaf=hRemainderPullbackDef; error_class=source_contract_gap_missing_remainder_pullback_definition; needed_shape=testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=remainderGeneratorLimit and normalizedRemainder are source-facing abstract fields in the compiled scalar-pushforward remainder bridge unless lower_2 finds a reducible local definition; lower_packet_artifact=runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/middle_remainder_pullback_packet.md; packet_type=dynamic-leaf worker packet.
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 cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle206_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_remainder_pullback_middle"
  statement := "Cycle 206 middle_formalizer dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hRemainderPullbackDef, the source-facing sample-space pullback definition required by SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward before hRemainderGeneratorLimitDef can be derived from scalar Brownian coordinate law transport. Existing compiled bridges SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward, SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw, and SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw already consume this field, so lower_2 must not add a same-shape consumer wrapper. The lower_2-ready shape is testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP. Source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 identify the EM increment, frozen interpolation, normalized Brownian coordinate, and weak-FP consumer while keeping sigma_eta^2 / 2 outside the scalar remainder pullback. Targeted source search excluding sald_version_2.tex found no named normalized-remainder or pullback definition in the original source, so if the local definitions do not reduce then lower_2 should record typed feedback leaf=hRemainderPullbackDef error_class=source_contract_gap_missing_remainder_pullback_definition. No source-Hessian work, selected-line raw Taylor replay, endpoint/naming replay, direct SLT dependency, project-article work, or wrapper churn is introduced."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.obligation
  dependsOn := [
    "hRemainderPullbackDef",
    "hRemainderGeneratorLimitDef",
    "hRemainderGeneratorNormalizedLawDef",
    "hScalarMeas",
    "hNormalizedCoordinateLawDef",
    "hNormalizedRemainderMeas",
    "hNormalizedVectorLaw",
    "hCoordinateLawDef",
    "hVarianceDef",
    "scalarBrownianCoordinate",
    "normalizedCoordinateLaw",
    "normalizedRemainder",
    "remainderGeneratorLimit",
    "MeasureTheory.integral_map",
    "SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward",
    "SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw",
    "SALD.selectedWeakTestRemainderGeneratorLimitDefOfScalarPushforwardAndStdGaussianVectorLaw",
    "AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw",
    "AutoSamplingTheory.TechnicalLemmas.Gaussian.nnrealVarianceOneOfGaussianRealUnitLaw",
    "runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/middle_remainder_pullback_packet.md",
    "needed_shape=testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP",
    "leaf=hRemainderPullbackDef",
    "error_class=source_contract_gap_missing_remainder_pullback_definition",
    "blocked_by=remainderGeneratorLimit and normalizedRemainder are source-facing abstract fields in the compiled scalar-pushforward remainder bridge unless lower_2 finds a reducible local definition",
    "eq:SALD_general_EM",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:958-970",
    "appendix.tex:983-996",
    "appendix.tex:1161-1170",
    "appendix.tex:1379-1387",
    "source_contract_gap_missing_remainder_pullback_definition",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "divergence/FI/IBP handoff",
    "thm:general-moving-target-SALD-discrete"
  ]
  note := "typed_verifier_feedback: leaf=hRemainderPullbackDef; error_class=source_contract_gap_missing_remainder_pullback_definition; needed_shape=testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=remainderGeneratorLimit and normalizedRemainder are source-facing abstract fields in the compiled scalar-pushforward remainder bridge unless lower_2 finds a reducible local definition; lower_packet_artifact=runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/middle_remainder_pullback_packet.md; packet_type=dynamic-leaf worker packet."

/-- Cycle-206 proof-DAG pane for the normalized-remainder pullback gap. -/

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