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

AutoSamplingTheory.SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Obligation

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 cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Obligation :
    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_lower2
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 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hRemainderPullbackDef, the sample-space normalized-remainder expectation required by SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward before hRemainderGeneratorLimitDef can be derived. Lean inspection shows remainderGeneratorLimit, normalizedRemainder, and scalarBrownianCoordinate are abstract parameters of the compiled scalar-pushforward and Gaussian-law remainder bridges rather than reducible local definitions, so lower_2 cannot close the pullback identity by rfl or simp. The needed source-backed shape is testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP. A targeted original-source search excluding sald_version_2.tex found no named normalizedRemainder, remainderGeneratorLimit, or remainder-pullback definition; the source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 only identify the EM increment, frozen interpolation, normalized Brownian coordinate representation, and weak-FP consumer. No source-Hessian work, selected-line Taylor replay, endpoint/naming replay, direct SLT dependency, theorem-status promotion, or consumer-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. SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation
  19. SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleDag
  20. AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw
  21. AutoSamplingTheory.TechnicalLemmas.Gaussian.nnrealVarianceOneOfGaussianRealUnitLaw
  22. runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_1_remainder_pullback_route.md
  23. runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/middle_remainder_pullback_packet.md
  24. runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_2_remainder_pullback_boundary.md
  25. needed_shape=testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP
  26. leaf=hRemainderPullbackDef
  27. error_class=source_contract_gap_missing_remainder_pullback_definition
  28. blocked_by=remainderGeneratorLimit, normalizedRemainder, and scalarBrownianCoordinate are abstract parameters in the compiled scalar-pushforward remainder bridge
  29. eq:SALD_general_EM
  30. eq:general_moving_target_SALD_frozen_interp
  31. appendix.tex:958-970
  32. appendix.tex:983-996
  33. appendix.tex:1161-1170
  34. appendix.tex:1379-1387
  35. source_contract_gap_missing_remainder_pullback_definition
  36. sald.general_moving_target_discrete.em_interpolation_fp
  37. sald.general_moving_target_discrete.kl_derivative
  38. divergence/FI/IBP handoff
  39. 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, normalizedRemainder, and scalarBrownianCoordinate are abstract parameters of the compiled scalar-pushforward remainder bridge and no original-paper or local Lean definition identifies remainderGeneratorLimit with the sample-space expectation of normalizedRemainder along the scalar Brownian coordinate; lower_1_route_artifact=runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_1_remainder_pullback_route.md; lower_2_artifact=runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_2_remainder_pullback_boundary.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 cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle206_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_remainder_pullback_lower2"
  statement := "Cycle 206 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hRemainderPullbackDef, the sample-space normalized-remainder expectation required by SALD.selectedWeakTestRemainderGeneratorNormalizedLawDefOfScalarPushforward before hRemainderGeneratorLimitDef can be derived. Lean inspection shows remainderGeneratorLimit, normalizedRemainder, and scalarBrownianCoordinate are abstract parameters of the compiled scalar-pushforward and Gaussian-law remainder bridges rather than reducible local definitions, so lower_2 cannot close the pullback identity by rfl or simp. The needed source-backed shape is testRegular -> forall phi x i, remainderGeneratorLimit phi x i = integral omega, normalizedRemainder phi x i (scalarBrownianCoordinate phi x i omega) dP. A targeted original-source search excluding sald_version_2.tex found no named normalizedRemainder, remainderGeneratorLimit, or remainder-pullback definition; the source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 only identify the EM increment, frozen interpolation, normalized Brownian coordinate representation, and weak-FP consumer. No source-Hessian work, selected-line Taylor replay, endpoint/naming replay, direct SLT dependency, theorem-status promotion, or consumer-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",
    "SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleObligation",
    "SALD.cycle206GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderPullbackMiddleDag",
    "AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw",
    "AutoSamplingTheory.TechnicalLemmas.Gaussian.nnrealVarianceOneOfGaussianRealUnitLaw",
    "runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_1_remainder_pullback_route.md",
    "runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/middle_remainder_pullback_packet.md",
    "runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_2_remainder_pullback_boundary.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, normalizedRemainder, and scalarBrownianCoordinate are abstract parameters in the compiled scalar-pushforward remainder bridge",
    "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, normalizedRemainder, and scalarBrownianCoordinate are abstract parameters of the compiled scalar-pushforward remainder bridge and no original-paper or local Lean definition identifies remainderGeneratorLimit with the sample-space expectation of normalizedRemainder along the scalar Brownian coordinate; lower_1_route_artifact=runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_1_remainder_pullback_route.md; lower_2_artifact=runs/20260613-052444-683667-ASTIS-SALD-001-cycle206/lower_2_remainder_pullback_boundary.md; packet_type=dynamic-leaf worker packet."

/-- Cycle-206 proof-DAG pane for the lower_2 remainder-pullback gap. -/

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