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

AutoSamplingTheory.SALD.cycle204GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandSelectedIncrementLower2Obligation

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 cycle204GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandSelectedIncrementLower2Obligation :
    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.cycle204_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_taylor_integrand_selected_increment_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 204 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hSourceTaylorIntegrandSelectedIncrementDef is the source-facing naming field still required after the compiled cycle-189 raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef and the cycle-190 endpoint/raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef. Lean inspection shows sourceTaylorIntegrand and sourceSelectedLineIncrement are abstract parameters of those bridges rather than reducible local definitions, so the needed source-backed shape is testRegular -> forall phi x i z, sourceTaylorIntegrand phi x i z = sourceSelectedLineIncrement phi x i z. 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 this scalar naming field. No endpoint replay, normalized-remainder replay, source-Hessian work, testRegular repackaging, VP score-Hessian substitution, direct SLT dependency, broad route audit, 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. hSourceTaylorIntegrandSelectedIncrementDef
  2. hSourceTaylorIntegrandRawDef
  3. hSelectedIncrementCoordinateLineDef
  4. hSelectedIncrementEndpointDef
  5. hSelectedEndpointCoordinateLineDef
  6. sourceTaylorIntegrand
  7. sourceSelectedLineIncrement
  8. sourceSelectedEndpoint
  9. selectedTest
  10. stdOrthonormalBasis
  11. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
  12. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef
  13. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
  14. SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation
  15. SALD.cycle203GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementEndpointLower2Obligation
  16. needed_shape=testRegular -> forall phi x i z, sourceTaylorIntegrand phi x i z = sourceSelectedLineIncrement phi x i z
  17. leaf=hSourceTaylorIntegrandSelectedIncrementDef
  18. error_class=source_contract_gap_missing_source_taylor_integrand_selected_increment_definition
  19. blocked_by=sourceTaylorIntegrand and sourceSelectedLineIncrement are abstract parameters in the compiled selected-increment/raw-integrand bridges
  20. eq:SALD_general_EM
  21. eq:general_moving_target_SALD_frozen_interp
  22. appendix.tex:958-970
  23. appendix.tex:983-996
  24. appendix.tex:1161-1170
  25. appendix.tex:1379-1387
  26. source_contract_gap_missing_source_taylor_integrand_selected_increment_definition
  27. sald.general_moving_target_discrete.em_interpolation_fp
  28. sald.general_moving_target_discrete.kl_derivative
  29. divergence/FI/IBP handoff
  30. 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=hSourceTaylorIntegrandSelectedIncrementDef; error_class=source_contract_gap_missing_source_taylor_integrand_selected_increment_definition; needed_shape=testRegular -> forall phi x i z, sourceTaylorIntegrand phi x i z = sourceSelectedLineIncrement phi x i z; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=sourceTaylorIntegrand and sourceSelectedLineIncrement are abstract parameters of the compiled cycle-189/190 bridges and no original-paper Lean-facing definition identifying the source Taylor integrand with the selected weak-test increment was found; lower_1_handoff=absent_from_dialogue_at_lower_2_start; 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 cycle204GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandSelectedIncrementLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle204_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_taylor_integrand_selected_increment_lower2"
  statement := "Cycle 204 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hSourceTaylorIntegrandSelectedIncrementDef is the source-facing naming field still required after the compiled cycle-189 raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef and the cycle-190 endpoint/raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef. Lean inspection shows sourceTaylorIntegrand and sourceSelectedLineIncrement are abstract parameters of those bridges rather than reducible local definitions, so the needed source-backed shape is testRegular -> forall phi x i z, sourceTaylorIntegrand phi x i z = sourceSelectedLineIncrement phi x i z. 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 this scalar naming field. No endpoint replay, normalized-remainder replay, source-Hessian work, testRegular repackaging, VP score-Hessian substitution, direct SLT dependency, broad route audit, or consumer-wrapper churn is introduced."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.obligation
  dependsOn := [
    "hSourceTaylorIntegrandSelectedIncrementDef",
    "hSourceTaylorIntegrandRawDef",
    "hSelectedIncrementCoordinateLineDef",
    "hSelectedIncrementEndpointDef",
    "hSelectedEndpointCoordinateLineDef",
    "sourceTaylorIntegrand",
    "sourceSelectedLineIncrement",
    "sourceSelectedEndpoint",
    "selectedTest",
    "stdOrthonormalBasis",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef",
    "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
    "SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation",
    "SALD.cycle203GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementEndpointLower2Obligation",
    "needed_shape=testRegular -> forall phi x i z, sourceTaylorIntegrand phi x i z = sourceSelectedLineIncrement phi x i z",
    "leaf=hSourceTaylorIntegrandSelectedIncrementDef",
    "error_class=source_contract_gap_missing_source_taylor_integrand_selected_increment_definition",
    "blocked_by=sourceTaylorIntegrand and sourceSelectedLineIncrement are abstract parameters in the compiled selected-increment/raw-integrand bridges",
    "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_source_taylor_integrand_selected_increment_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=hSourceTaylorIntegrandSelectedIncrementDef; error_class=source_contract_gap_missing_source_taylor_integrand_selected_increment_definition; needed_shape=testRegular -> forall phi x i z, sourceTaylorIntegrand phi x i z = sourceSelectedLineIncrement phi x i z; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=sourceTaylorIntegrand and sourceSelectedLineIncrement are abstract parameters of the compiled cycle-189/190 bridges and no original-paper Lean-facing definition identifying the source Taylor integrand with the selected weak-test increment was found; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet."

/-- Cycle-204 proof-DAG pane for the source Taylor integrand naming gap. -/

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