AutoSamplingTheory.SALD.cycle203GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementEndpointLower2Obligation

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.

def cycle203GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementEndpointLower2Obligation :
    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.cycle203_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_selected_increment_endpoint_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 203 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hSelectedIncrementEndpointDef is the remaining source-facing selected-increment endpoint definition after the compiled cycle-190 bridge SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef and raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef. Lean inspection shows sourceSelectedLineIncrement, like sourceSelectedEndpoint, is an abstract parameter of those bridges rather than a reducible local definition, so the needed source-backed shape is testRegular -> forall phi x i z, sourceSelectedLineIncrement phi x i z = selectedTest phi (sourceSelectedEndpoint phi x i z) - selectedTest phi x. 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 endpoint, normalized Brownian scalar coordinate, and weak-FP diffusion consumer while keeping sigma_eta^2 / 2 outside this scalar selected-test increment field. No endpoint-coordinate 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. hSelectedIncrementEndpointDef
2. hSelectedEndpointCoordinateLineDef
3. hSelectedIncrementCoordinateLineDef
4. hSourceTaylorIntegrandRawDef
5. sourceSelectedLineIncrement
6. sourceSelectedEndpoint
7. sourceTaylorIntegrand
8. selectedTest
9. stdOrthonormalBasis
10. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
11. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef
12. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
13. SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation
14. needed_shape=testRegular -> forall phi x i z, sourceSelectedLineIncrement phi x i z = selectedTest phi (sourceSelectedEndpoint phi x i z) - selectedTest phi x
15. leaf=hSelectedIncrementEndpointDef
16. error_class=source_contract_gap_missing_selected_increment_endpoint_definition
17. blocked_by=sourceSelectedLineIncrement is an abstract source-facing parameter in the compiled cycle-190 bridges
18. eq:SALD_general_EM
19. eq:general_moving_target_SALD_frozen_interp
20. appendix.tex:958-970
21. appendix.tex:983-996
22. appendix.tex:1161-1170
23. appendix.tex:1379-1387
24. source_contract_gap_missing_selected_increment_endpoint_definition
25. sald.general_moving_target_discrete.em_interpolation_fp
26. sald.general_moving_target_discrete.kl_derivative
27. divergence/FI/IBP handoff
28. 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=hSelectedIncrementEndpointDef; error_class=source_contract_gap_missing_selected_increment_endpoint_definition; needed_shape=testRegular -> forall phi x i z, sourceSelectedLineIncrement phi x i z = selectedTest phi (sourceSelectedEndpoint phi x i z) - selectedTest phi x; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=sourceSelectedLineIncrement is an abstract parameter of the compiled cycle-190 bridges and no original-paper Lean-facing definition of the selected increment as an endpoint difference was found; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet.

def cycle203GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementEndpointLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle203_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_selected_increment_endpoint_lower2"
  statement := "Cycle 203 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hSelectedIncrementEndpointDef is the remaining source-facing selected-increment endpoint definition after the compiled cycle-190 bridge SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef and raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef. Lean inspection shows sourceSelectedLineIncrement, like sourceSelectedEndpoint, is an abstract parameter of those bridges rather than a reducible local definition, so the needed source-backed shape is testRegular -> forall phi x i z, sourceSelectedLineIncrement phi x i z = selectedTest phi (sourceSelectedEndpoint phi x i z) - selectedTest phi x. 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 endpoint, normalized Brownian scalar coordinate, and weak-FP diffusion consumer while keeping sigma_eta^2 / 2 outside this scalar selected-test increment field. No endpoint-coordinate 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 := [
    "hSelectedIncrementEndpointDef",
    "hSelectedEndpointCoordinateLineDef",
    "hSelectedIncrementCoordinateLineDef",
    "hSourceTaylorIntegrandRawDef",
    "sourceSelectedLineIncrement",
    "sourceSelectedEndpoint",
    "sourceTaylorIntegrand",
    "selectedTest",
    "stdOrthonormalBasis",
    "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
    "SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation",
    "needed_shape=testRegular -> forall phi x i z, sourceSelectedLineIncrement phi x i z = selectedTest phi (sourceSelectedEndpoint phi x i z) - selectedTest phi x",
    "leaf=hSelectedIncrementEndpointDef",
    "error_class=source_contract_gap_missing_selected_increment_endpoint_definition",
    "blocked_by=sourceSelectedLineIncrement is an abstract source-facing parameter in the compiled cycle-190 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_selected_increment_endpoint_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=hSelectedIncrementEndpointDef; error_class=source_contract_gap_missing_selected_increment_endpoint_definition; needed_shape=testRegular -> forall phi x i z, sourceSelectedLineIncrement phi x i z = selectedTest phi (sourceSelectedEndpoint phi x i z) - selectedTest phi x; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=sourceSelectedLineIncrement is an abstract parameter of the compiled cycle-190 bridges and no original-paper Lean-facing definition of the selected increment as an endpoint difference was found; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet."

/-- Cycle-203 proof-DAG pane for the selected-increment endpoint gap. -/