AutoSamplingTheory.SALD.cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation

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 cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation :
    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.cycle202_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_selected_endpoint_coordinate_line_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 202 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hSelectedEndpointCoordinateLineDef is the source-facing field still needed after the compiled bridge SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef and the raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef. Lean inspection shows sourceSelectedEndpoint is an abstract parameter of those bridges, not a reducible local definition, so the needed source-backed shape is testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i. 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 line while keeping sigma_eta^2 / 2 outside this scalar endpoint field. No source-Hessian work, testRegular repackaging, VP score-Hessian substitution, hNormalizedRemainderBoundDef replay, hSelectedTestLaplacianContinuous replay, 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. hSelectedEndpointCoordinateLineDef
2. hSelectedIncrementEndpointDef
3. hSelectedIncrementCoordinateLineDef
4. hSourceTaylorIntegrandRawDef
5. sourceSelectedEndpoint
6. sourceSelectedLineIncrement
7. sourceTaylorIntegrand
8. selectedTest
9. stdOrthonormalBasis
10. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
11. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef
12. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
13. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs
14. AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw
15. needed_shape=testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i
16. leaf=hSelectedEndpointCoordinateLineDef
17. error_class=source_contract_gap_missing_selected_endpoint_coordinate_line_definition
18. blocked_by=sourceSelectedEndpoint is an abstract Lean parameter and the original paper source does not provide a Lean-facing endpoint coordinate-line definition
19. eq:SALD_general_EM
20. eq:general_moving_target_SALD_frozen_interp
21. appendix.tex:958-970
22. appendix.tex:983-996
23. appendix.tex:1161-1170
24. appendix.tex:1379-1387
25. source_contract_gap_missing_selected_endpoint_coordinate_line_definition
26. sald.general_moving_target_discrete.em_interpolation_fp
27. sald.general_moving_target_discrete.kl_derivative
28. divergence/FI/IBP handoff
29. 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=hSelectedEndpointCoordinateLineDef; error_class=source_contract_gap_missing_selected_endpoint_coordinate_line_definition; needed_shape=testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=sourceSelectedEndpoint is an abstract parameter of the compiled cycle-190 bridges and no original-paper Lean-facing definition of that endpoint coordinate line was found; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet.

def cycle202GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedEndpointCoordinateLineLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle202_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_selected_endpoint_coordinate_line_lower2"
  statement := "Cycle 202 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact missing theorem boundary narrowed: hSelectedEndpointCoordinateLineDef is the source-facing field still needed after the compiled bridge SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef and the raw-integrand bridge SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef. Lean inspection shows sourceSelectedEndpoint is an abstract parameter of those bridges, not a reducible local definition, so the needed source-backed shape is testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i. 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 line while keeping sigma_eta^2 / 2 outside this scalar endpoint field. No source-Hessian work, testRegular repackaging, VP score-Hessian substitution, hNormalizedRemainderBoundDef replay, hSelectedTestLaplacianContinuous replay, direct SLT dependency, broad route audit, or consumer-wrapper churn is introduced."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.obligation
  dependsOn := [
    "hSelectedEndpointCoordinateLineDef",
    "hSelectedIncrementEndpointDef",
    "hSelectedIncrementCoordinateLineDef",
    "hSourceTaylorIntegrandRawDef",
    "sourceSelectedEndpoint",
    "sourceSelectedLineIncrement",
    "sourceTaylorIntegrand",
    "selectedTest",
    "stdOrthonormalBasis",
    "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
    "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfScalarPushforwardRawTaylorAndTermDefs",
    "AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw",
    "needed_shape=testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i",
    "leaf=hSelectedEndpointCoordinateLineDef",
    "error_class=source_contract_gap_missing_selected_endpoint_coordinate_line_definition",
    "blocked_by=sourceSelectedEndpoint is an abstract Lean parameter and the original paper source does not provide a Lean-facing endpoint coordinate-line 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_selected_endpoint_coordinate_line_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=hSelectedEndpointCoordinateLineDef; error_class=source_contract_gap_missing_selected_endpoint_coordinate_line_definition; needed_shape=testRegular -> forall phi x i z, sourceSelectedEndpoint phi x i z = x + z smul stdOrthonormalBasis Real E i; source_lines=appendix.tex:958-970;appendix.tex:983-996;appendix.tex:1161-1170;appendix.tex:1379-1387; blocked_by=sourceSelectedEndpoint is an abstract parameter of the compiled cycle-190 bridges and no original-paper Lean-facing definition of that endpoint coordinate line was found; lower_1_handoff=absent_from_dialogue_at_lower_2_start; packet_type=dynamic-leaf worker packet."

/-- Cycle-202 proof-DAG pane for the selected endpoint coordinate-line gap. -/