AutoSamplingTheory.SALD.cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineMiddleObligation

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 cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineMiddleObligation :
    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.cycle190_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_selected_increment_coordinate_line_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 190 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hSelectedIncrementCoordinateLineDef is no longer primitive once the source correspondence supplies hSelectedIncrementEndpointDef and hSelectedEndpointCoordinateLineDef. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef compiles the local endpoint rewrite, and SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef removes the older hSelectedIncrementCoordinateLineDef supplied hypothesis from the raw source-integrand route. Source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 keep the normalized Brownian coordinate and weak-FP sigma_eta^2/2 diffusion prefactor separate. Remaining exact Brownian/Ito backend: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar law/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets.

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.formalized — 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. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef
2. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef
3. SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef
4. hSelectedIncrementCoordinateLineDef
5. hSelectedIncrementEndpointDef
6. hSelectedEndpointCoordinateLineDef
7. sourceSelectedLineIncrement
8. sourceSelectedEndpoint
9. selectedTest
10. stdOrthonormalBasis
11. appendix.tex:958-970
12. appendix.tex:983-996
13. appendix.tex:1161-1170
14. appendix.tex:1379-1387
15. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

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

No external SLT file was consulted, imported, ported, called, or marked formalized. Mathlib use is limited to existing stdOrthonormalBasis and scalar-line notation. The compiled proof does not prove hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, scalar Taylor expansion fields, normalized-remainder domination fields, or selected weak-test Hessian fields.

def cycle190GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSelectedIncrementCoordinateLineMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle190_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_selected_increment_coordinate_line_middle"
  statement := "Cycle 190 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hSelectedIncrementCoordinateLineDef is no longer primitive once the source correspondence supplies hSelectedIncrementEndpointDef and hSelectedEndpointCoordinateLineDef. SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef compiles the local endpoint rewrite, and SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef removes the older hSelectedIncrementCoordinateLineDef supplied hypothesis from the raw source-integrand route. Source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 keep the normalized Brownian coordinate and weak-FP sigma_eta^2/2 diffusion prefactor separate. Remaining exact Brownian/Ito backend: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar law/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestSelectedIncrementCoordinateLineDefOfEndpointAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementEndpointAndLineDef",
    "SALD.selectedWeakTestSourceTaylorIntegrandRawDefOfSelectedIncrementAndLineDef",
    "hSelectedIncrementCoordinateLineDef",
    "hSelectedIncrementEndpointDef",
    "hSelectedEndpointCoordinateLineDef",
    "sourceSelectedLineIncrement",
    "sourceSelectedEndpoint",
    "selectedTest",
    "stdOrthonormalBasis",
    "appendix.tex:958-970",
    "appendix.tex:983-996",
    "appendix.tex:1161-1170",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No external SLT file was consulted, imported, ported, called, or marked formalized. Mathlib use is limited to existing stdOrthonormalBasis and scalar-line notation. The compiled proof does not prove hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, scalar Taylor expansion fields, normalized-remainder domination fields, or selected weak-test Hessian fields."

/-- Cycle-190 proof-DAG pane for the selected-increment endpoint bridge. -/