AutoSamplingTheory.SALD.cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseCoordinateLowerObligation

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 cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseCoordinateLowerObligation :
    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.cycle160_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_pointwise_coordinate

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 160 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef is no longer primitive; it follows from the smaller coordinate-generator source pair hFrozenScalarBrownianItoEventFieldCoordinateSum : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = sum_i brownianCoordinateGenerator phi x i and hFrozenScalarBrownianItoCoordinateGeneratorDef : testRegular -> forall phi x i, brownianCoordinateGenerator phi x i = iteratedFDeriv Real 2 (selectedTest phi) x ![(stdOrthonormalBasis Real E) i, (stdOrthonormalBasis Real E) i]. The remaining source-cited boundary is to prove those coordinate decomposition and per-coordinate Ito/Taylor generator facts directly from eq:general_moving_target_SALD_frozen_interp and appendix.tex:1379-1387, with sigma_eta^2/2 kept outside the event field and without weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM, wrapper, broad-audit, fake-closure, theorem-status-promotion, Lake/toolchain, SLT-import, or sald_version_2 routes.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator
2. SALD.emFrozenScalarBrownianItoGeneratorEventField
3. hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef
4. hFrozenScalarBrownianItoEventFieldCoordinateSum
5. hFrozenScalarBrownianItoCoordinateGeneratorDef
6. eq:general_moving_target_SALD_frozen_interp
7. appendix.tex:984-995
8. appendix.tex:1379-1387
9. 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.

Dynamic-leaf lower_2 proof-producing packet inside the EM conditional-law/state-event backend. The compiled theorem is only a finite coordinate-sum assembly from two source-cited stochastic-generator facts; it rejects weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM fallback, broad audit, theorem-status promotion, fake closure, Lake/toolchain change, SLT import, and sald_version_2.tex routes.

def cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseCoordinateLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle160_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_pointwise_coordinate"
  statement := "Cycle 160 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef is no longer primitive; it follows from the smaller coordinate-generator source pair hFrozenScalarBrownianItoEventFieldCoordinateSum : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = sum_i brownianCoordinateGenerator phi x i and hFrozenScalarBrownianItoCoordinateGeneratorDef : testRegular -> forall phi x i, brownianCoordinateGenerator phi x i = iteratedFDeriv Real 2 (selectedTest phi) x ![(stdOrthonormalBasis Real E) i, (stdOrthonormalBasis Real E) i]. The remaining source-cited boundary is to prove those coordinate decomposition and per-coordinate Ito/Taylor generator facts directly from eq:general_moving_target_SALD_frozen_interp and appendix.tex:1379-1387, with sigma_eta^2/2 kept outside the event field and without weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM, wrapper, broad-audit, fake-closure, theorem-status-promotion, Lake/toolchain, SLT-import, or sald_version_2 routes."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseDefOfCoordinateGenerator",
    "SALD.emFrozenScalarBrownianItoGeneratorEventField",
    "hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef",
    "hFrozenScalarBrownianItoEventFieldCoordinateSum",
    "hFrozenScalarBrownianItoCoordinateGeneratorDef",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_2 proof-producing packet inside the EM conditional-law/state-event backend. The compiled theorem is only a finite coordinate-sum assembly from two source-cited stochastic-generator facts; it rejects weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM fallback, broad audit, theorem-status promotion, fake closure, Lake/toolchain change, SLT import, and sald_version_2.tex routes."

/-- Cycle-160 proof-DAG pane for the frozen scalar Brownian Ito generator split. -/