AutoSamplingTheory.SALD.cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoLowerObligation

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 cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoLowerObligation :
    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

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 middle compiles SALD.emFrozenScalarBrownianItoGeneratorEventField and SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDefOfFrozenScalarBrownianItoGenerator. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef is no longer primitive; it follows from the named source-cited stochastic-generator interface hFrozenScalarBrownianItoGeneratorEventFieldDef : testRegular -> emGeneratorLaplacianEventField = SALD.emFrozenScalarBrownianItoGeneratorEventField selectedTest. The remaining source-cited boundary is to prove that named frozen scalar Brownian/Ito generator event-field equality directly from eq:general_moving_target_SALD_frozen_interp and appendix.tex:1379-1387, with the sigma_eta^2/2 coefficient 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.emFrozenScalarBrownianItoGeneratorEventField
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDefOfFrozenScalarBrownianItoGenerator
3. hFrozenScalarBrownianItoGeneratorEventFieldDef
4. hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis
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 / illness-area middle worker packet inside the EM conditional-law/state-event backend. The configured local SLT project path was checked and is absent; no SLT theorem was consulted or imported. The only Mathlib/local ingredient already in scope is the finite-dimensional standard-basis calculus vocabulary, but this cycle's remaining work is the paper-internal frozen scalar Brownian/Ito generator identification.

def cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle160_em_generator_laplacian_event_field_frozen_scalar_brownian_ito"
  statement := "Cycle 160 middle compiles SALD.emFrozenScalarBrownianItoGeneratorEventField and SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDefOfFrozenScalarBrownianItoGenerator. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef is no longer primitive; it follows from the named source-cited stochastic-generator interface hFrozenScalarBrownianItoGeneratorEventFieldDef : testRegular -> emGeneratorLaplacianEventField = SALD.emFrozenScalarBrownianItoGeneratorEventField selectedTest. The remaining source-cited boundary is to prove that named frozen scalar Brownian/Ito generator event-field equality directly from eq:general_moving_target_SALD_frozen_interp and appendix.tex:1379-1387, with the sigma_eta^2/2 coefficient 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.emFrozenScalarBrownianItoGeneratorEventField",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDefOfFrozenScalarBrownianItoGenerator",
    "hFrozenScalarBrownianItoGeneratorEventFieldDef",
    "hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis",
    "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 / illness-area middle worker packet inside the EM conditional-law/state-event backend. The configured local SLT project path was checked and is absent; no SLT theorem was consulted or imported. The only Mathlib/local ingredient already in scope is the finite-dimensional standard-basis calculus vocabulary, but this cycle's remaining work is the paper-internal frozen scalar Brownian/Ito generator identification."

/-- Cycle-160 lower_1 pointwise scout split of the frozen scalar Ito generator boundary. -/