AutoSamplingTheory.SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation

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 cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation :
    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.cycle159_em_generator_laplacian_event_field_brownian_pointwise_stdbasis

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 159 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldBrownianPointwiseDef is no longer primitive; it follows from the smaller coordinate Brownian-generator Hessian-trace display hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = sum_i iteratedFDeriv Real 2 (selectedTest phi) x ![e_i,e_i], together with SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv and SALD.emFrozenBrownianLaplacianEventField. The remaining source-cited boundary is to prove this coordinate trace display directly from eq:general_moving_target_SALD_frozen_interp and the Fokker--Planck diffusion display at appendix.tex:1379-1387, 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis
2. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
3. SALD.emFrozenBrownianLaplacianEventField
4. hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef
5. hEmGeneratorLaplacianEventFieldBrownianPointwiseDef
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 worker packet inside the EM conditional-law/state-event backend. Consulted local Mathlib Laplacian support through the existing SALD bridge; no local SLT file was consulted or imported because the remaining theorem is the paper-internal Brownian coordinate trace display.

def cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle159_em_generator_laplacian_event_field_brownian_pointwise_stdbasis"
  statement := "Cycle 159 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldBrownianPointwiseDef is no longer primitive; it follows from the smaller coordinate Brownian-generator Hessian-trace display hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = sum_i iteratedFDeriv Real 2 (selectedTest phi) x ![e_i,e_i], together with SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv and SALD.emFrozenBrownianLaplacianEventField. The remaining source-cited boundary is to prove this coordinate trace display directly from eq:general_moving_target_SALD_frozen_interp and the Fokker--Planck diffusion display at appendix.tex:1379-1387, 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseDefOfStdBasis",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "SALD.emFrozenBrownianLaplacianEventField",
    "hEmGeneratorLaplacianEventFieldBrownianPointwiseStdBasisDef",
    "hEmGeneratorLaplacianEventFieldBrownianPointwiseDef",
    "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 worker packet inside the EM conditional-law/state-event backend. Consulted local Mathlib Laplacian support through the existing SALD bridge; no local SLT file was consulted or imported because the remaining theorem is the paper-internal Brownian coordinate trace display."

/-- Cycle-159 proof-DAG pane for the Brownian event-field pointwise split. -/