AutoSamplingTheory.SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation

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 cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation :
    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.cycle158_em_generator_laplacian_event_field_pointwise_scalar_audit

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 158 middle rejects wrapper churn around hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian. Classification: rejected-wrapper-churn. Exact boundary reviewed: hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian remains the live scalar source Delta identity for the named frozen EM Laplacian event field at each selected weak test and state point. Source-dependency audit classification: source-contract-gap/internal-paper-step. Lean still treats emGeneratorLaplacianEventField as an abstract field, while appendix.tex:984-995 gives the frozen EM interpolation and appendix.tex:1379-1387 gives the Fokker--Planck diffusion term that must define the Brownian-generator Laplacian event field as Laplacian.laplacian (selectedTest phi) x. Valid lower work must prove that source definition directly, or narrow it to one smaller named Brownian-generator event-field definition; wrappers that assume the same scalar identity, weak-FP source-field or trace-field detours, downstream total-event/source-functional consumers, broad audits, theorem-status promotion, fake closure, SLT import, Lake/toolchain change, non-EM fallback, and sald_version_2.tex use are rejected.

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. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
2. emGeneratorLaplacianEventField
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise
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.

Middle illness-area packet for the active EM conditional-law/state-event backend. Local SLT was not consulted beyond verifying the configured SLT project is absent; the missing ingredient is the paper-internal source definition of the frozen Brownian generator Laplacian event field, not an external SLT theorem.

def cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarAuditObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle158_em_generator_laplacian_event_field_pointwise_scalar_audit"
  statement := "Cycle 158 middle rejects wrapper churn around hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian. Classification: rejected-wrapper-churn. Exact boundary reviewed: hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian remains the live scalar source Delta identity for the named frozen EM Laplacian event field at each selected weak test and state point. Source-dependency audit classification: source-contract-gap/internal-paper-step. Lean still treats emGeneratorLaplacianEventField as an abstract field, while appendix.tex:984-995 gives the frozen EM interpolation and appendix.tex:1379-1387 gives the Fokker--Planck diffusion term that must define the Brownian-generator Laplacian event field as Laplacian.laplacian (selectedTest phi) x. Valid lower work must prove that source definition directly, or narrow it to one smaller named Brownian-generator event-field definition; wrappers that assume the same scalar identity, weak-FP source-field or trace-field detours, downstream total-event/source-functional consumers, broad audits, theorem-status promotion, fake closure, SLT import, Lake/toolchain change, non-EM fallback, and sald_version_2.tex use are rejected."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
    "emGeneratorLaplacianEventField",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfPointwise",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle illness-area packet for the active EM conditional-law/state-event backend. Local SLT was not consulted beyond verifying the configured SLT project is absent; the missing ingredient is the paper-internal source definition of the frozen Brownian generator Laplacian event field, not an external SLT theorem."

/-- Cycle-158 lower_2 source-definition boundary after the Brownian event-field split. -/