OpenAI reports strong locality for strongly rational unitary vertex algebras

Every simple unitary strongly rational complex vertex operator algebra has polynomial energy bounds and CKLW strong locality; its smeared fields generate an irreducible conformal net.

Sources for this record

What was already known

Carpi, Kawahigashi, Longo and Weiner constructed nets for strongly local unitary vertex operator algebras and proved locality for several model classes. Automatic strong locality for the full strongly rational unitary class remained conjectural.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Major

Establishes the analytic construction of a conformal net for every algebra in this class.

Limitations

The Lean scope matches this first construction step. It does not check complete rationality, unitarizability of all modules, braided equivalence or extension classification in the manuscript.

Technical verification Formal (Lean 4)

OpenAI reports a Lean proof matching the selected claim.

Formal checking

The pinned Lean note states polynomial energy bounds, CKLW strong locality and construction of an irreducible conformal net for the stated class.

Checker
OpenAI-reported Lean 4 / Comparator
Scope
Every simple unitary strongly rational complex vertex operator algebra has polynomial energy bounds and CKLW strong locality; its smeared fields generate an irreducible conformal net.
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision