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The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras

Claims Theorem 1.1: every simple unitary strongly rational VOA has polynomial energy bounds and is CKLW-strongly local, generating an irreducible conformal net $A_V$ ; moreover $V$ is completely unitary (all simple modules unitarizable, fusion forms positive), every unitary module is strongly integrable, $A_V$ is completely rational, and the Carpi-Weiner-Xu functor is a braided unitary tensor equivalence $\mathrm{Rep}(V)\simeq\mathrm{Rep}^f(A_V)$ . It does not treat non-rational or non-C2-cofinite unitary VOAs, so the general conjecture remains open.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 25, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras · Strong locality, strongly rational VOAs

Confidence: Not scored

Registry verification: lean checked · announcement · partial

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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras

specialist registry · passed

No independent mathematician has checked this yet. Checked here: abstract, introduction and Theorem 1.1, read against CKLW Conjecture 8.18 as cited. The proof was not refereed. The result covers only strongly rational VOAs (CFT type, self-contragredient, rational, C2-cofinite); the general conjecture stays open. Lean-checked on the release's own Comparator challenge VertexAlgebraNet together with its solution module OAI.RepresentationTheory.VertexAlgebra.MinimalComparator, both fetched at the pinned commit; the challenge is not listed in the release's formalization catalogue (lean/formalization.yaml), the statement was read here but not independently audited, and the development was not rebuilt here. The formal statement (OAI.MinimalVertex.main) assumes a simple CFT-type VOA with a unitary structure that is self-contragredient, rational and C2-cofinite, and concludes polynomial energy bounds, CKLW strong locality (interval algebras contained in the commutant of the complementary interval's algebra) and an irreducible conformal net. That is the headline claim of this partial entry. The 47 kB statement file was read for its main theorem and key definitions only. Not formalized: complete rationality, complete unitarity, the braided equivalence and the extension correspondence (parts 2 to 5).

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The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras

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Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Carpi, Kawahigashi, Longo and Weiner, Mem. Amer. Math. Soc. 254 (2018), Conjecture 8.18

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problem-record link supplied by the VibeMathed registry.

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Lean Comparator challenge VertexAlgebraNet (not in formalization.yaml)

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lean-proof link supplied by the VibeMathed registry.

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Lean solution module OAI/RepresentationTheory/VertexAlgebra/MinimalComparator.lean

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lean-proof link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean Comparator challenge VertexAlgebraNet (not in formalization.yaml)

lean artifact · pending

Artifact ↗

Lean solution module OAI/RepresentationTheory/VertexAlgebra/MinimalComparator.lean

lean artifact · pending

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This event attributed to Unreleased internal OpenAI model

Lean solution module OAI/RepresentationTheory/VertexAlgebra/MinimalComparator.lean evidence for this event

The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras evidence for this event

Lean Comparator challenge VertexAlgebraNet (not in formalization.yaml) evidence for this event

Carpi, Kawahigashi, Longo and Weiner, Mem. Amer. Math. Soc. 254 (2018), Conjecture 8.18 evidence for this event

VibeMathed record: The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras evidence for this event

The CKLW strong-locality conjecture for strongly rational unitary vertex operator algebras parent of this event

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