OpenAI · 280-01 · 2026-09-25 · Mathematical physics
Strongly rational unitary vertex operator algebras and conformal nets
preprints/Strongly-rational-unitary-vertex-operator-algebras-and-conformal-nets-September-25-2026
Family 280. Strong locality for strongly rational unitary vertex operator algebras.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves the strongly rational case of the strong-locality conjecture: every simple unitary strongly rational complex vertex operator algebra generates a completely rational conformal net. Its simple modules are unitarizable, and its representation category agrees with the net’s finite-index sectors as a braided unitary tensor category.
Every simple unitary strongly rational vertex operator algebra generates a completely rational conformal net. All its simple grading-restricted modules are unitarizable, its canonical fusion forms are positive, and the Carpi–Weiner–Xu functor gives a braided unitary tensor equivalence from its grading-restricted finite-length module category onto the finite-index sectors of the net. Gui's extension theorems then identify normalized irreducible finite-index local extensions of these nets with simple CFT-type conformal extensions of the vertex operator algebras.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 280: Unitary vertex operator algebras and conformal nets. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
VertexAlgebraNet.lean · VertexAlgebraNet.lean
Emergence
A VOA-net correspondence is not spacetime
Family 280 records a conditional correspondence from simple unitary strongly rational vertex operator algebras to completely rational conformal nets. That correspondence is not a gravitational metric, not a Page curve, and not spacetime emergence. Oai280-A records the claim and does not verify the preprint. Oai280-B's five-qubit certificate is not this net. Oai280-C's logical-algebra certificate is not this net and is not a gravitational dictionary. The Lean scope note names VertexAlgebraNet.lean for 280-01 only. The authors are OpenAI. The companion does not verify those proofs. O.1 stays NOT_CLOSED.
EmergenceOai280-A sector-label certificateOai280-B five-qubit certificateOai280-C logical-algebra certificateOai211-A path-sum certificateEn07-C Hawking comparison