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.

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.