A vertex operator algebra is a 
-graded vector space 
with finite-dimensional
homogeneous pieces and 
for sufficiently negative 
with a vacuum, a conformal vector, and a state-field correspondence
satisfying the vacuum, translation, and Jacobi identities.
For a state 
, its field is the formal series of linear operators
 |
For each 
, lower truncation means 
, the space of vector-valued formal
Laurent series. The conformal vector supplies the grading operator 
and Virasoro algebra
relations. CFT type means 
with 
, where 
is the vacuum.
For a family outside CFT type, Evans and Riesen (2026) announced that, for every odd 
, there is a simple, self-contragredient, regular,
rational, 
-cofinite
vertex operator algebra 
with central charge 
and exactly 
irreducible modules. Here the central charge is the scalar
parameter of the Virasoro algebra determined
by the conformal vector. The least conformal degree of 
is 
,
so 
is not of CFT type. Its representation category is announced to realize the Drinfeld
center of a constructed untwisted cyclic Haagerup-Izumi fusion
category on a nonunitary spherical branch. The identification is with the category
constructed in the paper; an equivalence with an independently prescribed category
is not asserted.
Evans and Riesen (2026) state that AI generated substantial initial mathematical arguments under human guidance. They report further human checking but explicitly leave complete independent verification pending.
