Direct computation of class functions

Compute the commutative algebra of class functions CF(V) directly from the vertex operator algebra V and its chosen module category.

Background

The modular functor with singularities associates to a puncture an action of the algebra CF(V), defined as the endomorphism algebra of the tensor unit in the factorization homology of Rep(V) over the circle. This algebra generalizes class-function algebras known in finite rigid settings.

The paper establishes the abstract definition and its role in conformal blocks, but does not provide a direct description in terms of the vertex operator algebra itself. Such a description would make the construction more computable and connect the categorical class functions with vertex-algebraic data.