Reduced associated rings of finite vertex algebra orbifolds

This manuscript establishes a parameter-lifting criterion for nilpotence of kernels of graded algebra surjections and applies it to finite-group orbifolds of vertex operator algebras. A conformal-weight filtration gives cofiniteness uniformly over all homogeneous lifts of a parameter system. Using Riesen’s Proposition 4.1 as external input, the argument yields the canonical reduced-ring isomorphism conjectured by Lian and Linshaw and preservation of the quasi-lisse property under finite-group orbifolds. The manuscript explicitly separates its algebraic reduction from the external bounded-length weight statement.