Giambruno's polynomial exponent conjecture for basic PI algebras

Let $F$ be an algebraically closed field of characteristic zero. Let $A$ be a finite-dimensional basic algebra with Wedderburn–Malcev decomposition

$$A \cong M_{d_1}(F) \times \cdots \times M_{d_q}(F) \oplus J(A),$$

where $J(A)$ is the Jacobson radical. Let $t(A)$ denote the exponent of the polynomial part of the codimension growth, and let $s+1$ be the nilpotency degree of $J(A)$. Giambruno's conjecture. One has

$$t(A)=\frac{q-d}{2}+s,$$

where

$$d=d_1^2+\cdots+d_q^2.$$

This conjecture gives an algebraic formula for the polynomial exponent of codimension growth in the basic case. The source states that it was proved by Giambruno and Zaicev, and the paper presents the result as an established theorem.