Cuntz's associativity conjecture for the absolute fusion algebra

Let $d,n$ be the parameters defining the symbol set $\Psi^{\#}(Y,\pi)$, and let $N_{f,g}^k\in\mathbb{Z}$ be the structure constants defined by the fusion algebra associated with the matrix $\mathbb{S}$. Let $A^{\mathrm{abs}}$ be a free $\mathbb{Z}$-module with basis $(b_f^{\mathrm{abs}})_{f\in\Psi^{\#}(Y,\pi)}$, and define multiplication by

$$b_f^{\mathrm{abs}}\cdot b_g^{\mathrm{abs}}=\sum_{k\in\Psi^{\#}(Y,\pi)}\left\lvert N_{f,g}^k\right\rvert b_k^{\mathrm{abs}}.$$

Cuntz's conjecture. This multiplication is associative.

The conjecture asserts that replacing the possibly signed fusion coefficients by their absolute values still produces an associative fusion algebra. The supplied text identifies this as Cuntz's conjecture but gives no evidence of a resolution.