Convergence conjecture for non-negative dyadic subdivision schemes

Let $I=\{i:c_i>0\}$ be the support of the mask of a dyadic subdivision scheme with non-negative coefficients. Convergence conjecture. The subdivision scheme converges unless the greatest common divisor of $I$ is not equal to $1$. The preceding criterion gives an exact convergence characterization in terms of the sets $I_N$, while this conjectured gcd condition is presented as a simpler sufficient criterion; its status is not established in the source.