Example: A candidate need not divide the input

Modulo $12$, the unit $5$ has order $2$, since $5\not\equiv 1(\mathrm{mod}12)$ and $5^2\equiv 1(\mathrm{mod}12)$. The candidate $d=10$ satisfies the order-multiple test, but $10\nmid 12$. For the true order the proposed mass is

This number does not appear as an input to the finite circuit below.