Minimal ascending number conjecture for reduced alternating diagrams

For each positive integer $c$, let $a^{\min}(c)$ denote the smallest ascending number attained by a knot having a reduced alternating diagram with $c$ crossings.

Minimal ascending number conjecture. One has

$$a^{\min}(c)=\lceil c/4\rceil.$$

This conjecture is presented as related to the divisibility conjecture above. The supplied context gives no broader resolution beyond the computational results for knots with at most 12 crossings, so the assertion remains open.