Strict log-concavity conjecture for the rank and crank of ordinary partitions

Let $N(m,n)$ and $M(m,n)$ denote, respectively, the rank and crank counting functions for ordinary partitions of $n$ with statistic $m$. Strict log-concavity conjecture. The following inequalities hold:

$$N(m,n)^2 > N(m-1,n)N(m+1,n) \qquad\text{for } n\ge123 \text{ and } |m|\le n-72,$$ $$M(m,n)^2 > M(m-1,n)M(m+1,n) \qquad\text{for } n\ge125 \text{ and } |m|\le n-71.$$

These are recorded as analogous conjectural strict log-concavity statements for the rank and crank of ordinary partitions; the supplied text gives no proof or resolution.