Concavity conjecture for the bridge-braid spectrum

Let $b(d)$ denote the entries of the bridge-braid spectrum of a knot, indexed by the relevant integer parameter $d$. Concavity conjecture. The sequence $\{b(d)\}$ is concave upwards, that is,

$$b(d-1)-b(d)\geq b(d)-b(d+1).$$

The conjecture is motivated by the observation that resolving successive critical points may require progressively more stabilizations. Its relationship with the known monotonicity and endpoint constraints is discussed in the paper, but no proof or disproof is supplied.