Arnold's density-profile conjecture for numerical semigroups

Let ${\bf d}^m=(d_1,\ldots,d_m)$ be a vector of generators, and let ${\sf S}({\bf d}^m)$ be the associated numerical semigroup with conductor ${\sf C}({\bf d}^m)$. For $s<{\sf C}({\bf d}^m)$, let $p_m(s)$ denote the typical density with which the semigroup fills the segment up to $s$.

Arnold's density-profile conjecture. Asymptotically for large ${\bf d}^m$, the density at $s$ is

$$p_m(s)=\left(\frac{s}{{\sf C}({\bf d}^m)}\right)^{m-1}.$$

Consequently, the semigroup occupies one $m$th of the segment from $0$ to ${\sf C}({\bf d}^m)-1$, since

$$\int_0^{{\sf C}({\bf d}^m)}p_m(s)\,ds=\frac{{\sf C}({\bf d}^m)}{m}.$$

This is Arnold's Conjecture #1999–10 on the typical density profile below the conductor. The supplied text gives no evidence of a resolution, so it remains open.