The slope-bound interpolation conjecture for $d$-gonal loci

Let $\mathcal{F}_d(g)$ be the exact upper bound for slopes of families of stable curves with smooth $d$-gonal general member, and let $g_d=2d-3$ for $d\geq 3$ and $g_2=2$. Slope-bound interpolation conjecture.

$$\mathcal{F}_d(g)=6+\frac{12}{g+1}+6\frac{(1-f_d)(g-g_d)(g-1)}{(g+f_d)(g_d+1)(g+1)},$$

or equivalently,

$$\mathcal{F}_d(g)=6+\frac{6}{g+f_d}\left(1+f_d+\frac{1-f_d}{g_d+1}(g-1)\right).$$

The preceding conjecture fixes the values at $g=1$ and $g=g_d$; this conjecture proposes the exact rational interpolation for all relevant genera, with the remaining factor $f_d$ discussed separately in the source. It is supported there by known hyperelliptic and trigonal results and partial tetragonal results.