Codimension formula for Severi varieties of unicuspidal rational curves

Let ${\bf r}=(r_1,\ldots,r_n)\in \mathbb{N}_{>0}^n$, and let $\mathcal{V}_{\bf r}\subset M^n_{d,g;\mathrm{S}}$ be the subvariety of maps $f:\mathbb{P}^1\rightarrow\mathbb{P}^n$ with a unique cuspidal singularity having semigroup $\mathrm{S}$ and ramification profile ${\bf r}$. Assume $d=\deg(f)\geq\max(n,2g-2)$. For $s\in\mathrm{S}$, let $\rho(s)$ be the number of elements of $\mathbb{N}\setminus\mathrm{S}$ strictly greater than $s$. Codimension conjecture.

$$\operatorname{cod}(\mathcal{V}_{\bf r},M^n_d)=\sum_{i=1}^n(r_i-i)+\sum_{s\in B}\phi(s)\rho(s)-\sum_{s\in{\bf r}^{\bullet}}\rho(s)-1.$$

Here $B$, $\phi$, and ${\bf r}^{\bullet}$ are the combinatorial quantities defined from the semigroup and ramification profile in the preceding setup. The formula predicts the codimension of the corresponding Severi variety, accounting for both ramification conditions and the additional conditions imposed by Betti elements. The supplied text gives no evidence that the conjecture has been resolved.