Generic quadratic graph degree conjecture

Let $m$ and $s$ be nonnegative integers, and consider the rational map

$$\gamma: \mathbb P^m \dashrightarrow \mathbb P^{m+s}$$

whose coordinates on $\mathbb P^m\setminus \operatorname{V}(z_0)$ are given by

$$y_i=\begin{cases}z_0^2&\text{if }i=0,\z_0z_i&\text{if }i\in\{1,\ldots,m\},\gamma_i(z)&\text{if }i\in\{m+1,\ldots,m+s\},\end{cases}$$

where the $\gamma_i(z)$ are general homogeneous quadratic polynomials for $i=m+1,\ldots,m+s$. Generic quadratic graph degree conjecture. The graph of $\gamma$ has degree

$$\deg(\operatorname{graph}(\gamma))=\begin{cases}(m-s+2)2^s-1&\text{if }s<m,\\2^{m+1}-1&\text{if }s\geq m.\end{cases}$$

This conjectural formula is motivated by computational evidence and is intended to provide a tractable degree calculation for the graphs arising in the coupled-cluster truncation problem. Its status is not resolved in the supplied source.