Ahanjideh–Ekim–Yıldız conjecture for intermediate triangle-free extremal values

For natural numbers $d$ and $i$, let $f_{\vartriangle}(d,i)$ be the maximum number of edges in a triangle-free graph with maximum degree at most $d$ and matching number at most $i$. Let $Z(d)$ be the largest matching number of the factor-critical, almost regular, triangle-free graph used in the paper's decomposition of edge-extremal graphs.

Intermediate-value conjecture. For $7\leq d<i<Z(d)$,

$$f_{\vartriangle}(d,i)=di+i-d+1.$$

This conjecture supplies the missing values of $f_{\vartriangle}(d,i)$ between $d$ and $Z(d)$ and is intended to imply the paper's general formula for $f_{\vartriangle}(d,m)$. These intermediate cases are left open in the paper.