Jia–Fan–Liu's spectral-radius conjecture for fractional ID-[a,b]-factor-critical graphs

Let $a$ and $b$ be positive integers with $a\leq b$, let $r\geq 1$ be an integer, and let $G$ be a graph of order $n\geq a+r+1$. Write $\lambda(G)$ for the spectral radius of $G$, let $I_r$ be the edgeless graph on $r$ vertices, let $K_m$ be the complete graph on $m$ vertices, let $\cup$ denote disjoint union, and let $\vee$ denote join. A graph is fractional $ID$-$[a,b]$-factor-critical if, for every independent set $I$ of size $r$, the graph $G-I$ has a fractional $[a,b]$-factor.

Jia–Fan–Liu's conjecture. If

$$\lambda(G)\geq\lambda\left(I_r\vee\left(K_{a-1}\vee\left(K_{n-a-r}\cup K_1\right)\right)\right),$$

then $G$ is fractional $ID$-$[a,b]$-factor-critical unless

$$G\cong I_r\vee\left(K_{a-1}\vee\left(K_{n-a-r}\cup K_1\right)\right).$$

This conjecture seeks a sharp spectral-radius condition guaranteeing fractional $ID$-$[a,b]$-factor-criticality, with the displayed join graph as the sole exceptional case. The supplied source does not state whether the conjecture has been resolved.