The two-round minimal percolating set conjecture

Let $\Pi_q$ be a finite projective plane of order $q$, let $r$ be the infection rate, and let $t_r(A)$ denote the percolation time of a percolating set $A$. Two-round minimal percolating set conjecture. For each $r$ with

$$4\leq r\leq q,$$

there exists a minimal percolating set $A_r$ with

$$t_r(A_r)=2.$$

This asserts the existence of minimal percolating configurations that infect the entire plane in exactly two rounds throughout the stated range. The source gives a construction and proof around the conjecture, but the supplied parser status is unresolved.