The bipartite Turán graph conjecture for cycle-maximal triangle-free graphs

Let a cycle-maximal triangle-free graph be a triangle-free graph to which no edge can be added without creating a triangle. For a graph on $n$ vertices, let $K_{\lfloor n/2 \rfloor, \lceil n/2 \rceil}$ denote the balanced complete bipartite graph. The bipartite Turán graph conjecture. The cycle-maximal triangle-free graphs are exactly the bipartite Turán graphs

$$K_{\lfloor n/2 \rfloor, \lceil n/2 \rceil}$$

for all $n$. The conjecture was verified by exhaustive computer search for $n\leq 13$; it proposes that balanced complete bipartite graphs maximize the number of cycles among cycle-maximal triangle-free graphs.