Erdős' existence conjecture for high-girth Steiner triple systems

A Steiner system with parameters $(n,q,r)$ is a design with parameters $(n,q,r,1)$. In a partial $(n,q,r)$-Steiner system, a $(j,i)$-configuration is a set of $i$ $q$-element subsets spanning at most $j$ vertices, and the girth is the smallest integer $g\geq2$ for which the system has a $((q-r)g+r,g)$-configuration. Erdős' high-girth conjecture. For every integer $g\geq2$, there exists $n_g$ such that for all $n \geq n_g$ with $n\equiv 1,3 \mod 6$, there exists an $(n,3,2)$-Steiner system with girth at least $g$. This conjecture was stated by Erdős in 1973 and, according to the source, was proved in full by Kwan, Sah, Sawhney, and Simkin in 2022; approximate versions and earlier partial results preceded that resolution.