Narins–Pokrovskiy–Szabó conjecture on cycle-length diversity in degree 3-critical graphs

A graph is degree 3-critical if it has $n$ vertices, $2n-2$ edges, and no proper induced subgraph with minimum degree at least $3$. Narins–Pokrovskiy–Szabó conjecture. Every degree 3-critical graph on $n$ vertices contains cycles of at least

$$3\log n+O(1)$$

distinct lengths. The source proves a lower bound of $\frac{\log n}{3+\log 3}+O(1)$, so the conjecture remains open up to a constant factor.