Triply-transitivity conjecture for collinearity graphs of elliptic polar spaces

Let $q$ be a prime power, and let the collinearity graph of the polar space $\mathcal{Q}^{-}(5,q)$ be the graph whose vertices are the points of $\mathcal{Q}^{-}(5,q)$, with two vertices adjacent when they are collinear. Triply-transitivity conjecture. For any prime power $q$, the collinearity graph of the polar space $\mathcal{Q}^{-}(5,q)$ is triply-transitive. This is one of the two infinite families left unresolved in the near-complete classification of triply-transitive strongly regular graphs; it is supported by analysis of small examples, but its general validity remains open.