Distinctness conjecture for graph invariants of finite polar spaces

Let $\Delta_i$ denote the graph associated with the $i$-dimensional subspaces of the finite polar space, and let $\kappa_i$, $\chi_i$, and $\xi_i$ be its corresponding graph parameters. For $0 \leq i < n$, let $\theta_i$ be any of $\kappa_i$, $\chi_i$, or $\xi_i$. Distinctness conjecture. If $0 \leq i < j < n$, then

$$(|\Delta_i|,\theta_i)\neq (|\Delta_j|,\theta_j).$$

The claim asserts that the order and any one of these graph parameters together distinguish the graphs associated with different dimensions. The surrounding text indicates that the result follows from preceding propositions comparing the parameters, but the supplied span does not explicitly establish whether this statement is proved or conjectural.