OD-characterizability conjecture for projective special linear groups over the binary field

Let $L_n(2)$ denote the projective special linear group over the binary field, for an integer $n\geqslant 2$. A finite group is OD-characterizable if it is uniquely determined, up to isomorphism, by its order and degree pattern. OD-characterizability conjecture. The groups $L_n(2)$ are OD-characterizable for all integers $n\geqslant 2$. This conjecture concerns recognition of these finite simple groups from their order and prime graph degree pattern; the source confirms the claim for $L_{10}(2)$ and $L_{11}(2)$, while the general case remains open in the provided text.