Bang–Koolen's classification conjecture for geometric distance-regular graphs

Let $m\geq 2$ be a fixed integer. A geometric distance-regular graph is a distance-regular graph admitting a geometric structure, and let $\mu$ denote its intersection parameter and $-m$ its smallest eigenvalue. Assume the graph has diameter at least $3$.

Bang–Koolen's classification conjecture. Any such graph is a Johnson graph, a Hamming graph, a Grassmann graph, a bilinear forms graph, or has a number of vertices bounded by a function of $m$.

This conjecture proposes that, for fixed smallest eigenvalue and $\mu\geq 2$, the listed classical families account for all sufficiently large geometric distance-regular graphs. The paper proves classification results under additional hypotheses, while the general statement remains open.