We prove that in any unitary, modular-invariant 2d CFT with central charge $c>1$, a normalizable vacuum, and a twist gap in the spectrum of Virasoro primaries, there exists a continuous family of twist accumulation points above $(c-1)/12$ [the BTZ threshold]. We derive an asymptotic formula for the number of spin-J Virasoro primaries within a fixed twist window, as $J\to\infty$. This formula implies that the spectrum at large spin is Dense!! (Based on a joint work with Jiaxin Qiao and Balt van Rees)

(online talk)