GOE bulk universality for random regular graphs of fixed degree

Claims fixed-energy GOE bulk universality of the full microscopic eigenvalue point process for uniform random $d$-regular graphs, every fixed $d\ge3$ including cubic graphs, at every energy in the open Kesten-McKay bulk. The companion extends this to sufficiently weak fixed iid uniform diagonal disorder on compact subintervals of the clean band. It does NOT address the spectral edges (already known), energy-averaged spacing statistics in the original JMRR form beyond what the point-process limit implies, or strong disorder.

Claims fixed-energy GOE bulk universality of the full microscopic eigenvalue point process for uniform random $d$-regular graphs, every fixed $d\ge3$ including cubic graphs, at every energy in the open Kesten-McKay bulk. The companion extends this to sufficiently weak fixed iid uniform diagonal disorder on compact subintervals of the clean band. It does NOT address the spectral edges (already known), energy-averaged spacing statistics in the original JMRR form beyond what the point-process limit implies, or strong disorder.