What was already known
Prior work gave local laws, delocalization and edge universality at fixed degree. Bourgade and Huang proved fixed-energy point-process universality only for growing degree and stated the fixed-degree conjecture.
AI involvement
OpenAI credits its internal model with the manuscript’s Gaussian-mark and continuous-switching argument. Earlier local-law and Dyson Brownian motion methods are human inputs.
OpenAI receives manuscript authorship and the repository attributes these preprints to its internal model; human oversight and exact prompting are not specified.
Importance
The result resolves fixed-energy GOE bulk universality even for cubic random regular graphs.
Limitations
No claim-matching formalization or completed human proof review is documented. The weak-Anderson extension uses this clean result and does not independently verify it.
Technical verification
The original TeX provides a detailed argument, but the repository’s formalization catalogue does not identify a matching Lean check and no completed human proof review was found. A proof manuscript alone is not a check.
Human understanding
No named human explanation of the new central mechanism is documented; Few is the evidence default.
Correction and publication history
If correct, the result resolves fixed-energy GOE bulk universality even for cubic random regular graphs.
Read this published revision