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.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: GOE bulk universality for random regular graphs of fixed degree · GOE bulk universality, random regular graphs

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: GOE bulk universality for random regular graphs of fixed degree

specialist registry · passed

No independent mathematician has checked this yet. Theorem 1.1 was read against the conjecture: for every fixed $d\ge3$ and fixed $E$ in the open Kesten-McKay bulk, Laplace functionals of the unfolded point process of a uniform simple labelled $d$ -regular graph converge to those of the GOE bulk process, along all admissible $n$ with no conditioning. The paper says this proves Bourgade-Huang Conjecture 2.11 in a fixed-energy Laplace-functional form; the 1999 prediction was phrased via empirical nearest-neighbor spacings. Uses Huang-Yau rigidity and delocalization as input. No Lean formalization.

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GOE bulk universality for random regular graphs of fixed degree

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Companion: Fixed-energy universality for weak Anderson disorder on random regular graphs

paper · pending

paper link supplied by the VibeMathed registry.

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Bourgade and Huang, Loop equations characterize random matrix statistics (Conjecture 2.11)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Lineage and corrections

This event attributed to Unreleased internal OpenAI model

Companion: Fixed-energy universality for weak Anderson disorder on random regular graphs evidence for this event

GOE bulk universality for random regular graphs of fixed degree evidence for this event

GOE bulk universality for random regular graphs of fixed degree parent of this event

Bourgade and Huang, Loop equations characterize random matrix statistics (Conjecture 2.11) evidence for this event

VibeMathed record: GOE bulk universality for random regular graphs of fixed degree evidence for this event

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