Random regular graph spectral calibration

Family 219: GOE bulk universality for regular graphs with weak Anderson disorder. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Graph and spectral researchers can compare bulk eigenvalue spacings of finite random regular graphs, including weak diagonal disorder, to the GOE reference.

Applicability and commercial boundary

Fixed degree, random graph law, bulk energy and sufficiently small disorder are essential. Asymptotic universality does not certify finite anomaly probabilities or arbitrary real-world graph spectra.

Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

Next verification action

Build a seeded finite-graph spacing study and quantify finite-size sensitivity before proposing anomaly detection.

Evidence scope

The catalog statement was individually reviewed. Main-paper abstract passages and available family scope notes were also inspected; paper-level theorem and algorithm details still require deeper review. No independent Lean check was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Main source

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