# 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](source.json).

## Main source

[Fixed-energy universality for weak Anderson disorder on random regular graphs](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fixed-energy-universality-for-weak-Anderson-disorder-on-random-regular-graphs-October-5-2026/fixed-energy-universality-weak-anderson-disorder-random-regular-graphs.pdf).