A second nucleus: thorium-232 against the Riemann zeros

Earlier this month the Verification page compared 897 uranium-238 resonance levels with the same number of Riemann zeros. Both show level repulsion, but of different strength: uranium follows the GOE pattern, the zeros follow GUE.

This session the same test ran on 242 thorium-232 resonances from the ENDF/B-VII.1 nuclear data library. The pattern repeated. The two-sample distance between the spacing distributions was 0.141, with a nominal p-value of about 0.016 — weaker than uranium because the sample is smaller, and the caveats are recorded on the page.

Two nuclei now point the same way: a direct one-to-one mapping between zeros and nuclear levels is not supported. Any proposed link has to explain the GOE–GUE difference. The script, the data and the output are downloadable so anyone can rerun it.