{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"080500c1a78ecf1b11ca1ee8d4512e5e37a9fa0c9a47f5d5785ec0b88c277c23","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","7ac9dc1f2c61b3f228a529e27f06d1c4e0fcdde3fcd25c0bef263aee0d566d66"],"salt":"7289ccb9a0370e291ad7d7dd5a22025a5c3514ddc6233a6302c9c1c5908c8d43","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.quantum-chaos.bgs-billiard","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"7ac9dc1f2c61b3f228a529e27f06d1c4e0fcdde3fcd25c0bef263aee0d566d66","relation":"special_case"}],"plain":"Prove for one concrete chaotic shape, such as a stadium-shaped drum, that its high vibration frequencies have random-matrix spacing statistics. No single example is proven.","posed_since":"1984","precise":"Dirichlet Laplacian on the Bunimovich stadium or the Sinai billiard, eigenvalues $\\lambda_n \\to \\infty$ unfolded by Weyl's law. Prove that the pair correlation converges to the GOE two-point function, or at least that the spectral form factor satisfies $K(\\tau) = 2 \\tau - \\tau \\log(1 + 2 \\tau)$ for small $\\tau > 0$. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof for one billiard or one negatively curved surface without arithmetic symmetry.","status_note":"","title":"Random-matrix pair correlation for a specific chaotic billiard","topic_ref":"ea13ab5f74a1c82c80da965948277a56b113b5df57a11f41c996b317accddd90"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9f982576b3f2f357f6e69fcc3255f8023bd74f6686ad0cd8e3449055b86c481c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"90a3a2c491a919710230d05e4dd59c287f63196d4363f994d677b16a00d02fe1","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"3KblsHYMh7mMp9E1RWsg5sRYXlg4dqekiKkA6KNDJ7NhpPi3pIofxXG277Fp5WqouELI_3m1SP9RRzlWFVl-BQ"},"schema":"pubphys.envelope/1"},"record_hash":"9f982576b3f2f357f6e69fcc3255f8023bd74f6686ad0cd8e3449055b86c481c","leaf_index":1647}