{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6639ed876fcf2c9344b3a3c271225ad270bf7a10c7dd9d5d2a4994ad4f7751d6","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a7e0d0950e4a54a9114b1a6df7c25c8032f2b79871e42522d343b924f8afc288","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.quantum-chaos.berry-tabor","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"For systems with regular classical motion, quantum levels should be spaced like uncorrelated random numbers. Even for a flat rectangular drum this is only partly proven.","posed_since":"1977","precise":"Laplacian on the flat torus with eigenvalues $m^{2} + \\alpha n^{2}$ (m, n integers). Prove that the nearest-neighbour spacing distribution of the unfolded eigenvalues is $\\exp(-s)$ for almost every $\\alpha$, or for an explicit Diophantine $\\alpha$. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of Poisson higher correlations or spacing distribution for almost every $\\alpha$.","status_note":"Pair correlation is Poisson for almost every $\\alpha$ (Sarnak, 1997) and for explicit Diophantine $\\alpha$ (Eskin, Margulis and Mozes, 2005); higher correlations and the spacing distribution remain open.","title":"Poisson spacing statistics for generic integrable systems","topic_ref":"ea13ab5f74a1c82c80da965948277a56b113b5df57a11f41c996b317accddd90"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"c368a038ebe449a32cab524473a2c77a491344c6e4bd19107719a371b9b9dd24","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"8e5ac7d5b0fa95ce725a95c119d9ea24fb0c5de466a73ac267d6776268b81315","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"YpW1uAg3nuL83NtNSbCNbi55-VTa0HLfaSMWyzDPZowScpKDFu_jykq2kqvwJOeIb0EP0-HH5o78NhTE7wRHBw"},"schema":"pubphys.envelope/1"},"record_hash":"c368a038ebe449a32cab524473a2c77a491344c6e4bd19107719a371b9b9dd24","leaf_index":1645}