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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"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"c368a038ebe449a32cab524473a2c77a491344c6e4bd19107719a371b9b9dd24","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"8e5ac7d5b0fa95ce725a95c119d9ea24fb0c5de466a73ac267d6776268b81315","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"YpW1uAg3nuL83NtNSbCNbi55-VTa0HLfaSMWyzDPZowScpKDFu_jykq2kqvwJOeIb0EP0-HH5o78NhTE7wRHBw"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIjlrH1bD6lc5yWpXBGdnqJPsMXeRmpzrCZ9Z3Ymi4ExXwII5cStbrW9k_4y34nj9tRn7ugtrLib_IaO0PhJTvV6trCPAgTmSwYEPTHfveUV75bXRmqA-hNji-1kTC8Db6QgQ2nYwI8SAujNEZPbQul_oXmbUcOYtJPfbw5rJqtjdyP0Jzaekh2wjwIO-UH0Ub4lt1bJ6M1AkUbw6XQKF8vG97sInnt1DpguKpCPEgpODYWocrOEkEyCj2DYZJiIfHeufTuFlAmp0wiJaAdvUI8CBYYUQhbZK85w81LfXKqkfKcfmWcro4e5k6OJXBzEi2OwjwIBuXyrcwi8vWjA4uFLMsDvI7QxQ03VAxIfMd0CQI4GySCPAgyYYKAjmHpniaTNWfQfwaMNMI3Vm3FjqZ7JUny3t_J48I8SAzYkfrMCtnlPZF7RCs0vhySIZDq30HHv5Q-Y2E93F_lgjwIIhzmnVeFxVHRiBmi7SsQd_gIBRvsrzzZf-fzyEkp8wnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvACD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIkVp-kOP6OowYyEn1rPXBe2fWDBzNnuiLNwZAL2HumdfwIJFnfO8XHKj5RqZB1eotHDSnIsrKiZOnRLdYYyZ3G1sECPAg2c1_BJ3LcVozB-D6y2uEJFl6rFTPFp422rrMEoTdeVEI8CClGwX2HuFfc3imQVeIYKGYgcF9fM__W8Tw1SDRPOKrUwjwIE_paJQgzJtz_AIGuh_cUlMTLxiblH7x63A3yGn1-uBxCPEgp9zJCwjD-pxWhOw-oufxmOznjCr8AAdaVwutqJkzciQI8CAEwc_TDAArJnS7L12hyepqNpIfWdUKeTwknlQYdJa64wjxID4GM9LaCJsrZhWbEPtHBfDrOPGQi4CH8Bu_7M-4ow1RCPAgyYYKAjmHpniaTNWfQfwaMNMI3Vm3FjqZ7JUny3t_J48I8SAzYkfrMCtnlPZF7RCs0vhySIZDq30HHv5Q-Y2E93F_lgjwIIhzmnVeFxVHRiBmi7SsQd_gIBRvsrzzZf-fzyEkp8wnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvACD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn"]},"log":{"leaf_index":"1645","tree_size":"2123","proof":["aa75aa144e9b6846f64d4a328652cd9a74951ff5069cb7f831fba25c140fe2d3","4602265e6feabd9d256c1d53a59bad5b4a8c9f4d2b875f63f784ffe0c46bfc42","ca80ca1862eca13042de8259b970e1c17c691abbc6a9bcf28c801c1c99903c75","1361380c06eb7be82a18479f43058d7e0c0844169ecc44bfd09c5ab9759f9c43","1389dfb25e6722dfbcd3171651f84b69130ec8415cd7f1e9717f7dad8046e5d0","594f9ab8a5cbdde0cccfba43624659f96df1cdc69fb04da06f16a50a95f3ad3b","0bfc77bd061b3d7ef211c4f18a6ac184c91d825819cd6cc52c171e49aaa9d794","b78ddae6ec4f50645dafadd88148aea3eac280e472349d3dbe77576e43fa2780","a8cef064ef9c15524538954d820d60e39424932bbb86df562c6b87106df2eda9","35f1d0a5e69da98f9992a5251e4e3df1933c2f26543c7a40b2681ecfa194443a","2b97406e15e4d451a5450b3b53b677749fe0fa759579146dbfa1544c1e61a0ed","addcf2e0ff7974e4aa99af5e30d409f90d9f4311a4d85f5baf3e125eeb45b4c1"],"checkpoint":"pubphys.com/log/v1\n2123\npXVcluz7BF4vgChQs6lShuU0386gCH0RxrC1sxyE3rI=\n\n— pubphys.com/log/v1 JFPwIOLzsUD22XoTVyTfk/FMVj/u3f3DxZk4V/Ws10KVSS+8WQSwhunQ//EAhyS9Td5CyM0E++85GMezmKd8240j9Q8=\n","promise":null},"orcid_key_evidence":[],"attesting":null}