{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9fdad42931e853ad51d50213b9d9ca195b8da33ec03aeb6bd3f263f21c7beda9","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["19324b47103d38f2308232f62aeedd21c2f750fbcee81b9c4d8d74fb26b1d280","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"5a0c96453f4f387c8cdc05095636df314d3905ea6ec78938ccc7e3592e6ec066","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.sic-mub.mub-dimension-six","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"In dimension 6, the smallest that is not a power of a prime, three mutually unbiased bases are known and a perfect set would have seven. Whether even a fourth exists is unknown.","posed_since":"","precise":"Do there exist four orthonormal bases of $C^6$ such that $\\left|\\langle a \\mid b\\rangle\\right|^2 = 1/6$ for any vectors a, b taken from different bases? Three are known; numerics and partial classifications of $6 \\times 6$ complex Hadamard matrices suggest that four do not exist.","problem_ref":"19324b47103d38f2308232f62aeedd21c2f750fbcee81b9c4d8d74fb26b1d280","references":"","settled_by":"A proof of non-existence (for example via a complete classification of order-6 complex Hadamard matrices), or explicit four bases.","status_note":"Still described as open in September 2026; a claimed complete classification of order-6 complex Hadamard matrices (arXiv:2608.18053) has not closed it.","title":"Do four mutually unbiased bases exist in dimension six?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"4fa13519b224d0902a2a98bbe24874bbd8ce52c5168a8ce7cd79c419dd889daf","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"062702cd1e77b8d25569640ffb8944056e4ecd900553fe1b67d808c3ec482acf","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"5ztQEah_wh7EbK3xKUzOp7mkUeo5AAAQsV3E__A2wXazwLIVd7M0QWoA9ZGxvv9sFn7h-gCK7p2F6yKULHaECg"},"schema":"pubphys.envelope/1"},"record_hash":"4fa13519b224d0902a2a98bbe24874bbd8ce52c5168a8ce7cd79c419dd889daf","leaf_index":3760}