{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ad525b2c210f46c0d7791a7dc17d21942a5119b7b1bd56905ac3bec2babff631","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","f40998596bac10f98640f4ea60b24897b7408f7ec3baa5aaeaece28c93fa5538"],"salt":"6d0e782d5f4304d5de6d72bd0c95d564d8987f2e93b32fd23dbee26fc3aafb61","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":"1","parents":[{"note":"","parent_revision":"f40998596bac10f98640f4ea60b24897b7408f7ec3baa5aaeaece28c93fa5538","relation":"special_case"}],"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 $6 x 6$ complex Hadamard matrices suggest that four do not exist.","problem_ref":null,"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":"1bdfc0d09903d73034d6e6510c6d21f380d002328cb4a356dee914b540fb53cc"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"19324b47103d38f2308232f62aeedd21c2f750fbcee81b9c4d8d74fb26b1d280","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7065d945f5ad89d67e719a872999a835453504c43ab2e1cb477aeb6ea7d24b01","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"lsEnlDaHkjQvBedSyi65l5yuMulb8MwUOCJB1Rwwj-rhX7eDXzg9sJB6PlIHL4cfxfjGaU6aIL5ctbaj0xkcAw"},"schema":"pubphys.envelope/1"},"record_hash":"19324b47103d38f2308232f62aeedd21c2f750fbcee81b9c4d8d74fb26b1d280","leaf_index":2054}