{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"c065bcb7a86f67f2decbe5115d887bc52aeb88e190b09adc6ad77cfb5078113f","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0d1577c696befbedfdfa5b101e1bcb7fa9db165e328d0a0f49ff04899bd7e3df","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"qft.spacetime-entanglement.entropy-cone-six","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Entanglement between regions of a holographic system obeys special inequalities that general quantum systems need not obey. The full list is known only up to five regions.","posed_since":"2015","precise":"For n boundary regions, the Ryu-Takayanagi entropies of all $2^n - 1$ unions form a polyhedral cone (Bao et al. 2015). Determine the complete list of facets (holographic entropy inequalities) for $n = 6$; the cone is known for $n \\le 5$.","problem_ref":null,"references":"","settled_by":"A complete list of $n = 6$ facets with a proof that each is valid and tight and that no others exist.","status_note":"$n = 5$ was completed in 2019; 2024-2026 work computed extreme rays of the 6-party strong-subadditivity-compatible cone and applied reinforcement-learning searches, without a complete 6-party facet list.","title":"Holographic entropy inequalities for six regions","topic_ref":"a8de1433c3e67a1501a86682e650f763fed755c7d64a2db5a831f9cb7611369e"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8f4a67f30ac80b4cd6b7ebad93c079fc830ff497d2214080bc2e1f858d990869","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"3346cd333eb28996a8a5edfcb9d7dba3b1f13714425f0d37e6732c5c35239795","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"dYbrHzGgCc8hq_LDErZ9tdSNueW3zvxKDKpIrBeGrMvVlWD1iJ2EOz92TVddTf3rBR3pyp1TDgxSwi7sJzzhDg"},"schema":"pubphys.envelope/1"},"record_hash":"8f4a67f30ac80b4cd6b7ebad93c079fc830ff497d2214080bc2e1f858d990869","leaf_index":1949}