{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"55c9930c32d22b7efdf7e72cb5ca4641ac02bb167925ece1ce0f311b72e8c3de","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4fde298a1367ec8a6a935afbe86973f138b7fa64e2a68be8d0304d6c9b453a84","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.interacting-topology.crystalline-fermionic-spt","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Crystal symmetries such as rotations and reflections protect extra topological phases, and for interacting electrons in three dimensions the complete list for all 230 crystal symmetry groups is not known.","posed_since":"2017","precise":"For interacting fermions with U(1) charge conservation, spin-orbit coupling and time reversal, classify 3D symmetry-protected topological phases for each of the 230 space groups, for example by real-space block-state (topological crystal) constructions, and determine which free-fermion topological crystalline insulators stay distinct with interactions. An answer is a table of classification groups per space group with explicit generators.","problem_ref":null,"references":"","settled_by":"A complete block-state or equivalent computation for all 230 space groups, cross-checked against free-fermion symmetry-indicator results.","status_note":"Bosonic crystalline phases and 2D fermionic wallpaper-group cases were classified by about 2020; to this survey's knowledge the full 3D interacting fermionic table is not complete as of 2026.","title":"Interacting fermionic crystalline topological phases for all 3D space groups","topic_ref":"5eb253a73bbb2f4bfaa82a612ecbfee54b3948ffbf0c617f22b32326c4786743"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9d9d1abf333d946974debc073e80b0c9f4aa631fcb588edb69d7b29bba20d4f6","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"02b18c000fd4a3c5cb0a07c2cdf6e6bae272ee765c1823105eae800b85a161ee","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"e27sV0rCcDgQH_II7pCOorckiKIykvXJt4nyRdrA2I2W5FIYVkIk5IGKpI-gv_UdTslIu7TQPWjN7Bb5QhRJCQ"},"schema":"pubphys.envelope/1"},"record_hash":"9d9d1abf333d946974debc073e80b0c9f4aa631fcb588edb69d7b29bba20d4f6","leaf_index":1040}