{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b04929a8bb7d4103dd799f6fed69d45c7974d1b4c364248176b904beda1c93e6","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"af167626650dde99c322a3b2eb5e615bb9c2768c89b0c5744e0bd6b19c714897","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.interacting-topology.gapless-spt","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Some gapless (critical) states carry protected edge modes that no gapped phase with the same symmetry can have, and a general list of such gapless topological phases is missing.","posed_since":"2017","precise":"Classify symmetry-enriched gapless phases of 1D and 2D lattice models, including gapless SPT and intrinsically gapless SPT phases defined by an emergent anomaly in the low-energy symmetry action, and determine which carry protected edge modes. An answer is a classification in terms of symmetry extensions and anomalies with a lattice example in each class.","problem_ref":null,"references":"","settled_by":"A classification scheme in terms of symmetry extensions and anomalies, verified by explicit lattice realizations of every class in 1D and 2D.","status_note":"Gapless SPT phases were introduced in 1D (Scaffidi, Parker, Vasseur 2017), extended to intrinsically gapless SPT (Thorngren, Vishwanath, Verresen 2021) and classified in 1+1D by topological holography (Wen and Potter 2023); a general 2D classification is open as of 2026.","title":"Classification of intrinsically gapless topological phases","topic_ref":"5eb253a73bbb2f4bfaa82a612ecbfee54b3948ffbf0c617f22b32326c4786743"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"317ab7cd798bf94ad3fccb1859981ff7fae2483a5ff0d6cd7432c00100b4dbde","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"6ffb3d4ca44cc67b154fed97b2c50a787adc053c2937405c50c3b94608d5f2d2","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"8ofx4AkDCOtzZ1TooyKJEbhiv6ehmh_xlHoG2UKrV0EVgqJVLG4Ks1BBDv17y3Tqwv3P4npBoGX9t3D1kJ13BQ"},"schema":"pubphys.envelope/1"},"record_hash":"317ab7cd798bf94ad3fccb1859981ff7fae2483a5ff0d6cd7432c00100b4dbde","leaf_index":1042}