{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"72819202a237658c8d4696171a60720533c30fc4ce363e5e6b7c6705eb033267","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ab3993f26f18dcd785b962bce44dd3dc96eedcf5af55bc06a58c0be9ce73ccd2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.interacting-topology.fracton-classification","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In three dimensions some gapped phases have excitations that cannot move freely (fractons), and no complete list of 3D gapped phases that includes them exists.","posed_since":"","precise":"Classify gapped phases of 3D local bosonic and fermionic lattice Hamiltonians up to adiabatic deformation and stacking with decoupled 2D gapped layers (foliation equivalence), including fracton phases whose ground-state degeneracy grows with system size. Existing classifications of 3D topological orders (Lan, Kong, Wen 2018; Lan, Wen 2019) assume no fracton excitations. An answer is a set of invariants that distinguish all phases, including a criterion separating foliated from non-foliated fracton orders.","problem_ref":null,"references":"","settled_by":"A set of invariants for 3D gapped lattice phases shown to distinguish all known fracton models and to be complete within a stated framework.","status_note":"3D bosonic topological orders with bosonic (Lan, Kong, Wen 2018) and fermionic (Lan, Wen 2019) pointlike excitations were classified for non-fracton orders; a classification including fracton orders is incomplete as of 2026.","title":"Classification of three-dimensional gapped phases including fractons","topic_ref":"5eb253a73bbb2f4bfaa82a612ecbfee54b3948ffbf0c617f22b32326c4786743"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"798e0fc92882b798bdb23617f88cb12243147d278d77cebc31893cad2b406c36","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"cae846a3dd43f8e28e9a1d7c9c16e4b68286e7a25ab42db420aae8b2b52fa5f0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"sbbxjwwqaq8-cfehAVYAPgPqwvHyp5XfEbHWdiLNn3h4ygrTPr2-bT6QT1mTnihtA3CmaHkh1N0PsO4BGMeLCw"},"schema":"pubphys.envelope/1"},"record_hash":"798e0fc92882b798bdb23617f88cb12243147d278d77cebc31893cad2b406c36","leaf_index":1041}