{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:K445DZUSNWDGHSEFJVZ3I2YS5H","short_pith_number":"pith:K445DZUS","schema_version":"1.0","canonical_sha256":"5739d1e6926d8663c8854d73b46b12e9e61aa598726e04afc640cd77e5d9072f","source":{"kind":"arxiv","id":"2502.20440","version":2},"attestation_state":"computed","paper":{"title":"Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part II","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.CT","math.MP"],"primary_cat":"hep-th","authors_text":"Alison Warman, Apoorv Tiwari, Lakshya Bhardwaj, Sakura Schafer-Nameki","submitted_at":"2025-02-27T19:00:01Z","abstract_excerpt":"We use the Symmetry Topological Field Theory (SymTFT) to systematically characterize gapped phases in 2+1 dimensions with categorical symmetries. The SymTFTs that we consider are (3+1)d Dijkgraaf-Witten (DW) theories for finite groups $G$, whose gapped boundaries realize all so-called ``All Bosonic type\" fusion 2-category symmetries. In arXiv:2408.05266 we provided the general framework and studied the case where $G$ is an abelian group. In this work we focus on the case of non-Abelian $G$. Gapped boundary conditions play a central role in the SymTFT construction of symmetric gapped phases. Th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2502.20440","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-27T19:00:01Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.CT","math.MP"],"title_canon_sha256":"c98df3ab22eedd1e7e6e3e67495ede11e859407a39170d7b99667734394bead6","abstract_canon_sha256":"ed2bc7ba70fd42776d8842ed3fb44b80014a2d3dcc80d0f0227ec1922f2cef00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:15.095007Z","signature_b64":"0uEAvyQ1mb1Eo2Xjrk5xKi/ZUPRcy4E+BOyfK5Lt2q0pfRCD56RnmC/V5/wz54XcZ33pjWQ0oQKnsh4bJnwMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5739d1e6926d8663c8854d73b46b12e9e61aa598726e04afc640cd77e5d9072f","last_reissued_at":"2026-07-05T10:26:15.094505Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:15.094505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part II","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.CT","math.MP"],"primary_cat":"hep-th","authors_text":"Alison Warman, Apoorv Tiwari, Lakshya Bhardwaj, Sakura Schafer-Nameki","submitted_at":"2025-02-27T19:00:01Z","abstract_excerpt":"We use the Symmetry Topological Field Theory (SymTFT) to systematically characterize gapped phases in 2+1 dimensions with categorical symmetries. The SymTFTs that we consider are (3+1)d Dijkgraaf-Witten (DW) theories for finite groups $G$, whose gapped boundaries realize all so-called ``All Bosonic type\" fusion 2-category symmetries. In arXiv:2408.05266 we provided the general framework and studied the case where $G$ is an abelian group. In this work we focus on the case of non-Abelian $G$. Gapped boundary conditions play a central role in the SymTFT construction of symmetric gapped phases. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20440","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.20440/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.20440","created_at":"2026-07-05T10:26:15.094562+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.20440v2","created_at":"2026-07-05T10:26:15.094562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.20440","created_at":"2026-07-05T10:26:15.094562+00:00"},{"alias_kind":"pith_short_12","alias_value":"K445DZUSNWDG","created_at":"2026-07-05T10:26:15.094562+00:00"},{"alias_kind":"pith_short_16","alias_value":"K445DZUSNWDGHSEF","created_at":"2026-07-05T10:26:15.094562+00:00"},{"alias_kind":"pith_short_8","alias_value":"K445DZUS","created_at":"2026-07-05T10:26:15.094562+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.31602","citing_title":"Twin Algebras: Condensable Algebras beyond Anyons","ref_index":85,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H","json":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H.json","graph_json":"https://pith.science/api/pith-number/K445DZUSNWDGHSEFJVZ3I2YS5H/graph.json","events_json":"https://pith.science/api/pith-number/K445DZUSNWDGHSEFJVZ3I2YS5H/events.json","paper":"https://pith.science/paper/K445DZUS"},"agent_actions":{"view_html":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H","download_json":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H.json","view_paper":"https://pith.science/paper/K445DZUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.20440&json=true","fetch_graph":"https://pith.science/api/pith-number/K445DZUSNWDGHSEFJVZ3I2YS5H/graph.json","fetch_events":"https://pith.science/api/pith-number/K445DZUSNWDGHSEFJVZ3I2YS5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H/action/storage_attestation","attest_author":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H/action/author_attestation","sign_citation":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H/action/citation_signature","submit_replication":"https://pith.science/pith/K445DZUSNWDGHSEFJVZ3I2YS5H/action/replication_record"}},"created_at":"2026-07-05T10:26:15.094562+00:00","updated_at":"2026-07-05T10:26:15.094562+00:00"}