{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OXWFUXAZREOPSQ4TX7R52HL5AA","short_pith_number":"pith:OXWFUXAZ","schema_version":"1.0","canonical_sha256":"75ec5a5c19891cf94393bfe3dd1d7d0031d47a2b88d5b1fa79107c687df14874","source":{"kind":"arxiv","id":"2508.08245","version":1},"attestation_state":"computed","paper":{"title":"Symmetry-Enriched Topological Phases and Their Gauging: A String-Net Model Realization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Nianrui Fu, Yidun Wan, Yu Zhao","submitted_at":"2025-08-11T17:58:03Z","abstract_excerpt":"We present a systematic framework for constructing exactly-solvable lattice models of symmetry-enriched topological (SET) phases based on an enlarged version of the string-net model. We also gauge the global symmetries of our SET models to obtain string-net models of pure topological phases. Without invoking externally imposed onsite symmetry actions, our approach promotes the string-net model of a pure topological order, specified by an input unitary fusion category $\\mathscr{F}$, to an SET model, specified by a multifusion category together with a set of isomorphisms. Two complementary const"},"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":"2508.08245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2025-08-11T17:58:03Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"title_canon_sha256":"5944a560eabd5afbfbd2a78959578ff385dd97e9a2d5eeb03a474d5ee049143d","abstract_canon_sha256":"ada71a356ae18625aa1f66bc85041e7d326b59e68be31f32a9ff5473a964012c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:52:10.196361Z","signature_b64":"5oUR8rA0+7K0l4o807SvvJUiq47zRBKNkzApStMF+bO7iQBm+TdRtKpPEQ6K0Pwe1L3bnMRoHe1A5+W2zyLPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75ec5a5c19891cf94393bfe3dd1d7d0031d47a2b88d5b1fa79107c687df14874","last_reissued_at":"2026-07-05T11:52:10.195624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:52:10.195624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetry-Enriched Topological Phases and Their Gauging: A String-Net Model Realization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Nianrui Fu, Yidun Wan, Yu Zhao","submitted_at":"2025-08-11T17:58:03Z","abstract_excerpt":"We present a systematic framework for constructing exactly-solvable lattice models of symmetry-enriched topological (SET) phases based on an enlarged version of the string-net model. We also gauge the global symmetries of our SET models to obtain string-net models of pure topological phases. Without invoking externally imposed onsite symmetry actions, our approach promotes the string-net model of a pure topological order, specified by an input unitary fusion category $\\mathscr{F}$, to an SET model, specified by a multifusion category together with a set of isomorphisms. Two complementary const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08245","kind":"arxiv","version":1},"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/2508.08245/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":"2508.08245","created_at":"2026-07-05T11:52:10.195874+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.08245v1","created_at":"2026-07-05T11:52:10.195874+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.08245","created_at":"2026-07-05T11:52:10.195874+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXWFUXAZREOP","created_at":"2026-07-05T11:52:10.195874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXWFUXAZREOPSQ4T","created_at":"2026-07-05T11:52:10.195874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXWFUXAZ","created_at":"2026-07-05T11:52:10.195874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.05294","citing_title":"Self-dual $S_3$ gauge theory in 2+1d: lattice model and topological phase transitions","ref_index":81,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA","json":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA.json","graph_json":"https://pith.science/api/pith-number/OXWFUXAZREOPSQ4TX7R52HL5AA/graph.json","events_json":"https://pith.science/api/pith-number/OXWFUXAZREOPSQ4TX7R52HL5AA/events.json","paper":"https://pith.science/paper/OXWFUXAZ"},"agent_actions":{"view_html":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA","download_json":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA.json","view_paper":"https://pith.science/paper/OXWFUXAZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.08245&json=true","fetch_graph":"https://pith.science/api/pith-number/OXWFUXAZREOPSQ4TX7R52HL5AA/graph.json","fetch_events":"https://pith.science/api/pith-number/OXWFUXAZREOPSQ4TX7R52HL5AA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA/action/storage_attestation","attest_author":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA/action/author_attestation","sign_citation":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA/action/citation_signature","submit_replication":"https://pith.science/pith/OXWFUXAZREOPSQ4TX7R52HL5AA/action/replication_record"}},"created_at":"2026-07-05T11:52:10.195874+00:00","updated_at":"2026-07-05T11:52:10.195874+00:00"}