{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:BP6LP36HLKK6NLKZI3BJOIHSJW","short_pith_number":"pith:BP6LP36H","schema_version":"1.0","canonical_sha256":"0bfcb7efc75a95e6ad5946c29720f24da6b7064e815c09eadc1a4674eb4d8465","source":{"kind":"arxiv","id":"2403.03973","version":1},"attestation_state":"computed","paper":{"title":"MTC$[M_3, G]$: 3d Topological Order Labeled by Seifert Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.GT","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Federico Bonetti, Jingxiang Wu, Sakura Schafer-Nameki","submitted_at":"2024-03-06T19:00:00Z","abstract_excerpt":"We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group $G$. Topological order in 2+1d is known to be characterized in terms of modular tensor categories (MTCs), and we thus propose a relation between MTCs and Seifert three-manifolds. The correspondence defines for every Seifert manifold and choice of $G$ a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the center of $G$. The construction determines the spins of anyons and their S-m"},"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":"2403.03973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-03-06T19:00:00Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.GT","math.MP","math.QA"],"title_canon_sha256":"08534fa2fdf9b9e8ed110c491cc9b86cb0cfa27d2680432d0d940c5b84950690","abstract_canon_sha256":"9dfeceaa57ea6b1cd36fe4caf06fdf45913b42756d6379c81c18868a1a736f32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:53:16.455523Z","signature_b64":"VUrUVe3wEwU3NPvPeyieK+YekqE5TUhv2HICtk2GQB4aliA1+MD7RbuRZHuX8IOnMl4ebz0kwxyFx9pzJ1huDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bfcb7efc75a95e6ad5946c29720f24da6b7064e815c09eadc1a4674eb4d8465","last_reissued_at":"2026-07-05T07:53:16.455108Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:53:16.455108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"MTC$[M_3, G]$: 3d Topological Order Labeled by Seifert Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.GT","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Federico Bonetti, Jingxiang Wu, Sakura Schafer-Nameki","submitted_at":"2024-03-06T19:00:00Z","abstract_excerpt":"We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group $G$. Topological order in 2+1d is known to be characterized in terms of modular tensor categories (MTCs), and we thus propose a relation between MTCs and Seifert three-manifolds. The correspondence defines for every Seifert manifold and choice of $G$ a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the center of $G$. The construction determines the spins of anyons and their S-m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.03973","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/2403.03973/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":"2403.03973","created_at":"2026-07-05T07:53:16.455162+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.03973v1","created_at":"2026-07-05T07:53:16.455162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.03973","created_at":"2026-07-05T07:53:16.455162+00:00"},{"alias_kind":"pith_short_12","alias_value":"BP6LP36HLKK6","created_at":"2026-07-05T07:53:16.455162+00:00"},{"alias_kind":"pith_short_16","alias_value":"BP6LP36HLKK6NLKZ","created_at":"2026-07-05T07:53:16.455162+00:00"},{"alias_kind":"pith_short_8","alias_value":"BP6LP36H","created_at":"2026-07-05T07:53:16.455162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW","json":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW.json","graph_json":"https://pith.science/api/pith-number/BP6LP36HLKK6NLKZI3BJOIHSJW/graph.json","events_json":"https://pith.science/api/pith-number/BP6LP36HLKK6NLKZI3BJOIHSJW/events.json","paper":"https://pith.science/paper/BP6LP36H"},"agent_actions":{"view_html":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW","download_json":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW.json","view_paper":"https://pith.science/paper/BP6LP36H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.03973&json=true","fetch_graph":"https://pith.science/api/pith-number/BP6LP36HLKK6NLKZI3BJOIHSJW/graph.json","fetch_events":"https://pith.science/api/pith-number/BP6LP36HLKK6NLKZI3BJOIHSJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW/action/storage_attestation","attest_author":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW/action/author_attestation","sign_citation":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW/action/citation_signature","submit_replication":"https://pith.science/pith/BP6LP36HLKK6NLKZI3BJOIHSJW/action/replication_record"}},"created_at":"2026-07-05T07:53:16.455162+00:00","updated_at":"2026-07-05T07:53:16.455162+00:00"}