{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OPEUZFNK2GRWQNKCTWX4LSUHII","short_pith_number":"pith:OPEUZFNK","schema_version":"1.0","canonical_sha256":"73c94c95aad1a36835429dafc5ca87422c60a2f0541d988033b6970c827224e4","source":{"kind":"arxiv","id":"1404.7854","version":3},"attestation_state":"computed","paper":{"title":"Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Juven Wang, Xiao-Gang Wen","submitted_at":"2014-04-30T19:59:09Z","abstract_excerpt":"String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\\omega_4$ of $G$'s cohomology group $\\mathcal{H}^4(G,\\mathbb{R}/\\mathbb{Z})$ in 3 dimensional space and 1 dimensional time (3+1D). We establish the topological spin and the spin-statistics relation for the closed strings, and their multi-string braiding statistics. The 3+1D twisted gauge theory can be characterized by a representation of a modular transformation group SL$(3,\\mathbb{Z})$. We express the SL$(3,\\mathbb{Z})$ genera"},"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":"1404.7854","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-04-30T19:59:09Z","cross_cats_sorted":["hep-th","math.QA","quant-ph"],"title_canon_sha256":"2b4c3e5685d8ff477ae388fc473ccf45795ddbcad64c86ec9ce5ca0701ee4c57","abstract_canon_sha256":"00fdd0355549428175846d9478d838f121c4e28fbc8ba762c4841b06cf625664"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:23.031998Z","signature_b64":"zAxTdUdsHadGsdoCvrlXN4OW4EpJJFLJI/cO9p7VbVoMOaUtSPNXnGeSyRjgOOmtnh9DUcrSUevcYjOJ5057DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73c94c95aad1a36835429dafc5ca87422c60a2f0541d988033b6970c827224e4","last_reissued_at":"2026-05-18T02:28:23.031448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:23.031448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Juven Wang, Xiao-Gang Wen","submitted_at":"2014-04-30T19:59:09Z","abstract_excerpt":"String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\\omega_4$ of $G$'s cohomology group $\\mathcal{H}^4(G,\\mathbb{R}/\\mathbb{Z})$ in 3 dimensional space and 1 dimensional time (3+1D). We establish the topological spin and the spin-statistics relation for the closed strings, and their multi-string braiding statistics. The 3+1D twisted gauge theory can be characterized by a representation of a modular transformation group SL$(3,\\mathbb{Z})$. We express the SL$(3,\\mathbb{Z})$ genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7854","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1404.7854","created_at":"2026-05-18T02:28:23.031566+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.7854v3","created_at":"2026-05-18T02:28:23.031566+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7854","created_at":"2026-05-18T02:28:23.031566+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPEUZFNK2GRW","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPEUZFNK2GRWQNKC","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPEUZFNK","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.12323","citing_title":"On the SymTFTs of Finite Non-Abelian Symmetries","ref_index":70,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII","json":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII.json","graph_json":"https://pith.science/api/pith-number/OPEUZFNK2GRWQNKCTWX4LSUHII/graph.json","events_json":"https://pith.science/api/pith-number/OPEUZFNK2GRWQNKCTWX4LSUHII/events.json","paper":"https://pith.science/paper/OPEUZFNK"},"agent_actions":{"view_html":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII","download_json":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII.json","view_paper":"https://pith.science/paper/OPEUZFNK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.7854&json=true","fetch_graph":"https://pith.science/api/pith-number/OPEUZFNK2GRWQNKCTWX4LSUHII/graph.json","fetch_events":"https://pith.science/api/pith-number/OPEUZFNK2GRWQNKCTWX4LSUHII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII/action/storage_attestation","attest_author":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII/action/author_attestation","sign_citation":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII/action/citation_signature","submit_replication":"https://pith.science/pith/OPEUZFNK2GRWQNKCTWX4LSUHII/action/replication_record"}},"created_at":"2026-05-18T02:28:23.031566+00:00","updated_at":"2026-05-18T02:28:23.031566+00:00"}