{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EJXBKH72WNEHGVJLAVJNH7ULVM","short_pith_number":"pith:EJXBKH72","schema_version":"1.0","canonical_sha256":"226e151ffab34873552b0552d3fe8bab2625b881c697d49882472092f303760f","source":{"kind":"arxiv","id":"1706.01845","version":1},"attestation_state":"computed","paper":{"title":"Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. Thuillier, Ph. Mathieu","submitted_at":"2017-06-06T16:29:31Z","abstract_excerpt":"In this article we construct the Reshetikhin-Turaev invariant associated with the Drinfeld Center of the spherical category arising from the $U(1)$ BF theory on a closed $3$-manifold $M$. This invariant is shown to coincide with the Turaev-Viro invariant of $M$ thus providing an example of the Turaev-Virelizier theorem. Finally we exhibit some surgery formulas for the abelian Turaev-Viro invariant which are very similar to the surgery formulas of the abelian Reshetikhin-Turaev invariant obtained in the $U(1)$ Chern-Simons context."},"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":"1706.01845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-06T16:29:31Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b0d9fbce5369fa14d013512bdc8b7d58a90d1f4099856a8a26ab7b06c3c2c449","abstract_canon_sha256":"2302d94fc351e56a806b0ccbbb976c5d8dbafe81815ecea263c6f40f3c3f9d20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:09.693057Z","signature_b64":"CoCFV3UEgiEzTwghzr+6jHEtAOcjEMsaokojFqfLbfYcJc+BryM/7cc4HvKBQdNQahnFryrxSGo/CPjO0TooAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"226e151ffab34873552b0552d3fe8bab2625b881c697d49882472092f303760f","last_reissued_at":"2026-05-18T00:32:09.692297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:09.692297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. Thuillier, Ph. Mathieu","submitted_at":"2017-06-06T16:29:31Z","abstract_excerpt":"In this article we construct the Reshetikhin-Turaev invariant associated with the Drinfeld Center of the spherical category arising from the $U(1)$ BF theory on a closed $3$-manifold $M$. This invariant is shown to coincide with the Turaev-Viro invariant of $M$ thus providing an example of the Turaev-Virelizier theorem. Finally we exhibit some surgery formulas for the abelian Turaev-Viro invariant which are very similar to the surgery formulas of the abelian Reshetikhin-Turaev invariant obtained in the $U(1)$ Chern-Simons context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01845","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":""},"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":"1706.01845","created_at":"2026-05-18T00:32:09.692438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01845v1","created_at":"2026-05-18T00:32:09.692438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01845","created_at":"2026-05-18T00:32:09.692438+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJXBKH72WNEH","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJXBKH72WNEHGVJL","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJXBKH72","created_at":"2026-05-18T12:31:12.930513+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/EJXBKH72WNEHGVJLAVJNH7ULVM","json":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM.json","graph_json":"https://pith.science/api/pith-number/EJXBKH72WNEHGVJLAVJNH7ULVM/graph.json","events_json":"https://pith.science/api/pith-number/EJXBKH72WNEHGVJLAVJNH7ULVM/events.json","paper":"https://pith.science/paper/EJXBKH72"},"agent_actions":{"view_html":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM","download_json":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM.json","view_paper":"https://pith.science/paper/EJXBKH72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01845&json=true","fetch_graph":"https://pith.science/api/pith-number/EJXBKH72WNEHGVJLAVJNH7ULVM/graph.json","fetch_events":"https://pith.science/api/pith-number/EJXBKH72WNEHGVJLAVJNH7ULVM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM/action/storage_attestation","attest_author":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM/action/author_attestation","sign_citation":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM/action/citation_signature","submit_replication":"https://pith.science/pith/EJXBKH72WNEHGVJLAVJNH7ULVM/action/replication_record"}},"created_at":"2026-05-18T00:32:09.692438+00:00","updated_at":"2026-05-18T00:32:09.692438+00:00"}