{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:H7HDBEH4YXGO2I3EDAATHWZ65F","short_pith_number":"pith:H7HDBEH4","schema_version":"1.0","canonical_sha256":"3fce3090fcc5cced2364180133db3ee97b0500067bb580737b8150d41f42589c","source":{"kind":"arxiv","id":"1109.5558","version":1},"attestation_state":"computed","paper":{"title":"On the structure of the Witt group of braided fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Alexei Davydov, Dmitri Nikshych, Victor Ostrik","submitted_at":"2011-09-26T13:35:34Z","abstract_excerpt":"We analyze the structure of the Witt group W of braided fusion categories introduced in the previous paper arXiv:1009.2117v2. We define a \"super\" version of the categorical Witt group, namely, the group sW of slightly degenerate braided fusion categories. We prove that sW is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism S: W --> sW is generated by Ising categories and is isomorphic to Z/16Z. Finally, we give a complete description of etale algebras in tensor products of braided fus"},"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":"1109.5558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-26T13:35:34Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9537abc2fab17d1a4b584ccc5e04941be4223ec395fc250ef3347b3acad00d09","abstract_canon_sha256":"8fb24f14231b4e6a63fa278b9ad37e978344d79372cfa6e060d15766323407f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.139246Z","signature_b64":"VaDo7jDMQpLxFKUEdUV+tGZzTd8xP86YyU0BwrIyaEGJrJQkESuQvYvcFESabyF9Ar25l4g7/OP1b/obqXACDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fce3090fcc5cced2364180133db3ee97b0500067bb580737b8150d41f42589c","last_reissued_at":"2026-05-18T03:12:58.138388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.138388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of the Witt group of braided fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Alexei Davydov, Dmitri Nikshych, Victor Ostrik","submitted_at":"2011-09-26T13:35:34Z","abstract_excerpt":"We analyze the structure of the Witt group W of braided fusion categories introduced in the previous paper arXiv:1009.2117v2. We define a \"super\" version of the categorical Witt group, namely, the group sW of slightly degenerate braided fusion categories. We prove that sW is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism S: W --> sW is generated by Ising categories and is isomorphic to Z/16Z. Finally, we give a complete description of etale algebras in tensor products of braided fus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5558","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":"1109.5558","created_at":"2026-05-18T03:12:58.138531+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5558v1","created_at":"2026-05-18T03:12:58.138531+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5558","created_at":"2026-05-18T03:12:58.138531+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7HDBEH4YXGO","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7HDBEH4YXGO2I3E","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7HDBEH4","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2308.00747","citing_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","ref_index":270,"is_internal_anchor":true},{"citing_arxiv_id":"2604.24847","citing_title":"The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F","json":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F.json","graph_json":"https://pith.science/api/pith-number/H7HDBEH4YXGO2I3EDAATHWZ65F/graph.json","events_json":"https://pith.science/api/pith-number/H7HDBEH4YXGO2I3EDAATHWZ65F/events.json","paper":"https://pith.science/paper/H7HDBEH4"},"agent_actions":{"view_html":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F","download_json":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F.json","view_paper":"https://pith.science/paper/H7HDBEH4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5558&json=true","fetch_graph":"https://pith.science/api/pith-number/H7HDBEH4YXGO2I3EDAATHWZ65F/graph.json","fetch_events":"https://pith.science/api/pith-number/H7HDBEH4YXGO2I3EDAATHWZ65F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F/action/storage_attestation","attest_author":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F/action/author_attestation","sign_citation":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F/action/citation_signature","submit_replication":"https://pith.science/pith/H7HDBEH4YXGO2I3EDAATHWZ65F/action/replication_record"}},"created_at":"2026-05-18T03:12:58.138531+00:00","updated_at":"2026-05-18T03:12:58.138531+00:00"}