{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:22FL7UK5XZJHBAU2MLSR2FHAKN","short_pith_number":"pith:22FL7UK5","schema_version":"1.0","canonical_sha256":"d68abfd15dbe5270829a62e51d14e0534a0377271212df6d5291bf43fbb2d58a","source":{"kind":"arxiv","id":"1511.07982","version":2},"attestation_state":"computed","paper":{"title":"Torsion-freeness for fusion rings and tensor C*-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.QA"],"primary_cat":"math.RA","authors_text":"Kenny De Commer, Yuki Arano","submitted_at":"2015-11-25T08:00:42Z","abstract_excerpt":"Torsion-freeness for discrete quantum groups was introduced by R. Meyer in order to formulate a version of the Baum-Connes conjecture for discrete quantum groups. In this note, we introduce torsion-freeness for abstract fusion rings. We show that a discrete quantum group is torsion-free if its associated fusion ring is torsion-free. In the latter case, we say that the discrete quantum group is strongly torsion-free. As applications, we show that the discrete quantum group duals of the free unitary quantum groups are strongly torsion-free, and that torsion-freeness of discrete quantum groups is"},"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":"1511.07982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-25T08:00:42Z","cross_cats_sorted":["math.OA","math.QA"],"title_canon_sha256":"725fb98ef0c5b7a8158cab2c0d3d0e90f7f5820d8b9ce8e8dcd5dd1a995bd56a","abstract_canon_sha256":"1222be516617296be4eed764167c2d28a70b8afad8926a3f00b349ef7995045f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:11.012659Z","signature_b64":"DvyLCxjvBaj87AL2PvIgrxhJJ/evjdU+t83NpVfo8l/NKyj6kOkW2cKPLdhVWe8/RmgLBD1S7cj9i7EjIKAQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d68abfd15dbe5270829a62e51d14e0534a0377271212df6d5291bf43fbb2d58a","last_reissued_at":"2026-05-18T01:25:11.011997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:11.011997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torsion-freeness for fusion rings and tensor C*-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.QA"],"primary_cat":"math.RA","authors_text":"Kenny De Commer, Yuki Arano","submitted_at":"2015-11-25T08:00:42Z","abstract_excerpt":"Torsion-freeness for discrete quantum groups was introduced by R. Meyer in order to formulate a version of the Baum-Connes conjecture for discrete quantum groups. In this note, we introduce torsion-freeness for abstract fusion rings. We show that a discrete quantum group is torsion-free if its associated fusion ring is torsion-free. In the latter case, we say that the discrete quantum group is strongly torsion-free. As applications, we show that the discrete quantum group duals of the free unitary quantum groups are strongly torsion-free, and that torsion-freeness of discrete quantum groups is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07982","kind":"arxiv","version":2},"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":"1511.07982","created_at":"2026-05-18T01:25:11.012101+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.07982v2","created_at":"2026-05-18T01:25:11.012101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07982","created_at":"2026-05-18T01:25:11.012101+00:00"},{"alias_kind":"pith_short_12","alias_value":"22FL7UK5XZJH","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"22FL7UK5XZJHBAU2","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"22FL7UK5","created_at":"2026-05-18T12:28:59.999130+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/22FL7UK5XZJHBAU2MLSR2FHAKN","json":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN.json","graph_json":"https://pith.science/api/pith-number/22FL7UK5XZJHBAU2MLSR2FHAKN/graph.json","events_json":"https://pith.science/api/pith-number/22FL7UK5XZJHBAU2MLSR2FHAKN/events.json","paper":"https://pith.science/paper/22FL7UK5"},"agent_actions":{"view_html":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN","download_json":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN.json","view_paper":"https://pith.science/paper/22FL7UK5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.07982&json=true","fetch_graph":"https://pith.science/api/pith-number/22FL7UK5XZJHBAU2MLSR2FHAKN/graph.json","fetch_events":"https://pith.science/api/pith-number/22FL7UK5XZJHBAU2MLSR2FHAKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN/action/storage_attestation","attest_author":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN/action/author_attestation","sign_citation":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN/action/citation_signature","submit_replication":"https://pith.science/pith/22FL7UK5XZJHBAU2MLSR2FHAKN/action/replication_record"}},"created_at":"2026-05-18T01:25:11.012101+00:00","updated_at":"2026-05-18T01:25:11.012101+00:00"}