{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:3LUG22OSY57EBEX5WTRMAQ4CQ4","short_pith_number":"pith:3LUG22OS","schema_version":"1.0","canonical_sha256":"dae86d69d2c77e4092fdb4e2c0438287364a919a62da5227d7d79e9238bf1365","source":{"kind":"arxiv","id":"1103.1660","version":2},"attestation_state":"computed","paper":{"title":"Traces on ideals in pivotal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Alexis Virelizier, Bertrand Patureau-Mirand, Nathan Geer","submitted_at":"2011-03-08T22:51:31Z","abstract_excerpt":"We extend the notion of an ambidextrous trace on an ideal (developed by the first two authors) to the setting of a pivotal category. We show that under some conditions, these traces lead to invariants of colored spherical graphs (and so to modified 6j-symbols)."},"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":"1103.1660","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-08T22:51:31Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"5283e983663e28f884fb7378b13cc3a645145a21bd2d69b49549c02254c99d4e","abstract_canon_sha256":"af95fda9ee95f8965c0279256a72cfe850ba00c112d89f2a29e7e39c037c01fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:38.313078Z","signature_b64":"MOiDGf0H7MWQXw/Ey0kRTUdCQkvM9aJjc6NdEo9gpBau2xny41r8Q0wM6LjSv0Tmjc+1NPfr6QGrz3JQeJIoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dae86d69d2c77e4092fdb4e2c0438287364a919a62da5227d7d79e9238bf1365","last_reissued_at":"2026-05-18T03:59:38.312551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:38.312551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Traces on ideals in pivotal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Alexis Virelizier, Bertrand Patureau-Mirand, Nathan Geer","submitted_at":"2011-03-08T22:51:31Z","abstract_excerpt":"We extend the notion of an ambidextrous trace on an ideal (developed by the first two authors) to the setting of a pivotal category. We show that under some conditions, these traces lead to invariants of colored spherical graphs (and so to modified 6j-symbols)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1660","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":"1103.1660","created_at":"2026-05-18T03:59:38.312634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1660v2","created_at":"2026-05-18T03:59:38.312634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1660","created_at":"2026-05-18T03:59:38.312634+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LUG22OSY57E","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LUG22OSY57EBEX5","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LUG22OS","created_at":"2026-05-18T12:26:18.847500+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/3LUG22OSY57EBEX5WTRMAQ4CQ4","json":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4.json","graph_json":"https://pith.science/api/pith-number/3LUG22OSY57EBEX5WTRMAQ4CQ4/graph.json","events_json":"https://pith.science/api/pith-number/3LUG22OSY57EBEX5WTRMAQ4CQ4/events.json","paper":"https://pith.science/paper/3LUG22OS"},"agent_actions":{"view_html":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4","download_json":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4.json","view_paper":"https://pith.science/paper/3LUG22OS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1660&json=true","fetch_graph":"https://pith.science/api/pith-number/3LUG22OSY57EBEX5WTRMAQ4CQ4/graph.json","fetch_events":"https://pith.science/api/pith-number/3LUG22OSY57EBEX5WTRMAQ4CQ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4/action/storage_attestation","attest_author":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4/action/author_attestation","sign_citation":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4/action/citation_signature","submit_replication":"https://pith.science/pith/3LUG22OSY57EBEX5WTRMAQ4CQ4/action/replication_record"}},"created_at":"2026-05-18T03:59:38.312634+00:00","updated_at":"2026-05-18T03:59:38.312634+00:00"}