{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AYYX666PJEDYTXSG6RIJPNQDGS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"46cec2a8cebe010cb74c0f8006aff2b8b7befa589741bbe4712dcb60c59c6c11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T06:58:29Z","title_canon_sha256":"24f85966c29cf52d22e105a8e0ee0db6aca461679789344c9ea972deb7f1816a"},"schema_version":"1.0","source":{"id":"2408.09737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09737","created_at":"2026-07-05T08:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09737v1","created_at":"2026-07-05T08:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09737","created_at":"2026-07-05T08:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"AYYX666PJEDY","created_at":"2026-07-05T08:56:36Z"},{"alias_kind":"pith_short_16","alias_value":"AYYX666PJEDYTXSG","created_at":"2026-07-05T08:56:36Z"},{"alias_kind":"pith_short_8","alias_value":"AYYX666P","created_at":"2026-07-05T08:56:36Z"}],"graph_snapshots":[{"event_id":"sha256:a7b5065e1ea2cecad397ea795721863f57feb157b27761e14472ceae4b3383fb","target":"graph","created_at":"2026-07-05T08:56:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.09737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $m$, $n$ be two positive integers, $\\Bbbk$ be an algebraically closed field with char($\\Bbbk)\\nmid mn$. Radford constructed an $mn^{2}$-dimensional Hopf algebra $R_{mn}(q)$ such that its Jacobson radical is not a Hopf ideal. We show that the Drinfeld double $D(R_{mn}(q))$ of Radford Hopf algebra $R_{mn}(q)$ has ribbon elements if and only if $n$ is odd. Moreover, if $m$ is even and $n$ is odd, then $D(R_{mn}(q))$ has two ribbon elements, if both $m$ and $n$ are odd, then $D(R_{mn}(q))$ has only one ribbon element. Finally, we compute explicitly all ribbon elements of $D(R_{mn}(q))$.","authors_text":"Hua Sun, Libin Li, Yuyan Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T06:58:29Z","title":"The Ribbon Elements of Drinfeld Double of Radford Hopf Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09737","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5f8d11fe8788b9660382e3ea333b6b819dc0997bc6b6437e566f55487237eee8","target":"record","created_at":"2026-07-05T08:56:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"46cec2a8cebe010cb74c0f8006aff2b8b7befa589741bbe4712dcb60c59c6c11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T06:58:29Z","title_canon_sha256":"24f85966c29cf52d22e105a8e0ee0db6aca461679789344c9ea972deb7f1816a"},"schema_version":"1.0","source":{"id":"2408.09737","kind":"arxiv","version":1}},"canonical_sha256":"06317f7bcf490789de46f45097b60334933ae0ecce76f0dc59e3b2b2018ae3e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06317f7bcf490789de46f45097b60334933ae0ecce76f0dc59e3b2b2018ae3e7","first_computed_at":"2026-07-05T08:56:36.380603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:56:36.380603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Go4xIIxtMbdw8yaCELAop8jBs/emIkfL6O8FVnPKjmjvS7vgqbX9VcU3cP2ydMamBwLs0vnyPrjUl9S4hmsDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:56:36.381064Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.09737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f8d11fe8788b9660382e3ea333b6b819dc0997bc6b6437e566f55487237eee8","sha256:a7b5065e1ea2cecad397ea795721863f57feb157b27761e14472ceae4b3383fb"],"state_sha256":"bd27cb1f79cabfa2337ab719a14d6a56cc395e0b62462ba74f7b0b7ad0412859"}