{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BO2FTBBJIQO2KU35AV7Y6CUKXR","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":"a190e447aa5801ee56dd5d7c78fce44df3723e936d5a28ac12b85af39aa13b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-23T03:27:56Z","title_canon_sha256":"f254b8f18cf70c8d03c58a06e4e10191b5bb659f00d9e582b6cab58fc180e70e"},"schema_version":"1.0","source":{"id":"1105.4398","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4398","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4398v3","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4398","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"pith_short_12","alias_value":"BO2FTBBJIQO2","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BO2FTBBJIQO2KU35","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BO2FTBBJ","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:013412da588a21f1c91f3bcd8a01b4e08d1fd42dd30681018c7dd70ecae70f25","target":"graph","created_at":"2026-05-18T03:58:36Z","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"},"paper":{"abstract_excerpt":"Let $q$ be a prime number, $k$ an algebraically closed field of characteristic 0, and $H$ a non-trivial semisimple Hopf algebra of dimension $2q^3$. This paper proves that $H$ can be constructed either from group algebras and their duals by means of extensions, or from Radford's biproduct $H\\cong R#kG$, where $kG$ is the group algebra of $G$ of order 2, $R$ is a semisimple Yetter-Drinfeld Hopf algebra in ${}^{kG}_{kG}\\mathcal{YD}$ of dimension $q^3$.","authors_text":"Jingcheng Dong, Li Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-23T03:27:56Z","title":"Semisimple Hopf algebras of dimension $2q^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4398","kind":"arxiv","version":3},"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":"sha256:2c526d892c9509b3c0cf833516ef13588d6e5dfcefc4495761d5c779655849a1","target":"record","created_at":"2026-05-18T03:58:36Z","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":"a190e447aa5801ee56dd5d7c78fce44df3723e936d5a28ac12b85af39aa13b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-05-23T03:27:56Z","title_canon_sha256":"f254b8f18cf70c8d03c58a06e4e10191b5bb659f00d9e582b6cab58fc180e70e"},"schema_version":"1.0","source":{"id":"1105.4398","kind":"arxiv","version":3}},"canonical_sha256":"0bb4598429441da5537d057f8f0a8abc5e9c5beee05493983d0071442c8b29a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bb4598429441da5537d057f8f0a8abc5e9c5beee05493983d0071442c8b29a0","first_computed_at":"2026-05-18T03:58:36.913201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:36.913201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+Qqvvxk0EejxHKmCubLH6O86WMAcrISdw4de7FiBCvtCIxOf+tH5WWChBI2kvlxaFbZkBPABo4zGIGe4o7EBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:36.913980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4398","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c526d892c9509b3c0cf833516ef13588d6e5dfcefc4495761d5c779655849a1","sha256:013412da588a21f1c91f3bcd8a01b4e08d1fd42dd30681018c7dd70ecae70f25"],"state_sha256":"23aeff136c78415781e2907670fd7ae13d55d91e6f47546cdeecf2c36a4c2463"}