{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OMHRHH3WILKWWGKUXDTG325CBV","short_pith_number":"pith:OMHRHH3W","schema_version":"1.0","canonical_sha256":"730f139f7642d56b1954b8e66deba20d714cd45b9989aec5276d19b7c36cfdd6","source":{"kind":"arxiv","id":"1103.5117","version":2},"attestation_state":"computed","paper":{"title":"Semisimple Hopf algebras of dimension $9q^2$ and high-dimensional semisimple Hopf algebras of Frobenius type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jingcheng Dong","submitted_at":"2011-03-26T08:41:16Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic 0. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $9q^2$ over $k$, where $q$ is a prime number. We also prove that odd-dimensional semisimple Hopf algebras over $k$ of dimension less than 600 are of Frobenius type."},"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":"1103.5117","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-03-26T08:41:16Z","cross_cats_sorted":[],"title_canon_sha256":"7e4337c042b06ec7ea8c0f19ae94e829dca988db0912b5c3757990abbb39ea01","abstract_canon_sha256":"060610973149988ed3f6fb2e5e0d668cc861a89de4c0f590a1238c131734309d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:27.592492Z","signature_b64":"ddnyHsG989yXLwiCg1iwcb30GcOqPEeu2tuA1YtpNC6gsj5pVUXF1q2nIITbgtoDUvZgl8rsSP4R0B7oJ9v+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"730f139f7642d56b1954b8e66deba20d714cd45b9989aec5276d19b7c36cfdd6","last_reissued_at":"2026-05-18T04:05:27.592087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:27.592087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semisimple Hopf algebras of dimension $9q^2$ and high-dimensional semisimple Hopf algebras of Frobenius type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jingcheng Dong","submitted_at":"2011-03-26T08:41:16Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic 0. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $9q^2$ over $k$, where $q$ is a prime number. We also prove that odd-dimensional semisimple Hopf algebras over $k$ of dimension less than 600 are of Frobenius type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5117","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":"1103.5117","created_at":"2026-05-18T04:05:27.592152+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.5117v2","created_at":"2026-05-18T04:05:27.592152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5117","created_at":"2026-05-18T04:05:27.592152+00:00"},{"alias_kind":"pith_short_12","alias_value":"OMHRHH3WILKW","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OMHRHH3WILKWWGKU","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OMHRHH3W","created_at":"2026-05-18T12:26:37.096874+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/OMHRHH3WILKWWGKUXDTG325CBV","json":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV.json","graph_json":"https://pith.science/api/pith-number/OMHRHH3WILKWWGKUXDTG325CBV/graph.json","events_json":"https://pith.science/api/pith-number/OMHRHH3WILKWWGKUXDTG325CBV/events.json","paper":"https://pith.science/paper/OMHRHH3W"},"agent_actions":{"view_html":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV","download_json":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV.json","view_paper":"https://pith.science/paper/OMHRHH3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.5117&json=true","fetch_graph":"https://pith.science/api/pith-number/OMHRHH3WILKWWGKUXDTG325CBV/graph.json","fetch_events":"https://pith.science/api/pith-number/OMHRHH3WILKWWGKUXDTG325CBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV/action/storage_attestation","attest_author":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV/action/author_attestation","sign_citation":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV/action/citation_signature","submit_replication":"https://pith.science/pith/OMHRHH3WILKWWGKUXDTG325CBV/action/replication_record"}},"created_at":"2026-05-18T04:05:27.592152+00:00","updated_at":"2026-05-18T04:05:27.592152+00:00"}