{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q44KQHXFB3RULHKR5RGWQD7KGO","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":"48b3971a91b9458e73c38e9633c917668a306f9947dbf36d9c785fe31d200b78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-08T23:29:06Z","title_canon_sha256":"594fab7720bf2d8a9a8243ee2516b90385466b6563a5619a9e45982a4323e6e4"},"schema_version":"1.0","source":{"id":"1308.1998","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1998","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1998v2","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1998","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q44KQHXFB3RU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q44KQHXFB3RULHKR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q44KQHXF","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:e185e7eccd8386025498d3da5677b8daab72972be8992fdc05df67ad33154ccc","target":"graph","created_at":"2026-05-18T02:45:49Z","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":"We investigate when a skew polynomial extension T = R[x; {\\sigma}, {\\delta}] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic 0 one obtains a large family of connected noetherian Hopf algebras of finite Gelfand-Kirillov dimension, including for example all enveloping algebras of finite dimensional solvable Lie algebras and all coordinate rings of unipotent groups. The properties of these Hopf algebras are investigated.","authors_text":"G. Zhuang, J.J. Zhang, K.A. Brown, S. O'Hagan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-08T23:29:06Z","title":"Connected Hopf algebras and iterated Ore extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1998","kind":"arxiv","version":2},"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":"sha256:7c0f728db593c7463436073265848790c313e04c6f40013190b20801edcebbc3","target":"record","created_at":"2026-05-18T02:45:49Z","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":"48b3971a91b9458e73c38e9633c917668a306f9947dbf36d9c785fe31d200b78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-08T23:29:06Z","title_canon_sha256":"594fab7720bf2d8a9a8243ee2516b90385466b6563a5619a9e45982a4323e6e4"},"schema_version":"1.0","source":{"id":"1308.1998","kind":"arxiv","version":2}},"canonical_sha256":"8738a81ee50ee3459d51ec4d680fea33a126d3036593c27c1f0ac7d85997d015","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8738a81ee50ee3459d51ec4d680fea33a126d3036593c27c1f0ac7d85997d015","first_computed_at":"2026-05-18T02:45:49.751859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:49.751859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rQKBb/vbc+0x8Gvs8Re69PL2aWSYpCXYPFag0NAys3+W8LjUCboXMbVz26ZnyGIdyfnI09UBFl8yZGoPIpupBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:49.752293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1998","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c0f728db593c7463436073265848790c313e04c6f40013190b20801edcebbc3","sha256:e185e7eccd8386025498d3da5677b8daab72972be8992fdc05df67ad33154ccc"],"state_sha256":"c2d21ec84d68da0d65aebef3a48f76220c70418fa26693e1804854c8e453444f"}