{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IZVDDMUKGC2ZZIXBWNN3ANLJJC","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":"8f96b888dd53182e64afe200eb5ff49e28f262aa380172d7b2ef7983d747a05e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-04-28T13:10:47Z","title_canon_sha256":"d8dff761cb7928fec2c4e9bf0b6dcdad23bad66e41d306ed2571dec91f11ec63"},"schema_version":"1.0","source":{"id":"1004.5022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5022","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5022v1","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5022","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"IZVDDMUKGC2Z","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IZVDDMUKGC2ZZIXB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IZVDDMUK","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:959af2d08cfa0b9ffbf47737fb7948cb19457ba27a5ac9aa54dacc3de0c94c8b","target":"graph","created_at":"2026-05-18T02:24:15Z","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 show that in characteristic zero all irreducible symmetrically braided Hopf algebras are of PBW type. Consequently, we obtain conditions for a braided Hopf algebra to be of PBW type as module over a braided Hopf subalgebra containing the coradical.","authors_text":"Bogdan Ion","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-04-28T13:10:47Z","title":"Relative PBW type theorems for symmetrically braided Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5022","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":"sha256:4ab409780429487dcc7de7d4b4deffc0ab4dc311fcf37df1bf2265cf4277c4ef","target":"record","created_at":"2026-05-18T02:24:15Z","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":"8f96b888dd53182e64afe200eb5ff49e28f262aa380172d7b2ef7983d747a05e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-04-28T13:10:47Z","title_canon_sha256":"d8dff761cb7928fec2c4e9bf0b6dcdad23bad66e41d306ed2571dec91f11ec63"},"schema_version":"1.0","source":{"id":"1004.5022","kind":"arxiv","version":1}},"canonical_sha256":"466a31b28a30b59ca2e1b35bb03569488be17f12f6a26b087c2e7644872fc00e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"466a31b28a30b59ca2e1b35bb03569488be17f12f6a26b087c2e7644872fc00e","first_computed_at":"2026-05-18T02:24:15.451875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:15.451875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KFiJalEGn5secFMVOyLpt/lbZhLDKBHu/z+LwmpvmLaftUos8fHTRDnSHYikDSAEXIaxT4jrpvZnzJhJ7ylZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:15.452530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ab409780429487dcc7de7d4b4deffc0ab4dc311fcf37df1bf2265cf4277c4ef","sha256:959af2d08cfa0b9ffbf47737fb7948cb19457ba27a5ac9aa54dacc3de0c94c8b"],"state_sha256":"21d06a63e4655fef04d6f947bb1ef245d6c6c0283b67acf7726d63f7994c7b6e"}