{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WYY6UAZDOMXBRA2XXNYXQ2VQ43","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":"de8947f3d8724ed7cf336eedf84e6bbee2521d4fae7b88785aaa22a67c2a6eac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.QA","submitted_at":"2008-02-24T04:21:31Z","title_canon_sha256":"4dbe4687c38e3f09f3000cc801d8138da977cec25dbaf638e1123747ddab8cd2"},"schema_version":"1.0","source":{"id":"0802.3488","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3488","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3488v6","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3488","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"pith_short_12","alias_value":"WYY6UAZDOMXB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WYY6UAZDOMXBRA2X","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WYY6UAZD","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:3ac344695b82df81402efac9d065a68a678b2d3c7e84c08776bbbe0108811d39","target":"graph","created_at":"2026-05-18T03:30:13Z","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":"The quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one.","authors_text":"Hui-Xiang Chen, Shouchuan Zhang, Yao-Zhong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.QA","submitted_at":"2008-02-24T04:21:31Z","title":"Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3488","kind":"arxiv","version":6},"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":"sha256:96fb69b948053a5c2890ee9d75ac12ee121198e8ebc31f135c808b7e186aaf31","target":"record","created_at":"2026-05-18T03:30:13Z","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":"de8947f3d8724ed7cf336eedf84e6bbee2521d4fae7b88785aaa22a67c2a6eac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.QA","submitted_at":"2008-02-24T04:21:31Z","title_canon_sha256":"4dbe4687c38e3f09f3000cc801d8138da977cec25dbaf638e1123747ddab8cd2"},"schema_version":"1.0","source":{"id":"0802.3488","kind":"arxiv","version":6}},"canonical_sha256":"b631ea0323732e188357bb71786ab0e6d9a841de81057a77b2f7edc760edb7c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b631ea0323732e188357bb71786ab0e6d9a841de81057a77b2f7edc760edb7c7","first_computed_at":"2026-05-18T03:30:13.009452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:13.009452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/B+NAggQCpRlnLKyQyiwV3MVjjRSu8jpfcj78wZmaY5rQRv7u38g5YLoVWkOwDa8MNxKKElcCz0m4XJOgc8CAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:13.010063Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.3488","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96fb69b948053a5c2890ee9d75ac12ee121198e8ebc31f135c808b7e186aaf31","sha256:3ac344695b82df81402efac9d065a68a678b2d3c7e84c08776bbbe0108811d39"],"state_sha256":"a52bc9f1531049f138d00730c08e7b823f949e9998d47084067c3f98eb8cbbc9"}