{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IUNXCI4ALHOL6CRVHVWPEPPSE2","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":"10de82d527dba43537c0ea0152a8c4ac1a3b039258e9f25ccea7283aac0dbf79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-11-11T18:47:47Z","title_canon_sha256":"d83011aaa9ff2dcebe970ff542bb3b2bd65e162ed429696452130ca73f7e8ab6"},"schema_version":"1.0","source":{"id":"1011.2735","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2735","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2735v2","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2735","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"IUNXCI4ALHOL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IUNXCI4ALHOL6CRV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IUNXCI4A","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:fd4e966662ef1269f169f25b9e9c2fbfc6e77b331123de8deee1c31435480dfc","target":"graph","created_at":"2026-05-18T03:05:28Z","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 define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group homology, respectively.","authors_text":"Masoud Khalkhali, Mohammad Hassanzadeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-11-11T18:47:47Z","title":"Cup Coproducts in Hopf Cyclic Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2735","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:fbb1aba6db1791b773cc9be0ed4be1e0225c8b5761ebbf9de58745d369122d33","target":"record","created_at":"2026-05-18T03:05:28Z","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":"10de82d527dba43537c0ea0152a8c4ac1a3b039258e9f25ccea7283aac0dbf79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-11-11T18:47:47Z","title_canon_sha256":"d83011aaa9ff2dcebe970ff542bb3b2bd65e162ed429696452130ca73f7e8ab6"},"schema_version":"1.0","source":{"id":"1011.2735","kind":"arxiv","version":2}},"canonical_sha256":"451b71238059dcbf0a353d6cf23df2268ee7ef90f27f476de1754128c9970f92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"451b71238059dcbf0a353d6cf23df2268ee7ef90f27f476de1754128c9970f92","first_computed_at":"2026-05-18T03:05:28.740678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:28.740678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tRJ91EFTJKAJX5lDDqBVaWJBckos54IyCJMj6mgsRPGm6uy2/EYqsTgXT3LJ/mIBjyZyT4GQDb0h5Cs9RPxZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:28.741233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2735","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbb1aba6db1791b773cc9be0ed4be1e0225c8b5761ebbf9de58745d369122d33","sha256:fd4e966662ef1269f169f25b9e9c2fbfc6e77b331123de8deee1c31435480dfc"],"state_sha256":"25763fe532399b90d0e6b8a2351ef57513bcdc4bf67ce54c518931cc794ace86"}