{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:76HWUEKMFGAKBT2DP6MZMZ5ZHC","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":"f793eae4824e745771667a2878557ec6b50b645d78b71640bc9003197834e7d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:49:07Z","title_canon_sha256":"37bbe1952b6f2e4e532ea723a9157be7e986f904db409739c899e2129f812a1b"},"schema_version":"1.0","source":{"id":"1203.2455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2455","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2455v1","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2455","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"76HWUEKMFGAK","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"76HWUEKMFGAKBT2D","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"76HWUEKM","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:ad12c203c8fb00f0f85577f621711157b133758fcf3ca0cabf1b25633ad800ad","target":"graph","created_at":"2026-05-18T02:58:23Z","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":"Let $A \\subseteq E$ be an extension of Hopf algebras such that there exists a normal left $A$-module coalgebra map $\\pi : E \\to A$ that splits the inclusion. We shall describe the set of all coquasitriangular structures on the Hopf algebra $E$ in terms of the datum $(A, E, \\pi)$ as follows: first, any such extension $E$ is isomorphic to a unified product $A \\ltimes H$, for some unitary subcoalgebra $H$ of $E$ (\\cite{am2}). Then, as a main theorem, we establish a bijective correspondence between the set of all coquasitriangular structures on an arbitrary unified product $A \\ltimes H$ and a cert","authors_text":"A. L. Agore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:49:07Z","title":"Coquasitriangular structures for extensions of Hopf algebras. Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2455","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":"sha256:3f891a6029a70533fb58dad2274543c06252eaa1debd10ab9c873d613979a39d","target":"record","created_at":"2026-05-18T02:58:23Z","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":"f793eae4824e745771667a2878557ec6b50b645d78b71640bc9003197834e7d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:49:07Z","title_canon_sha256":"37bbe1952b6f2e4e532ea723a9157be7e986f904db409739c899e2129f812a1b"},"schema_version":"1.0","source":{"id":"1203.2455","kind":"arxiv","version":1}},"canonical_sha256":"ff8f6a114c2980a0cf437f999667b938ac3cb68004a73a79b6dc27b6c1398e7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff8f6a114c2980a0cf437f999667b938ac3cb68004a73a79b6dc27b6c1398e7a","first_computed_at":"2026-05-18T02:58:23.729394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:23.729394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aeQ5ZXw9vj7rfAMB92wSMwdDqWJ+8RhjQVaJlnvogfbQZfMR5kJX+6a7ZFUUKwFd+QIbea7V7KShE82p5pM2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:23.729788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f891a6029a70533fb58dad2274543c06252eaa1debd10ab9c873d613979a39d","sha256:ad12c203c8fb00f0f85577f621711157b133758fcf3ca0cabf1b25633ad800ad"],"state_sha256":"8b0829712374f4d86851683c0eb3c1658138aa061ff5618e8a97241e388fac4c"}