{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:M7NE7OKLS5NIXTJZ3RG7VRMMOF","short_pith_number":"pith:M7NE7OKL","schema_version":"1.0","canonical_sha256":"67da4fb94b975a8bcd39dc4dfac58c715632c0f58b21a4981a657bca10b43d7c","source":{"kind":"arxiv","id":"1207.0411","version":4},"attestation_state":"computed","paper":{"title":"Classifying coalgebra split extensions of Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"A. L. Agore, C. G. Bontea, G. Militaru","submitted_at":"2012-07-02T14:44:04Z","abstract_excerpt":"For a given Hopf algebra $A$ we classify all Hopf algebras $E$ that are coalgebra split extensions of $A$ by $H_4$, where $H_4$ is the Sweedler's 4-dimensional Hopf algebra. Equivalently, we classify all crossed products of Hopf algebras $A # H_4$ by computing explicitly two classifying objects: the cohomological 'group' ${\\mathcal H}^{2} (H_4, A)$ and $\\textsc{C}\\textsc{r}\\textsc{p} (H_4, A) :=$ the set of types of isomorphisms of all crossed products $A # H_4$. All crossed products $A #H_4$ are described by generators and relations and classified: they are parameterized by the set ${\\mathcal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.0411","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-02T14:44:04Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"47db2bae88cf6bb7c561103fd519bab03e0ec371bf4307e0d6ab5c849cbf7f05","abstract_canon_sha256":"43b096e9be4f1c403ee8ef446dd94feaf67757a561492a63872be3f107744f9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:23.700504Z","signature_b64":"up0dhLLzytK32epeSk2CFNR36uvTbhG9CiEVVr12quUWyDCiNcnKOP0l+1LOuFs++Vg6dZIdaaOqbjP3nHFMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67da4fb94b975a8bcd39dc4dfac58c715632c0f58b21a4981a657bca10b43d7c","last_reissued_at":"2026-05-18T02:58:23.700083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:23.700083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classifying coalgebra split extensions of Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"A. L. Agore, C. G. Bontea, G. Militaru","submitted_at":"2012-07-02T14:44:04Z","abstract_excerpt":"For a given Hopf algebra $A$ we classify all Hopf algebras $E$ that are coalgebra split extensions of $A$ by $H_4$, where $H_4$ is the Sweedler's 4-dimensional Hopf algebra. Equivalently, we classify all crossed products of Hopf algebras $A # H_4$ by computing explicitly two classifying objects: the cohomological 'group' ${\\mathcal H}^{2} (H_4, A)$ and $\\textsc{C}\\textsc{r}\\textsc{p} (H_4, A) :=$ the set of types of isomorphisms of all crossed products $A # H_4$. All crossed products $A #H_4$ are described by generators and relations and classified: they are parameterized by the set ${\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0411","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.0411","created_at":"2026-05-18T02:58:23.700149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.0411v4","created_at":"2026-05-18T02:58:23.700149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0411","created_at":"2026-05-18T02:58:23.700149+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7NE7OKLS5NI","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7NE7OKLS5NIXTJZ","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7NE7OKL","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF","json":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF.json","graph_json":"https://pith.science/api/pith-number/M7NE7OKLS5NIXTJZ3RG7VRMMOF/graph.json","events_json":"https://pith.science/api/pith-number/M7NE7OKLS5NIXTJZ3RG7VRMMOF/events.json","paper":"https://pith.science/paper/M7NE7OKL"},"agent_actions":{"view_html":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF","download_json":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF.json","view_paper":"https://pith.science/paper/M7NE7OKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.0411&json=true","fetch_graph":"https://pith.science/api/pith-number/M7NE7OKLS5NIXTJZ3RG7VRMMOF/graph.json","fetch_events":"https://pith.science/api/pith-number/M7NE7OKLS5NIXTJZ3RG7VRMMOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/action/storage_attestation","attest_author":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/action/author_attestation","sign_citation":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/action/citation_signature","submit_replication":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/action/replication_record"}},"created_at":"2026-05-18T02:58:23.700149+00:00","updated_at":"2026-05-18T02:58:23.700149+00:00"}