{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M7NE7OKLS5NIXTJZ3RG7VRMMOF","short_pith_number":"pith:M7NE7OKL","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"},"canonical_sha256":"67da4fb94b975a8bcd39dc4dfac58c715632c0f58b21a4981a657bca10b43d7c","source":{"kind":"arxiv","id":"1207.0411","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0411","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0411v4","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0411","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"M7NE7OKLS5NI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M7NE7OKLS5NIXTJZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M7NE7OKL","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M7NE7OKLS5NIXTJZ3RG7VRMMOF","target":"record","payload":{"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"},"canonical_sha256":"67da4fb94b975a8bcd39dc4dfac58c715632c0f58b21a4981a657bca10b43d7c","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"},"source_kind":"arxiv","source_id":"1207.0411","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"soYJZGpeFm6wnfzPYKcs35UdLf7rILN/lYNWm66yHMDwlp7H5v4C6DlmuEWCstX4Y1KLxkZ59lkM6h2+qBhxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:16:15.643232Z"},"content_sha256":"6594fc7f8ecbb3dba4fa46197772e073e63dcffe659ed0d3c61bd6001e747986","schema_version":"1.0","event_id":"sha256:6594fc7f8ecbb3dba4fa46197772e073e63dcffe659ed0d3c61bd6001e747986"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M7NE7OKLS5NIXTJZ3RG7VRMMOF","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93zGEeJdd20dlZnO2qyaJtjbh6tzgifwBMZoFcHGjccv3hzxu1efayVJ1FRKgvaEk3QtPkB+OvL8qiF4lihjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:16:15.643594Z"},"content_sha256":"808d996c420e2b11a00cef6fde22371e0bfa0636a4c55ceb6726254eb35ac176","schema_version":"1.0","event_id":"sha256:808d996c420e2b11a00cef6fde22371e0bfa0636a4c55ceb6726254eb35ac176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/bundle.json","state_url":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T05:16:15Z","links":{"resolver":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF","bundle":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/bundle.json","state":"https://pith.science/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7NE7OKLS5NIXTJZ3RG7VRMMOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M7NE7OKLS5NIXTJZ3RG7VRMMOF","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":"43b096e9be4f1c403ee8ef446dd94feaf67757a561492a63872be3f107744f9c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-02T14:44:04Z","title_canon_sha256":"47db2bae88cf6bb7c561103fd519bab03e0ec371bf4307e0d6ab5c849cbf7f05"},"schema_version":"1.0","source":{"id":"1207.0411","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0411","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0411v4","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0411","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"M7NE7OKLS5NI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M7NE7OKLS5NIXTJZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M7NE7OKL","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:808d996c420e2b11a00cef6fde22371e0bfa0636a4c55ceb6726254eb35ac176","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":"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","authors_text":"A. L. Agore, C. G. Bontea, G. Militaru","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-02T14:44:04Z","title":"Classifying coalgebra split extensions of Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0411","kind":"arxiv","version":4},"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":"sha256:6594fc7f8ecbb3dba4fa46197772e073e63dcffe659ed0d3c61bd6001e747986","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":"43b096e9be4f1c403ee8ef446dd94feaf67757a561492a63872be3f107744f9c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-02T14:44:04Z","title_canon_sha256":"47db2bae88cf6bb7c561103fd519bab03e0ec371bf4307e0d6ab5c849cbf7f05"},"schema_version":"1.0","source":{"id":"1207.0411","kind":"arxiv","version":4}},"canonical_sha256":"67da4fb94b975a8bcd39dc4dfac58c715632c0f58b21a4981a657bca10b43d7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67da4fb94b975a8bcd39dc4dfac58c715632c0f58b21a4981a657bca10b43d7c","first_computed_at":"2026-05-18T02:58:23.700083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:23.700083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"up0dhLLzytK32epeSk2CFNR36uvTbhG9CiEVVr12quUWyDCiNcnKOP0l+1LOuFs++Vg6dZIdaaOqbjP3nHFMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:23.700504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0411","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6594fc7f8ecbb3dba4fa46197772e073e63dcffe659ed0d3c61bd6001e747986","sha256:808d996c420e2b11a00cef6fde22371e0bfa0636a4c55ceb6726254eb35ac176"],"state_sha256":"78e35f0ccb319e1150c76ec34447dc623d97cd7b7acf15ed893a81005c8325ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8czghhUu1OBJFWoUJ01QCh+wBdXBzZa6qJIatu3Dtn3y4nKcGUZnj8MMD45uVg5T0+TumDUKsFo22jH/6DtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:16:15.645543Z","bundle_sha256":"5a98882ca28608bd46df393ac1c5962ac8aa49e2dd9580e1fd7a2c56f94feac2"}}