{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LA4Q6ZHMHKXAA56L5MJ6UDYUGX","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":"5c389564674391e7d4e64cd8d73e536a21dfa3dd39a5ab8b6e8ebe207c4b18da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-05T16:10:28Z","title_canon_sha256":"406e580a8586faafee4e45b908a9e88c503419cc1603a852d3dc16ea88387146"},"schema_version":"1.0","source":{"id":"1203.0957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0957","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0957v2","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0957","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"LA4Q6ZHMHKXA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LA4Q6ZHMHKXAA56L","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LA4Q6ZHM","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:c75f62dd23a93d900c4fdb50e9ab461871f797a57a573af6f452c7160936da37","target":"graph","created_at":"2026-05-18T00:14:35Z","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 introduce a method to construct explicitly multiplicative 2-cocycles for bosonizations of Nichols algebras B(V) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V tensor V and give a close formula to deform braided commutator-type relations.\n  Using this construction, we show that all known finite dimensional pointed Hopf algebras over the dihedral groups D_m with m=4t > 11, over the symmetric group S_3 and some families over S_4 are cocycle deformations of bosonizations of Nichols algebras.","authors_text":"Gaston Andres Garcia, Mitja Mastnak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-05T16:10:28Z","title":"Deformation by cocycles of pointed Hopf algebras over non-abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0957","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:d0f0212e9914c7bb0da6a7f53ff860fcdd4c35201497ce9cb964d82cf72f8ec2","target":"record","created_at":"2026-05-18T00:14:35Z","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":"5c389564674391e7d4e64cd8d73e536a21dfa3dd39a5ab8b6e8ebe207c4b18da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-05T16:10:28Z","title_canon_sha256":"406e580a8586faafee4e45b908a9e88c503419cc1603a852d3dc16ea88387146"},"schema_version":"1.0","source":{"id":"1203.0957","kind":"arxiv","version":2}},"canonical_sha256":"58390f64ec3aae0077cbeb13ea0f1435ca22a7ee0d0609eae1748831aebb50a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58390f64ec3aae0077cbeb13ea0f1435ca22a7ee0d0609eae1748831aebb50a4","first_computed_at":"2026-05-18T00:14:35.089008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:35.089008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7x7lYmisNo8AOMkgNkTqY5yEReI26T9md5BgqdXvHakC/sk7OZjn/8ARdSw81RkbouY+K0090iQr81NIzdzPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:35.089771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0f0212e9914c7bb0da6a7f53ff860fcdd4c35201497ce9cb964d82cf72f8ec2","sha256:c75f62dd23a93d900c4fdb50e9ab461871f797a57a573af6f452c7160936da37"],"state_sha256":"d766a1219a2d1b91e7c5bc27248f6063d108e56698ef6ca91582578399b33b29"}