{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ED4FDJ7OKD3ZBJIAQQ4UCOOAZX","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":"10e184e9e89dcdf9dcb513ddd6e615ea1910dc5fdef36fa1251cc6f671f1b6fe","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-05T21:28:42Z","title_canon_sha256":"d9ed7045052eba5cffea005314250a2c633cc3db16b71b6ee04742a6820598a8"},"schema_version":"1.0","source":{"id":"1412.2147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2147","created_at":"2026-05-18T01:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2147v2","created_at":"2026-05-18T01:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2147","created_at":"2026-05-18T01:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"ED4FDJ7OKD3Z","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"ED4FDJ7OKD3ZBJIA","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"ED4FDJ7O","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5f55d9509de878d0fdde7c49ba1849381e95b647d28c3995558377413bb72eec","target":"graph","created_at":"2026-05-18T01:59:58Z","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 study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch-Schneider program of classification of pointed Hopf algebras, are rigid. This result can be regarded as nonexistence of \"braided Lie algebras\" with nontrivial bracket.","authors_text":"Iv\\'an Angiono, Mikhail Kochetov, Mitja Mastnak","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-05T21:28:42Z","title":"On rigidity of Nichols algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2147","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:c9a4cce1ef0d6a02f075bfbbf4eb8660010767e4ffb1c3896b2c9546dca347ba","target":"record","created_at":"2026-05-18T01:59:58Z","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":"10e184e9e89dcdf9dcb513ddd6e615ea1910dc5fdef36fa1251cc6f671f1b6fe","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-05T21:28:42Z","title_canon_sha256":"d9ed7045052eba5cffea005314250a2c633cc3db16b71b6ee04742a6820598a8"},"schema_version":"1.0","source":{"id":"1412.2147","kind":"arxiv","version":2}},"canonical_sha256":"20f851a7ee50f790a50084394139c0cdf3c966a24cc970468ae6f793428d3711","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20f851a7ee50f790a50084394139c0cdf3c966a24cc970468ae6f793428d3711","first_computed_at":"2026-05-18T01:59:58.065679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:58.065679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oKMUh4XV6ry7bNzZiJUNWzlur7HHJuC+0tcGsozIuO5s8MhkaoNRRcwlrLrYcMABQyWZfKIQlQUXOl48pqm2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:58.066199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9a4cce1ef0d6a02f075bfbbf4eb8660010767e4ffb1c3896b2c9546dca347ba","sha256:5f55d9509de878d0fdde7c49ba1849381e95b647d28c3995558377413bb72eec"],"state_sha256":"149f6709d8447eed7edcb68e2f4c757644748467485270a7686892ee121cb959"}