{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RRKQUIH3K3DGBF6FRWGSY6QVXC","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":"1d1b6c217b174ed32a0a883cd4edd2df4d5e350660aebc6811fdc2f0a3e83e88","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-05-10T17:29:35Z","title_canon_sha256":"6482a748a874092ad6ff43f808ca4358e907d36af70b0e0dfbc5e206bdc2d688"},"schema_version":"1.0","source":{"id":"1605.03113","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03113","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03113v4","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03113","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"RRKQUIH3K3DG","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RRKQUIH3K3DGBF6F","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RRKQUIH3","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:109958617b176fec31a14e3e3780cc53deb7ff2b3ad89cee35e11002f3bc5e46","target":"graph","created_at":"2026-05-18T00:04:24Z","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 classify finite-dimensional pointed Hopf algebras with abelian coradical, up to isomorphism, and show that they are cocycle deformations of the associated graded Hopf algebra.\n  More generally, for any braided vector space of diagonal type $V$ with a principal realization in the category of Yetter-Drinfeld modules of a cosemisimple Hopf algebra $H$ and such that the Nichols algebra $\\mathfrak{B}(V)$ is finite-dimensional, thus presented by a finite set $\\mathcal G$ of relations, we define a family of Hopf algebras $\\mathfrak{u}(\\boldsymbol\\lambda)$, $\\boldsymbol\\lambda\\in \\Bbbk^{\\mathcal G}","authors_text":"Agust\\'in Garc\\'ia Iglesias, Iv\\'an Angiono","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-05-10T17:29:35Z","title":"Liftings of Nichols algebras of diagonal type II. All liftings are cocycle deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03113","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":"sha256:24813c1c23950ec89d45c46d5a4452ae96c7426524bdc9962fac9155ea107225","target":"record","created_at":"2026-05-18T00:04:24Z","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":"1d1b6c217b174ed32a0a883cd4edd2df4d5e350660aebc6811fdc2f0a3e83e88","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-05-10T17:29:35Z","title_canon_sha256":"6482a748a874092ad6ff43f808ca4358e907d36af70b0e0dfbc5e206bdc2d688"},"schema_version":"1.0","source":{"id":"1605.03113","kind":"arxiv","version":4}},"canonical_sha256":"8c550a20fb56c66097c58d8d2c7a15b880dfa1d2f1d6b7ef9d4ff04cae73317f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c550a20fb56c66097c58d8d2c7a15b880dfa1d2f1d6b7ef9d4ff04cae73317f","first_computed_at":"2026-05-18T00:04:24.376519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.376519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZVpKWvtc8eiGWC+Yztf4JZ4xvMiFbapFUNPWdwsCUYGg/VJBgFgJOyzwkHfp/w/vSB27JXuX6W7AxQmAeWH1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.377006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03113","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24813c1c23950ec89d45c46d5a4452ae96c7426524bdc9962fac9155ea107225","sha256:109958617b176fec31a14e3e3780cc53deb7ff2b3ad89cee35e11002f3bc5e46"],"state_sha256":"b00070b0fcc6fb4b4a2061db8416eadcb5010a9dcdf306bd36c8ffe36b8b69d2"}