{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FOK7HXJ6CKM5ENTQDF567TFKWP","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":"c3bdd1480bc262d912609250b78d772bd5eb04d5e15683793632d5b166a875c3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-12T01:56:39Z","title_canon_sha256":"5ac73e365e93c68ac0bcfd50ffb89d8685b477696c60d3cd3a61058b29d52dea"},"schema_version":"1.0","source":{"id":"2504.09044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09044","created_at":"2026-07-05T10:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09044v1","created_at":"2026-07-05T10:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09044","created_at":"2026-07-05T10:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"FOK7HXJ6CKM5","created_at":"2026-07-05T10:48:03Z"},{"alias_kind":"pith_short_16","alias_value":"FOK7HXJ6CKM5ENTQ","created_at":"2026-07-05T10:48:03Z"},{"alias_kind":"pith_short_8","alias_value":"FOK7HXJ6","created_at":"2026-07-05T10:48:03Z"}],"graph_snapshots":[{"event_id":"sha256:d45f77d9ad862e431079511a6331a6dbf2617d5c1a8450b5ae89dbff760a4ace","target":"graph","created_at":"2026-07-05T10:48:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.09044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A quadratic Novikov algebra is a Novikov algebra $(A, \\circ)$ with a symmetric and nondegenerate bilinear form $B(\\cdot,\\cdot)$ satisfying $B(a\\circ b, c)=-B(b, a\\circ c+c\\circ a)$ for all $a$, $b$, $c\\in A$. This notion appeared in the theory of Novikov bialgebras. In this paper, we first investigate some properties of quadratic Novikov algebras and give a decomposition theorem of quadratic Novikov algebras. Then we present a classification of quadratic Novikov algebras of dimensions $2$ and $3$ over $\\mathbb{C}$ up to isomorphism. Finally, a construction of quadratic Novikov algebras called ","authors_text":"Xiaofeng Dong, Yanyong Hong","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-12T01:56:39Z","title":"On quadratic Novikov algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09044","kind":"arxiv","version":1},"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:c8bade9c683daac2ee22c66b44062f5b0a1b93d0044a1b0e9f1fa710a18b4c5f","target":"record","created_at":"2026-07-05T10:48:03Z","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":"c3bdd1480bc262d912609250b78d772bd5eb04d5e15683793632d5b166a875c3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-12T01:56:39Z","title_canon_sha256":"5ac73e365e93c68ac0bcfd50ffb89d8685b477696c60d3cd3a61058b29d52dea"},"schema_version":"1.0","source":{"id":"2504.09044","kind":"arxiv","version":1}},"canonical_sha256":"2b95f3dd3e1299d23670197befccaab3eea7757f8d97aa6e14b6b97bf2234800","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b95f3dd3e1299d23670197befccaab3eea7757f8d97aa6e14b6b97bf2234800","first_computed_at":"2026-07-05T10:48:03.357404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:48:03.357404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UObRJDhiDyg/+p0pVaGsnSzRVILYSkem/C5TrE2hWAOish9thvkT3JFSJC3ZZ1aEvYNL86ka7Kk/8Iz9xCwyCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:48:03.357783Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.09044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8bade9c683daac2ee22c66b44062f5b0a1b93d0044a1b0e9f1fa710a18b4c5f","sha256:d45f77d9ad862e431079511a6331a6dbf2617d5c1a8450b5ae89dbff760a4ace"],"state_sha256":"df86eadfe542e02e32abed868d8948b227abe3406bccee0c56788db0db1a4a4f"}