{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FOK7HXJ6CKM5ENTQDF567TFKWP","short_pith_number":"pith:FOK7HXJ6","schema_version":"1.0","canonical_sha256":"2b95f3dd3e1299d23670197befccaab3eea7757f8d97aa6e14b6b97bf2234800","source":{"kind":"arxiv","id":"2504.09044","version":1},"attestation_state":"computed","paper":{"title":"On quadratic Novikov algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Xiaofeng Dong, Yanyong Hong","submitted_at":"2025-04-12T01:56:39Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.09044","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-12T01:56:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5ac73e365e93c68ac0bcfd50ffb89d8685b477696c60d3cd3a61058b29d52dea","abstract_canon_sha256":"c3bdd1480bc262d912609250b78d772bd5eb04d5e15683793632d5b166a875c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:03.357783Z","signature_b64":"UObRJDhiDyg/+p0pVaGsnSzRVILYSkem/C5TrE2hWAOish9thvkT3JFSJC3ZZ1aEvYNL86ka7Kk/8Iz9xCwyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b95f3dd3e1299d23670197befccaab3eea7757f8d97aa6e14b6b97bf2234800","last_reissued_at":"2026-07-05T10:48:03.357404Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:03.357404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On quadratic Novikov algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Xiaofeng Dong, Yanyong Hong","submitted_at":"2025-04-12T01:56:39Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09044","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.09044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.09044","created_at":"2026-07-05T10:48:03.357456+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.09044v1","created_at":"2026-07-05T10:48:03.357456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09044","created_at":"2026-07-05T10:48:03.357456+00:00"},{"alias_kind":"pith_short_12","alias_value":"FOK7HXJ6CKM5","created_at":"2026-07-05T10:48:03.357456+00:00"},{"alias_kind":"pith_short_16","alias_value":"FOK7HXJ6CKM5ENTQ","created_at":"2026-07-05T10:48:03.357456+00:00"},{"alias_kind":"pith_short_8","alias_value":"FOK7HXJ6","created_at":"2026-07-05T10:48:03.357456+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP","json":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP.json","graph_json":"https://pith.science/api/pith-number/FOK7HXJ6CKM5ENTQDF567TFKWP/graph.json","events_json":"https://pith.science/api/pith-number/FOK7HXJ6CKM5ENTQDF567TFKWP/events.json","paper":"https://pith.science/paper/FOK7HXJ6"},"agent_actions":{"view_html":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP","download_json":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP.json","view_paper":"https://pith.science/paper/FOK7HXJ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.09044&json=true","fetch_graph":"https://pith.science/api/pith-number/FOK7HXJ6CKM5ENTQDF567TFKWP/graph.json","fetch_events":"https://pith.science/api/pith-number/FOK7HXJ6CKM5ENTQDF567TFKWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP/action/storage_attestation","attest_author":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP/action/author_attestation","sign_citation":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP/action/citation_signature","submit_replication":"https://pith.science/pith/FOK7HXJ6CKM5ENTQDF567TFKWP/action/replication_record"}},"created_at":"2026-07-05T10:48:03.357456+00:00","updated_at":"2026-07-05T10:48:03.357456+00:00"}