{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NXCXHTUKMIDNJS3CYXTRXAD2P3","short_pith_number":"pith:NXCXHTUK","schema_version":"1.0","canonical_sha256":"6dc573ce8a6206d4cb62c5e71b807a7eef41cbaa53954f42f4ecb2ba5d35fa62","source":{"kind":"arxiv","id":"1104.2578","version":2},"attestation_state":"computed","paper":{"title":"On dibaric and evolution algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"B.A. Omirov, M. Ladra, U.A. Rozikov","submitted_at":"2011-04-13T18:51:12Z","abstract_excerpt":"We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f, g$ of the algebra to the set of the real numbers) and show that an algebra is dibaric if and only if it admits a non-zero bq-homomorphism. Using the pair $(f,g)$ we define conservative algebras and establish criteria for a dibaric algebra to be conservative. Moreover, the notions of a Bernstein algebra and an algebra induced by a linear operator are introdu"},"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":"1104.2578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-04-13T18:51:12Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"af115b4385e6dc80c74c68f66a1298567af0f711c48aded66d597d9e0eddef8b","abstract_canon_sha256":"71ca261c4c438e83ede276f2c22605bd95967e3c3f5d6d15b071a98213f51e88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:25.985177Z","signature_b64":"7H/4uLqbHpD4GUh4rTH2aj07y9GqDhRv09Z42HxGSduo2JyTJmDorcqXNQTYSfk4Pps2fRwyK/9X0sxl3QjyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dc573ce8a6206d4cb62c5e71b807a7eef41cbaa53954f42f4ecb2ba5d35fa62","last_reissued_at":"2026-05-18T03:25:25.984604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:25.984604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On dibaric and evolution algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"B.A. Omirov, M. Ladra, U.A. Rozikov","submitted_at":"2011-04-13T18:51:12Z","abstract_excerpt":"We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f, g$ of the algebra to the set of the real numbers) and show that an algebra is dibaric if and only if it admits a non-zero bq-homomorphism. Using the pair $(f,g)$ we define conservative algebras and establish criteria for a dibaric algebra to be conservative. Moreover, the notions of a Bernstein algebra and an algebra induced by a linear operator are introdu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2578","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1104.2578","created_at":"2026-05-18T03:25:25.984684+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2578v2","created_at":"2026-05-18T03:25:25.984684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2578","created_at":"2026-05-18T03:25:25.984684+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXCXHTUKMIDN","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXCXHTUKMIDNJS3C","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXCXHTUK","created_at":"2026-05-18T12:26:37.096874+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/NXCXHTUKMIDNJS3CYXTRXAD2P3","json":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3.json","graph_json":"https://pith.science/api/pith-number/NXCXHTUKMIDNJS3CYXTRXAD2P3/graph.json","events_json":"https://pith.science/api/pith-number/NXCXHTUKMIDNJS3CYXTRXAD2P3/events.json","paper":"https://pith.science/paper/NXCXHTUK"},"agent_actions":{"view_html":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3","download_json":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3.json","view_paper":"https://pith.science/paper/NXCXHTUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2578&json=true","fetch_graph":"https://pith.science/api/pith-number/NXCXHTUKMIDNJS3CYXTRXAD2P3/graph.json","fetch_events":"https://pith.science/api/pith-number/NXCXHTUKMIDNJS3CYXTRXAD2P3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3/action/storage_attestation","attest_author":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3/action/author_attestation","sign_citation":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3/action/citation_signature","submit_replication":"https://pith.science/pith/NXCXHTUKMIDNJS3CYXTRXAD2P3/action/replication_record"}},"created_at":"2026-05-18T03:25:25.984684+00:00","updated_at":"2026-05-18T03:25:25.984684+00:00"}