{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UPKQNNM7F2ZOGE23CCIJVYZBG4","short_pith_number":"pith:UPKQNNM7","schema_version":"1.0","canonical_sha256":"a3d506b59f2eb2e3135b10909ae3213727f8698b6ae44da2966edc86a6f8d8c8","source":{"kind":"arxiv","id":"2412.16273","version":1},"attestation_state":"computed","paper":{"title":"Compatible anti-pre-Lie algebras","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Zafar Normatov","submitted_at":"2024-12-20T15:57:58Z","abstract_excerpt":"In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti-$\\mathcal{O}$-operators, commutative $2$-cocycles on compatible Lie algebras. Moreover, we give the classification of $2$-dimensional compatible anti-pre-Lie algebras from the classification of anti-pre-Lie algebras of the same dimension."},"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":"2412.16273","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-12-20T15:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"0ce6455b09199878cd7fc07f80e020a7b635e81f3aa1cff214827714719ce648","abstract_canon_sha256":"97b026d4c9465f93cd7cf0aeb15dbf9cf9fad53deadf9b7be79f52a739a20c27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:44.054761Z","signature_b64":"0use/JsbBBo8FTL8daxUt1U2li/Ug+1hKxYxuR412lsh5bRCBs7y3D46SG9Rm0iZ8Y/RUcgM3gwS9UBp6jmPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3d506b59f2eb2e3135b10909ae3213727f8698b6ae44da2966edc86a6f8d8c8","last_reissued_at":"2026-07-05T09:52:44.054345Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:44.054345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compatible anti-pre-Lie algebras","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Zafar Normatov","submitted_at":"2024-12-20T15:57:58Z","abstract_excerpt":"In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti-$\\mathcal{O}$-operators, commutative $2$-cocycles on compatible Lie algebras. Moreover, we give the classification of $2$-dimensional compatible anti-pre-Lie algebras from the classification of anti-pre-Lie algebras of the same dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16273","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/2412.16273/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":"2412.16273","created_at":"2026-07-05T09:52:44.054402+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.16273v1","created_at":"2026-07-05T09:52:44.054402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16273","created_at":"2026-07-05T09:52:44.054402+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPKQNNM7F2ZO","created_at":"2026-07-05T09:52:44.054402+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPKQNNM7F2ZOGE23","created_at":"2026-07-05T09:52:44.054402+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPKQNNM7","created_at":"2026-07-05T09:52:44.054402+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/UPKQNNM7F2ZOGE23CCIJVYZBG4","json":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4.json","graph_json":"https://pith.science/api/pith-number/UPKQNNM7F2ZOGE23CCIJVYZBG4/graph.json","events_json":"https://pith.science/api/pith-number/UPKQNNM7F2ZOGE23CCIJVYZBG4/events.json","paper":"https://pith.science/paper/UPKQNNM7"},"agent_actions":{"view_html":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4","download_json":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4.json","view_paper":"https://pith.science/paper/UPKQNNM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.16273&json=true","fetch_graph":"https://pith.science/api/pith-number/UPKQNNM7F2ZOGE23CCIJVYZBG4/graph.json","fetch_events":"https://pith.science/api/pith-number/UPKQNNM7F2ZOGE23CCIJVYZBG4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4/action/storage_attestation","attest_author":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4/action/author_attestation","sign_citation":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4/action/citation_signature","submit_replication":"https://pith.science/pith/UPKQNNM7F2ZOGE23CCIJVYZBG4/action/replication_record"}},"created_at":"2026-07-05T09:52:44.054402+00:00","updated_at":"2026-07-05T09:52:44.054402+00:00"}