{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UPKQNNM7F2ZOGE23CCIJVYZBG4","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":"97b026d4c9465f93cd7cf0aeb15dbf9cf9fad53deadf9b7be79f52a739a20c27","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-12-20T15:57:58Z","title_canon_sha256":"0ce6455b09199878cd7fc07f80e020a7b635e81f3aa1cff214827714719ce648"},"schema_version":"1.0","source":{"id":"2412.16273","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16273","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16273v1","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16273","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"UPKQNNM7F2ZO","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"pith_short_16","alias_value":"UPKQNNM7F2ZOGE23","created_at":"2026-07-05T09:52:44Z"},{"alias_kind":"pith_short_8","alias_value":"UPKQNNM7","created_at":"2026-07-05T09:52:44Z"}],"graph_snapshots":[{"event_id":"sha256:b8197cab73ea2fca023540633625538a71c043bb9f8c1bd32962214a9e0a37f5","target":"graph","created_at":"2026-07-05T09:52:44Z","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/2412.16273/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Zafar Normatov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-12-20T15:57:58Z","title":"Compatible anti-pre-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16273","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":"sha256:0f834445bf3943151897a67be916e2416948a94c0d0538424d8c23ea881db3ac","target":"record","created_at":"2026-07-05T09:52:44Z","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":"97b026d4c9465f93cd7cf0aeb15dbf9cf9fad53deadf9b7be79f52a739a20c27","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RA","submitted_at":"2024-12-20T15:57:58Z","title_canon_sha256":"0ce6455b09199878cd7fc07f80e020a7b635e81f3aa1cff214827714719ce648"},"schema_version":"1.0","source":{"id":"2412.16273","kind":"arxiv","version":1}},"canonical_sha256":"a3d506b59f2eb2e3135b10909ae3213727f8698b6ae44da2966edc86a6f8d8c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3d506b59f2eb2e3135b10909ae3213727f8698b6ae44da2966edc86a6f8d8c8","first_computed_at":"2026-07-05T09:52:44.054345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:44.054345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0use/JsbBBo8FTL8daxUt1U2li/Ug+1hKxYxuR412lsh5bRCBs7y3D46SG9Rm0iZ8Y/RUcgM3gwS9UBp6jmPBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:44.054761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16273","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f834445bf3943151897a67be916e2416948a94c0d0538424d8c23ea881db3ac","sha256:b8197cab73ea2fca023540633625538a71c043bb9f8c1bd32962214a9e0a37f5"],"state_sha256":"fa8820c44dad3d00cc7a64a844a9174cd88a37329e3631ca7074eb92a9d7525c"}