{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FJGFAGBJ7KQYFTFFKBX6NAZATR","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":"4d8b344ba2ba2438349a4f4fec5f34df592a27f14812fc7e7b857c8b39ddeff4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-20T04:14:33Z","title_canon_sha256":"192e77f0b08f4a48d754b2d48110b723663a9395223c09f84858dcf01658afb4"},"schema_version":"1.0","source":{"id":"1810.09848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09848","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09848v1","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09848","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"FJGFAGBJ7KQY","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FJGFAGBJ7KQYFTFF","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FJGFAGBJ","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:fa31290c26664da81f0655da8419519742012dfa161c10ecd6e4752f776847d2","target":"graph","created_at":"2026-05-18T00:02:29Z","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"},"paper":{"abstract_excerpt":"We introduce the notion of Hom-co-represention and low-dimensional chain complex. We study universal central extensions of Hom-preLie algebras and generlize some classical results. As the same time, we introduce $\\alpha$-central extensions, universal $\\alpha$-central extensions and $\\alpha$-perfect Hom-preLie algebras. We construct universal ($\\alpha$)-central extensions of Hom-preLie algebras.","authors_text":"Bing Sun, Liangyun Chen, Xin Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-20T04:14:33Z","title":"On universal $\\alpha$-central extensions of Hom-preLie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09848","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:bb3241127e15e53e296637e9e085d734aae5b16234d5a1aff86510c7bf3bae85","target":"record","created_at":"2026-05-18T00:02:29Z","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":"4d8b344ba2ba2438349a4f4fec5f34df592a27f14812fc7e7b857c8b39ddeff4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-20T04:14:33Z","title_canon_sha256":"192e77f0b08f4a48d754b2d48110b723663a9395223c09f84858dcf01658afb4"},"schema_version":"1.0","source":{"id":"1810.09848","kind":"arxiv","version":1}},"canonical_sha256":"2a4c501829faa182cca5506fe683209c5ce3afda7ce5f0b6eed5fe54cd3cc52a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a4c501829faa182cca5506fe683209c5ce3afda7ce5f0b6eed5fe54cd3cc52a","first_computed_at":"2026-05-18T00:02:29.177772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:29.177772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"52yB6j1bafF1xJM+Lv54NlvB55c03vv2mbF86/h85XVbk9L0VTKkabGm9QSigB0+QwWwQNhYVzN0mfso0rS6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:29.178391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb3241127e15e53e296637e9e085d734aae5b16234d5a1aff86510c7bf3bae85","sha256:fa31290c26664da81f0655da8419519742012dfa161c10ecd6e4752f776847d2"],"state_sha256":"9b6500bf1a32af2826b120367938a7cf35833861addd2cb9f770f8f5f08bc7ca"}