{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D52S7SZXVLJD32IGYIUTSK4WH2","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":"142a1c89241d88845da40f29c27b127a5d2da10cb38f81351bc9a4677fadaa0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-01T05:27:49Z","title_canon_sha256":"bbbbef26ef1b10976ce175fec12937173d537a4e8e44bf7163ab82920baacd4b"},"schema_version":"1.0","source":{"id":"1603.00147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00147","created_at":"2026-05-18T01:15:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00147v2","created_at":"2026-05-18T01:15:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00147","created_at":"2026-05-18T01:15:13Z"},{"alias_kind":"pith_short_12","alias_value":"D52S7SZXVLJD","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D52S7SZXVLJD32IG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D52S7SZX","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:0bce5ce16695ae57c44da9271850cf360f0912d4d165edcb4edc1b7665e7dc5a","target":"graph","created_at":"2026-05-18T01:15:13Z","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":"Fix $a,b\\in\\C$, let $LW(a,b)$ be the loop $W(a,b)$ Lie algebra over $\\C$ with basis $\\{L_{\\a,i},I_{\\b,j} \\mid \\a,\\b,i,j\\in\\Z\\}$ and relations $[L_{\\a,i},L_{\\b,j}]=(\\a-\\b)L_{\\a+\\b,i+j}, [L_{\\a,i},I_{\\b,j}]=-(a+b\\a+\\b)I_{\\a+\\b,i+j},[I_{\\a,i},I_{\\b,j}]=0$, where $\\a,\\b,i,j\\in\\Z$. In this paper, a formal distribution Lie algebra of $LW(a,b)$ is constructed. Then the associated conformal algebra $CLW(a,b)$ is studied, where $CLW(a,b)$ has a $\\C[\\partial]$-basis $\\{L_i,I_j\\,|\\,i,j\\in\\Z\\}$ with $\\lambda$-brackets $[L_i\\, {}_\\lambda \\, L_j]=(\\partial+2\\lambda) L_{i+j}, [L_i\\, {}_\\lambda \\, I_j]=(\\part","authors_text":"Bo Yu, Guangzhe Fan, Henan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-01T05:27:49Z","title":"Loop W(a,b) Lie conformal algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00147","kind":"arxiv","version":2},"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:a26933950bbd190dbb13a92674d52d40b0684f13bcbeeb3230b0b7cc1d34e90b","target":"record","created_at":"2026-05-18T01:15:13Z","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":"142a1c89241d88845da40f29c27b127a5d2da10cb38f81351bc9a4677fadaa0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-01T05:27:49Z","title_canon_sha256":"bbbbef26ef1b10976ce175fec12937173d537a4e8e44bf7163ab82920baacd4b"},"schema_version":"1.0","source":{"id":"1603.00147","kind":"arxiv","version":2}},"canonical_sha256":"1f752fcb37aad23de906c229392b963ea96b23dd5537e4c42a071a7b721b932b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f752fcb37aad23de906c229392b963ea96b23dd5537e4c42a071a7b721b932b","first_computed_at":"2026-05-18T01:15:13.845177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:13.845177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3dBx/gexZZa3URfira+hwede/mvonkvZfBlRJdl3xWe1FAYsnXskbyzAUdtrMhfDMFgoFn9i2f4Sc+etyTWcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:13.845784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a26933950bbd190dbb13a92674d52d40b0684f13bcbeeb3230b0b7cc1d34e90b","sha256:0bce5ce16695ae57c44da9271850cf360f0912d4d165edcb4edc1b7665e7dc5a"],"state_sha256":"ff394758a05bc39c09fb9b1b34f074c55cbddef4befe44edc27c2904c244a193"}