{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KKKYRVLE4ZNARJ5M52SARYAMDT","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":"3cd0ef4d0503bf0522e2c6c38a504c7b664a8c33554661208060de27bbac448d","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-27T16:12:32Z","title_canon_sha256":"4a14be04326f4bb94bebcacd5dc4fb22498205436e21304a73395f150fe7e338"},"schema_version":"1.0","source":{"id":"1802.09993","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09993","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09993v1","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09993","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"KKKYRVLE4ZNA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KKKYRVLE4ZNARJ5M","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KKKYRVLE","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:ebe500099ee8b493c642102beccb3a821de13e71f1b5f3e101d9fb3b0b62359f","target":"graph","created_at":"2026-05-18T00:22:21Z","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":"Let $r:X^{2}\\rightarrow X^{2}$ be a set-theoretic solution of the Yang-Baxter equation on a finite set $X$. It was proven by Gateva-Ivanova and Van den Bergh that if $r$ is non-degenerate and involutive then the algebra $K\\langle x \\in X \\mid xy =uv \\mbox{ if } r(x,y)=(u,v)\\rangle$ shares many properties with commutative polynomial algebras in finitely many variables; in particular this algebra is Noetherian, satisfies a polynomial identity and has Gelfand-Kirillov dimension a positive integer. Lebed and Vendramin recently extended this result to arbitrary non-degenerate bijective solutions. S","authors_text":"Arne Van Antwerpen, Eric Jespers","cross_cats":["math.QA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-27T16:12:32Z","title":"Left semi-braces and solutions to the Yang-Baxter equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09993","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":"sha256:9f94ec49847c8533104307f87bdb84bfffe72a62c22f567a7900084181774738","target":"record","created_at":"2026-05-18T00:22:21Z","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":"3cd0ef4d0503bf0522e2c6c38a504c7b664a8c33554661208060de27bbac448d","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-27T16:12:32Z","title_canon_sha256":"4a14be04326f4bb94bebcacd5dc4fb22498205436e21304a73395f150fe7e338"},"schema_version":"1.0","source":{"id":"1802.09993","kind":"arxiv","version":1}},"canonical_sha256":"529588d564e65a08a7aceea408e00c1cc7f9a2dc116f3c394293acea4fd10fc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"529588d564e65a08a7aceea408e00c1cc7f9a2dc116f3c394293acea4fd10fc1","first_computed_at":"2026-05-18T00:22:21.664385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:21.664385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8V7qIBsLLPbCTqxtMAqdyj8xi1UGBau7AzGDFTx+Xm8c+GPTToYTLmBuZcyzSCtz8c7cj4hLT+nd1MnbRbXRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:21.665009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09993","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f94ec49847c8533104307f87bdb84bfffe72a62c22f567a7900084181774738","sha256:ebe500099ee8b493c642102beccb3a821de13e71f1b5f3e101d9fb3b0b62359f"],"state_sha256":"710b2825deb6bdd1ce6b0628849dfd6898bed375d894b42b176afc31265dccdd"}