{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NGMYRXEWDMZ5R5BGNYBVI5JXSH","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":"88d9c5b64d848d45d30a902e70952079fe2b74af40281a0a7ab6e226d6600764","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-02-03T20:06:07Z","title_canon_sha256":"77494628ea238ce09bdbb6c95f412375a62786dfaed28a51c56c863b0334caaf"},"schema_version":"1.0","source":{"id":"1902.00962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00962","created_at":"2026-05-17T23:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00962v1","created_at":"2026-05-17T23:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00962","created_at":"2026-05-17T23:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"NGMYRXEWDMZ5","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NGMYRXEWDMZ5R5BG","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NGMYRXEW","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:fd06b08de88b94ee65988a36b3df0c7b3b583bbb45079d4b8daf6fdf2f70e38a","target":"graph","created_at":"2026-05-17T23:54:42Z","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":"Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution $(X,r)$ consists of a set $X$ and a bijective map $r:X\\times X\\to X\\times X$ which satisfies the braid relations. In this work we study the braided group $G=G(X,r)$ of an involutive square-free solution $(X,r)$ of finite order $n$ and cyclic index $p=p(X,r)$ and the group algebra $\\textbf{k} [G]$ over a field $\\textbf{k}$. We show that $G$ contains a $G$-invariant normal subgroup $\\mathcal{F}_p$ of finite index $p^n$, $\\mathcal{F}_p$ is isomorphic to th","authors_text":"Tatiana Gateva-Ivanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-02-03T20:06:07Z","title":"The braided group of a square-free solution of the Yang-Baxter equation and its group algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00962","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:d0a30bdc7f1f508e86438c9b7acb9a86c8a0b88530d1997499b9ee66d2822616","target":"record","created_at":"2026-05-17T23:54:42Z","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":"88d9c5b64d848d45d30a902e70952079fe2b74af40281a0a7ab6e226d6600764","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-02-03T20:06:07Z","title_canon_sha256":"77494628ea238ce09bdbb6c95f412375a62786dfaed28a51c56c863b0334caaf"},"schema_version":"1.0","source":{"id":"1902.00962","kind":"arxiv","version":1}},"canonical_sha256":"699988dc961b33d8f4266e0354753791fdd3516d45c84c159e633c5e0ffe5ceb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"699988dc961b33d8f4266e0354753791fdd3516d45c84c159e633c5e0ffe5ceb","first_computed_at":"2026-05-17T23:54:42.323514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:42.323514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DgxM84AQIq3RcI55QiK/MR8dBPsHgNcaobafByqNdQC7rT1wWBp8BztIsBOecvVUVhJEeV2U7zlNbX43qG4bBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:42.323978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0a30bdc7f1f508e86438c9b7acb9a86c8a0b88530d1997499b9ee66d2822616","sha256:fd06b08de88b94ee65988a36b3df0c7b3b583bbb45079d4b8daf6fdf2f70e38a"],"state_sha256":"88ec814e73e753777d853ae031d59961d39462cfc61e92af5491140a3b8323e4"}