{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KRGNOSYKLZAI7SUSIP7PJPUWPS","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":"c7137154be0c7177cfdd5664bf3e0136fbb8259e76d2260c0c08aaeb3d14698e","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-07-17T13:14:50Z","title_canon_sha256":"44c53b276ac0a8a1785dfde1c6b55fa1a21eae632509302446bbc1262f0eb354"},"schema_version":"1.0","source":{"id":"2407.12533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.12533","created_at":"2026-07-05T08:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"2407.12533v1","created_at":"2026-07-05T08:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12533","created_at":"2026-07-05T08:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"KRGNOSYKLZAI","created_at":"2026-07-05T08:45:05Z"},{"alias_kind":"pith_short_16","alias_value":"KRGNOSYKLZAI7SUS","created_at":"2026-07-05T08:45:05Z"},{"alias_kind":"pith_short_8","alias_value":"KRGNOSYK","created_at":"2026-07-05T08:45:05Z"}],"graph_snapshots":[{"event_id":"sha256:8bce7419f598f7b7be6113a08b72853dad67d664a45771bf084c14566b7b4a3b","target":"graph","created_at":"2026-07-05T08:45:05Z","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/2407.12533/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As generalizations of inverse semibraces introduced by Catino, Mazzotta and Stefanelli, Miccoli has introduced regular $\\star$-semibraces under the name of involution semibraces and given a sufficient condition under which the associated map to a regular $\\star$-semibrace is a set-theoretic solution of the Yang-Baxter equation. From the viewpoint of universal algebra, regular $\\star$-semibraces are (2,2,1)-type algebras. In this paper we continue to study set-theoretic solutions of the Yang-Baxter equation and regular $\\star$-semibraces. We first consider several kinds of (2,2,1)-type algebras","authors_text":"Qianxue Liu, Shoufeng Wang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-07-17T13:14:50Z","title":"Set-theoretic solutions of the Yang-Baxter equation and regular *-semibraces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12533","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":"sha256:39460d61a9ea0e4d984a705b56dc4256f2f5696992640f00576fff8898c18e9c","target":"record","created_at":"2026-07-05T08:45:05Z","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":"c7137154be0c7177cfdd5664bf3e0136fbb8259e76d2260c0c08aaeb3d14698e","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-07-17T13:14:50Z","title_canon_sha256":"44c53b276ac0a8a1785dfde1c6b55fa1a21eae632509302446bbc1262f0eb354"},"schema_version":"1.0","source":{"id":"2407.12533","kind":"arxiv","version":1}},"canonical_sha256":"544cd74b0a5e408fca9243fef4be967c8dabc03e7d83e982211498a6cd122afc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"544cd74b0a5e408fca9243fef4be967c8dabc03e7d83e982211498a6cd122afc","first_computed_at":"2026-07-05T08:45:05.945668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:45:05.945668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cIwDMta+Cpg5elDnSfDgHmItxBeAy7GN2ALd3inriAwbRBPs60hx9SUh1lQr1wyMh03fTyG4LzehT8wOYJKICg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:45:05.946078Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.12533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39460d61a9ea0e4d984a705b56dc4256f2f5696992640f00576fff8898c18e9c","sha256:8bce7419f598f7b7be6113a08b72853dad67d664a45771bf084c14566b7b4a3b"],"state_sha256":"07c9d7fdbe6d1104c41f7ab61e9f0b7ce8c74a750d344e1fc43cedae111b9187"}