{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KRGNOSYKLZAI7SUSIP7PJPUWPS","short_pith_number":"pith:KRGNOSYK","schema_version":"1.0","canonical_sha256":"544cd74b0a5e408fca9243fef4be967c8dabc03e7d83e982211498a6cd122afc","source":{"kind":"arxiv","id":"2407.12533","version":1},"attestation_state":"computed","paper":{"title":"Set-theoretic solutions of the Yang-Baxter equation and regular *-semibraces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"Qianxue Liu, Shoufeng Wang","submitted_at":"2024-07-17T13:14:50Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2407.12533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-07-17T13:14:50Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"44c53b276ac0a8a1785dfde1c6b55fa1a21eae632509302446bbc1262f0eb354","abstract_canon_sha256":"c7137154be0c7177cfdd5664bf3e0136fbb8259e76d2260c0c08aaeb3d14698e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:45:05.946078Z","signature_b64":"cIwDMta+Cpg5elDnSfDgHmItxBeAy7GN2ALd3inriAwbRBPs60hx9SUh1lQr1wyMh03fTyG4LzehT8wOYJKICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"544cd74b0a5e408fca9243fef4be967c8dabc03e7d83e982211498a6cd122afc","last_reissued_at":"2026-07-05T08:45:05.945668Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:45:05.945668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Set-theoretic solutions of the Yang-Baxter equation and regular *-semibraces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"Qianxue Liu, Shoufeng Wang","submitted_at":"2024-07-17T13:14:50Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12533","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.12533/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2407.12533","created_at":"2026-07-05T08:45:05.945723+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.12533v1","created_at":"2026-07-05T08:45:05.945723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.12533","created_at":"2026-07-05T08:45:05.945723+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRGNOSYKLZAI","created_at":"2026-07-05T08:45:05.945723+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRGNOSYKLZAI7SUS","created_at":"2026-07-05T08:45:05.945723+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRGNOSYK","created_at":"2026-07-05T08:45:05.945723+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.05861","citing_title":"Some characterizations of weak left braces","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS","json":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS.json","graph_json":"https://pith.science/api/pith-number/KRGNOSYKLZAI7SUSIP7PJPUWPS/graph.json","events_json":"https://pith.science/api/pith-number/KRGNOSYKLZAI7SUSIP7PJPUWPS/events.json","paper":"https://pith.science/paper/KRGNOSYK"},"agent_actions":{"view_html":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS","download_json":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS.json","view_paper":"https://pith.science/paper/KRGNOSYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.12533&json=true","fetch_graph":"https://pith.science/api/pith-number/KRGNOSYKLZAI7SUSIP7PJPUWPS/graph.json","fetch_events":"https://pith.science/api/pith-number/KRGNOSYKLZAI7SUSIP7PJPUWPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS/action/storage_attestation","attest_author":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS/action/author_attestation","sign_citation":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS/action/citation_signature","submit_replication":"https://pith.science/pith/KRGNOSYKLZAI7SUSIP7PJPUWPS/action/replication_record"}},"created_at":"2026-07-05T08:45:05.945723+00:00","updated_at":"2026-07-05T08:45:05.945723+00:00"}