{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:F2Q6WROBR5O4OAW4U7IMM2EOIF","short_pith_number":"pith:F2Q6WROB","schema_version":"1.0","canonical_sha256":"2ea1eb45c18f5dc702dca7d0c6688e414320eea793c92dcc5d699073bab56227","source":{"kind":"arxiv","id":"1511.07769","version":2},"attestation_state":"computed","paper":{"title":"A family of irretractable square-free solutions of the Yang-Baxter equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"David Bachiller, Eric Jespers, Ferran Cedo, Jan Okninski","submitted_at":"2015-11-24T16:01:25Z","abstract_excerpt":"A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solutions of multipermutation level at most two. A large subfamily consists of irretractable and square-free solutions. This subfamily includes a recent example of Vendramin, who first gave a counterexample to Gateva-Ivanova's Strong Conjecture. All the solutions in this subfamily are new counterexamples to Gateva-Ivanova's Strong Conjecture and also they answer a question of Cameron and Gateva-Ivanova. It is proved that"},"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":"1511.07769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-24T16:01:25Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"d7e3335e1b1ddb81c70b7c7ea15d098e96a4890e52d1265ce4fc7c1cb4b7e028","abstract_canon_sha256":"958c628d2b09ad831515dd4a5378f6e8767e1b73be0b189a0207c291d2bcf007"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:10.751769Z","signature_b64":"j1Ixz3210sWAlOaqvvBDsGBBKWmS3G3Vz8BQKUeQeKpXJAJtFAbFofn5FJpsnhBLxeJaoScukIy7GfSO5nqCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea1eb45c18f5dc702dca7d0c6688e414320eea793c92dcc5d699073bab56227","last_reissued_at":"2026-05-18T01:03:10.751151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:10.751151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A family of irretractable square-free solutions of the Yang-Baxter equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"David Bachiller, Eric Jespers, Ferran Cedo, Jan Okninski","submitted_at":"2015-11-24T16:01:25Z","abstract_excerpt":"A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solutions of multipermutation level at most two. A large subfamily consists of irretractable and square-free solutions. This subfamily includes a recent example of Vendramin, who first gave a counterexample to Gateva-Ivanova's Strong Conjecture. All the solutions in this subfamily are new counterexamples to Gateva-Ivanova's Strong Conjecture and also they answer a question of Cameron and Gateva-Ivanova. It is proved that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07769","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1511.07769","created_at":"2026-05-18T01:03:10.751244+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.07769v2","created_at":"2026-05-18T01:03:10.751244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07769","created_at":"2026-05-18T01:03:10.751244+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2Q6WROBR5O4","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2Q6WROBR5O4OAW4","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2Q6WROB","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF","json":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF.json","graph_json":"https://pith.science/api/pith-number/F2Q6WROBR5O4OAW4U7IMM2EOIF/graph.json","events_json":"https://pith.science/api/pith-number/F2Q6WROBR5O4OAW4U7IMM2EOIF/events.json","paper":"https://pith.science/paper/F2Q6WROB"},"agent_actions":{"view_html":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF","download_json":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF.json","view_paper":"https://pith.science/paper/F2Q6WROB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.07769&json=true","fetch_graph":"https://pith.science/api/pith-number/F2Q6WROBR5O4OAW4U7IMM2EOIF/graph.json","fetch_events":"https://pith.science/api/pith-number/F2Q6WROBR5O4OAW4U7IMM2EOIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF/action/storage_attestation","attest_author":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF/action/author_attestation","sign_citation":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF/action/citation_signature","submit_replication":"https://pith.science/pith/F2Q6WROBR5O4OAW4U7IMM2EOIF/action/replication_record"}},"created_at":"2026-05-18T01:03:10.751244+00:00","updated_at":"2026-05-18T01:03:10.751244+00:00"}