{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:T4CT73HTG7IY7PY4RLF56AW3AM","short_pith_number":"pith:T4CT73HT","schema_version":"1.0","canonical_sha256":"9f053fecf337d18fbf1c8acbdf02db030c7b1eabcf0f9389dfed680ec8aca1b9","source":{"kind":"arxiv","id":"2405.19105","version":3},"attestation_state":"computed","paper":{"title":"Reflections to set-theoretic solutions of the Yang-Baxter equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Andrea Albano, Marzia Mazzotta, Paola Stefanelli","submitted_at":"2024-05-29T14:08:45Z","abstract_excerpt":"The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solutions. This is motivated by a recent description of left non-degenerate solutions in terms of a family of automorphisms of their associated left rack. In some cases, we show that the study of reflections for bijective and non-degenerate solutions can be reduced to those of derived type. Moreover, we extend some results obtained in the literature for reflections of involutive non-degenerate solutions to more arbitrary"},"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":"2405.19105","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2024-05-29T14:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"dbd8d97bcab98ff6503500319a54ee073bc98a46f157c230bc240aa9beb0e1e2","abstract_canon_sha256":"9c0bd86f6299519d59188091f54639ac24227f3354260c53d90d5520e8f5251b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:57:20.042374Z","signature_b64":"J13+un7aD4p9gafh+JFMs2Smfolgyow6iiqBw+NsLgJ733uypfzHcQyrO4bJnDknit/ZvAJHAIoNOq1GO9glBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f053fecf337d18fbf1c8acbdf02db030c7b1eabcf0f9389dfed680ec8aca1b9","last_reissued_at":"2026-07-05T10:57:20.040874Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:57:20.040874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reflections to set-theoretic solutions of the Yang-Baxter equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Andrea Albano, Marzia Mazzotta, Paola Stefanelli","submitted_at":"2024-05-29T14:08:45Z","abstract_excerpt":"The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solutions. This is motivated by a recent description of left non-degenerate solutions in terms of a family of automorphisms of their associated left rack. In some cases, we show that the study of reflections for bijective and non-degenerate solutions can be reduced to those of derived type. Moreover, we extend some results obtained in the literature for reflections of involutive non-degenerate solutions to more arbitrary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19105","kind":"arxiv","version":3},"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/2405.19105/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":"2405.19105","created_at":"2026-07-05T10:57:20.041784+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.19105v3","created_at":"2026-07-05T10:57:20.041784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19105","created_at":"2026-07-05T10:57:20.041784+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4CT73HTG7IY","created_at":"2026-07-05T10:57:20.041784+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4CT73HTG7IY7PY4","created_at":"2026-07-05T10:57:20.041784+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4CT73HT","created_at":"2026-07-05T10:57:20.041784+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2504.21678","citing_title":"Reflections and Drinfeld twists for set-theoretic Yang-Baxter maps","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM","json":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM.json","graph_json":"https://pith.science/api/pith-number/T4CT73HTG7IY7PY4RLF56AW3AM/graph.json","events_json":"https://pith.science/api/pith-number/T4CT73HTG7IY7PY4RLF56AW3AM/events.json","paper":"https://pith.science/paper/T4CT73HT"},"agent_actions":{"view_html":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM","download_json":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM.json","view_paper":"https://pith.science/paper/T4CT73HT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.19105&json=true","fetch_graph":"https://pith.science/api/pith-number/T4CT73HTG7IY7PY4RLF56AW3AM/graph.json","fetch_events":"https://pith.science/api/pith-number/T4CT73HTG7IY7PY4RLF56AW3AM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM/action/storage_attestation","attest_author":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM/action/author_attestation","sign_citation":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM/action/citation_signature","submit_replication":"https://pith.science/pith/T4CT73HTG7IY7PY4RLF56AW3AM/action/replication_record"}},"created_at":"2026-07-05T10:57:20.041784+00:00","updated_at":"2026-07-05T10:57:20.041784+00:00"}