{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZLAN5XIVCIFPC2RJU2DPATQGHP","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":"ba0f5118a6d5507cb96e5649e8fba4eefeac11fc537f7f2036a7559a56d68717","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.QA","submitted_at":"2025-06-14T13:33:15Z","title_canon_sha256":"cb422875c25eff0b25cb829786be9486e78d11d4b1ef798ff3200580deb4fd07"},"schema_version":"1.0","source":{"id":"2506.12503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.12503","created_at":"2026-07-05T11:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"2506.12503v1","created_at":"2026-07-05T11:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12503","created_at":"2026-07-05T11:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZLAN5XIVCIFP","created_at":"2026-07-05T11:21:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZLAN5XIVCIFPC2RJ","created_at":"2026-07-05T11:21:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZLAN5XIV","created_at":"2026-07-05T11:21:54Z"}],"graph_snapshots":[{"event_id":"sha256:c8f6620dfd52e1f17ef469ba7e64f25632d1b70b889ec4bbfe46b5997888bc59","target":"graph","created_at":"2026-07-05T11:21:54Z","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/2506.12503/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the class of one-generator solutions to the Yang-Baxter equation, extending some recent results concerning the classes of involutive and multipermutation solutions. Moreover we show the precise relationship between indecomposable solutions to the Yang-Baxter equation and finite one-generator skew braces, giving a positive answer to a question posed by Agata and Alicja Smoktunowicz. In the last part, we apply our results to the involutive case, and we present some numerical results involving solutions of small size.","authors_text":"Marco Castelli","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.QA","submitted_at":"2025-06-14T13:33:15Z","title":"One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12503","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":"sha256:8d31fa81af3026e7221695b40ba6f6a174a4ed51c32f68f85e4b6787743a0169","target":"record","created_at":"2026-07-05T11:21:54Z","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":"ba0f5118a6d5507cb96e5649e8fba4eefeac11fc537f7f2036a7559a56d68717","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.QA","submitted_at":"2025-06-14T13:33:15Z","title_canon_sha256":"cb422875c25eff0b25cb829786be9486e78d11d4b1ef798ff3200580deb4fd07"},"schema_version":"1.0","source":{"id":"2506.12503","kind":"arxiv","version":1}},"canonical_sha256":"cac0dedd15120af16a29a686f04e063bd1e334237533819672b915290904ccce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cac0dedd15120af16a29a686f04e063bd1e334237533819672b915290904ccce","first_computed_at":"2026-07-05T11:21:54.414369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:54.414369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKkZ4qBeyWtFbjOMx22bVZAtFJrG22lZmqwIezR1guujswZ7SkgJqTuCmspwCJdjvuLLjcbzWseWYa1+tR5kAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:54.414785Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.12503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d31fa81af3026e7221695b40ba6f6a174a4ed51c32f68f85e4b6787743a0169","sha256:c8f6620dfd52e1f17ef469ba7e64f25632d1b70b889ec4bbfe46b5997888bc59"],"state_sha256":"4ab1ff5b7fbfca23a4d383f30e86c9fed35970be63242557b7a63b3d3211f926"}