{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:THNUUWVYMD5ZVYRC2GGD4A6MC7","short_pith_number":"pith:THNUUWVY","schema_version":"1.0","canonical_sha256":"99db4a5ab860fb9ae222d18c3e03cc17cd5f662cf6aa6802019653283ad7b10e","source":{"kind":"arxiv","id":"2408.16318","version":2},"attestation_state":"computed","paper":{"title":"Quaternary Legendre pairs II","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arne Winterhof, Christoph Koutschan, Ilias S. Kotsireas","submitted_at":"2024-08-29T07:37:15Z","abstract_excerpt":"Quaternary Legendre pairs are pertinent to the construction of quaternary Hadamard matrices and have many applications, for example in coding theory and communications. In contrast to binary Legendre pairs, quaternary ones can exist for even length $\\ell$ as well. It is conjectured that there is a quaternary Legendre pair for any even $\\ell$. The smallest open case until now had been $\\ell=28$, and $\\ell=38$ was the only length $\\ell$ with $28\\le \\ell\\le 60$ resolved before. Here we provide constructions for $\\ell=28,30,32$, and $34$. In parallel and independently, Jedwab and Pender found a co"},"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":"2408.16318","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-29T07:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"b648bec348c4039680d6e6d924291db95ff0267fc8c75b4e44a40d846db4736f","abstract_canon_sha256":"8b3795c3e250d9854733ec977fab12dec70be8b4eec40a1772ce7cd2f265fdd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:12.706833Z","signature_b64":"4thRshEztQFDm9dDIhoRr2hojmJuhYb281MqDUXVevFRjRunfxH56Yz5LwOlZ06EXbww+8eJAfvgUjU9TlUGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99db4a5ab860fb9ae222d18c3e03cc17cd5f662cf6aa6802019653283ad7b10e","last_reissued_at":"2026-07-05T10:40:12.706380Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:12.706380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quaternary Legendre pairs II","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arne Winterhof, Christoph Koutschan, Ilias S. Kotsireas","submitted_at":"2024-08-29T07:37:15Z","abstract_excerpt":"Quaternary Legendre pairs are pertinent to the construction of quaternary Hadamard matrices and have many applications, for example in coding theory and communications. In contrast to binary Legendre pairs, quaternary ones can exist for even length $\\ell$ as well. It is conjectured that there is a quaternary Legendre pair for any even $\\ell$. The smallest open case until now had been $\\ell=28$, and $\\ell=38$ was the only length $\\ell$ with $28\\le \\ell\\le 60$ resolved before. Here we provide constructions for $\\ell=28,30,32$, and $34$. In parallel and independently, Jedwab and Pender found a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16318","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.16318/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":"2408.16318","created_at":"2026-07-05T10:40:12.706439+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.16318v2","created_at":"2026-07-05T10:40:12.706439+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.16318","created_at":"2026-07-05T10:40:12.706439+00:00"},{"alias_kind":"pith_short_12","alias_value":"THNUUWVYMD5Z","created_at":"2026-07-05T10:40:12.706439+00:00"},{"alias_kind":"pith_short_16","alias_value":"THNUUWVYMD5ZVYRC","created_at":"2026-07-05T10:40:12.706439+00:00"},{"alias_kind":"pith_short_8","alias_value":"THNUUWVY","created_at":"2026-07-05T10:40:12.706439+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/THNUUWVYMD5ZVYRC2GGD4A6MC7","json":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7.json","graph_json":"https://pith.science/api/pith-number/THNUUWVYMD5ZVYRC2GGD4A6MC7/graph.json","events_json":"https://pith.science/api/pith-number/THNUUWVYMD5ZVYRC2GGD4A6MC7/events.json","paper":"https://pith.science/paper/THNUUWVY"},"agent_actions":{"view_html":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7","download_json":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7.json","view_paper":"https://pith.science/paper/THNUUWVY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.16318&json=true","fetch_graph":"https://pith.science/api/pith-number/THNUUWVYMD5ZVYRC2GGD4A6MC7/graph.json","fetch_events":"https://pith.science/api/pith-number/THNUUWVYMD5ZVYRC2GGD4A6MC7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7/action/storage_attestation","attest_author":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7/action/author_attestation","sign_citation":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7/action/citation_signature","submit_replication":"https://pith.science/pith/THNUUWVYMD5ZVYRC2GGD4A6MC7/action/replication_record"}},"created_at":"2026-07-05T10:40:12.706439+00:00","updated_at":"2026-07-05T10:40:12.706439+00:00"}