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Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole. Using Hanani's SQS constructions, we show that for every v = 2, 4 mod 6 with v > 4 there exists an SQS(v) that admits a 1-overlap cycle."},"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":"1204.3215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-14T20:42:45Z","cross_cats_sorted":[],"title_canon_sha256":"93a18eda830ca92780eb078eff033d28dcf435d884508bb3fa308ad057cd2e4e","abstract_canon_sha256":"d50cb064bb4cfc42da3e8baaeb1335dff6d44e71d38cf3f1a6ab40aa0e4c8822"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.263586Z","signature_b64":"HhuBAez2Fw9g75LAFq+iocFKOQiSSHqGq9ijicujUf1JsRvOgqapS6vR9JoJVCFu5os20MXJkAsqKucPgAcNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf2b1ab4929626887812c647d4c6f74b8452621040809a4c335f7d93e9c82190","last_reissued_at":"2026-05-18T03:57:52.263080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.263080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Overlap Cycles for Steiner Quadruple Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Glenn Hurlbert, Victoria Horan","submitted_at":"2012-04-14T20:42:45Z","abstract_excerpt":"Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. 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