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Recently, it is shown that there exists a ${\\mathsf{PQ}}(2, (n^3+3n^2-2)/2, n^2+n)$ if and only if $n\\in\\{1, 2, 4\\}$. Let $\\mathcal{S}$ be a ${\\mathsf{PQ}}(3,(n+3)(n^2-1)/3, n^2+n)$ such that for every two non-collinear points $p_1$ and $p_2$, there is a point $q$ non-collinear with $p_1$, $p_2$, and all points collinear with both $p_1$ and $p_2$. In this article, we establish that $\\mathcal{S}$ exis"},"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":"1303.0473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-03T07:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"ad0f44eb666bfb9697531c3a2c502bf86a71934745e1521576b31d78d3a3319a","abstract_canon_sha256":"46aa7f713d748645998e9d9a1efe590a4a573e9438d6efb429af434fc1d773fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:55.904648Z","signature_b64":"J+eVTtN9FHZjng/tOdPdkfqj97rI9ic+24wOrHAaauJc03/nhtmQ4F+2fQ+vYDOXcDsBr4EVLyHOaWw8ioTPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35602e97f85612fff94a668f1c2d820e4ec9bc36fbbc1b0453a263f1572dc8b9","last_reissued_at":"2026-05-18T03:31:55.903966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:55.903966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a family of diamond-free strongly regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Mohammadian, B. Tayfeh-Rezaie","submitted_at":"2013-03-03T07:57:58Z","abstract_excerpt":"The existence of a partial quadrangle ${\\mathsf{PQ}}(s, t, \\mu)$ is equivalent to the existence of a diamond-free strongly regular graph ${\\mathsf{SRG}}(1+s(t+1)+s^2t(t+1)/\\mu, s(t+1), s-1, \\mu)$. Recently, it is shown that there exists a ${\\mathsf{PQ}}(2, (n^3+3n^2-2)/2, n^2+n)$ if and only if $n\\in\\{1, 2, 4\\}$. Let $\\mathcal{S}$ be a ${\\mathsf{PQ}}(3,(n+3)(n^2-1)/3, n^2+n)$ such that for every two non-collinear points $p_1$ and $p_2$, there is a point $q$ non-collinear with $p_1$, $p_2$, and all points collinear with both $p_1$ and $p_2$. 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