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In this short note, we use an explicit construction to establish that when $t$ is a prime power and $n = t^{2e - 1}$, then $$ ex(n, K_{t, t}, K_{2, t+1}) = (1 + o(1))\\frac{n^2}{2t(t-1)}. $$"},"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":"2606.02855","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T20:19:23Z","cross_cats_sorted":[],"title_canon_sha256":"f4f8f5aa1bec395d0e8827b18a57cf34c4d92d517bd7fa20ae89c98bd2897074","abstract_canon_sha256":"0454fb5c03a9e4b3193d6915e078c6bd0368937b5dead95f81196d8b4f57dd2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:24.636797Z","signature_b64":"swcNEhhSPX6JX6PpLgb4XgX5DH5IIR/bEHDwRiwMcxGKupHSkAlA63X3IK3z5BKgusERYlYcb06FiSvty7K6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59407d15a222216226a223208900c16796f2cfd9964ea9e07206524b7e16c9bd","last_reissued_at":"2026-06-03T01:05:24.636460Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:24.636460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$K_{2, t+1}$-free graphs containing an optimal number of $K_{t, t}$'s","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladislav Taranchuk","submitted_at":"2026-06-01T20:19:23Z","abstract_excerpt":"The generalized Tur\\'{a}n number $ex(n, K_{t, t}, K_{2, t+1})$ is the maximum number of copies of $K_{t, t}$ that a $K_{2, t+1}$-free graph on $n$ vertices can contain. 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