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The two-color bipartite Ramsey number $b(s,t)$ is the smallest integer $b$ such that any coloring of the edges of $K_{b,b}$ with two colors contains a $K_{s,s}$ in the first color or a $K_{t,t}$ in the second color.\n  In this work, we design and exploit a computational method for bounding and computing Zarankiewicz numbers. Using it, we obtain several new values and bounds on $z(b;s)$ for $3 \\le s \\le 6$. Our approach and new knowledge about $z(b;s)$ permit us to impr"},"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":"1604.01257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-05T13:48:11Z","cross_cats_sorted":[],"title_canon_sha256":"e5f642d41478b8c9d668f1edac480a171ad5f9dff73812a93007f838e09dc02b","abstract_canon_sha256":"ff79ccefd41f03426955babfb2bd8e61e54af60a78a74e9493bbec2037b56247"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:38.718060Z","signature_b64":"fWxLHWnW9DxzgXYWkopq73bmNlfXjo+ZCi2eSP6S2pT28lHFH5rnykBwhGyETWKkt00bOlEpx9iynWoJG9LjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d91a0dfc956ae04403d04b80042941c4ce1a140db73ae8cfbbf3afa66d6e8ddd","last_reissued_at":"2026-05-18T01:17:38.717278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:38.717278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zarankiewicz Numbers and Bipartite Ramsey Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Riasanovsky, Alex Collins, John Wallace, Stanis{\\l}aw Radziszowski","submitted_at":"2016-04-05T13:48:11Z","abstract_excerpt":"The Zarankiewicz number $z(b;s)$ is the maximum size of a subgraph of $K_{b,b}$ which does not contain $K_{s,s}$ as a subgraph. 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