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Almost thirty years ago, Burr and Erd\\H{o}s conjectured that r(K_3,Q_n) = 2^{n+1} - 1 for every n \\in \\N, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K_3,Q_n) \\le 7000 \\cdot 2^n. Here we show that r(K_3,Q_n) = (1 + o(1)) 2^{n+1} as n \\to \\infty."},"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":"1302.3840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-15T18:32:18Z","cross_cats_sorted":[],"title_canon_sha256":"6ee3fa46c15bf14972ddc947c55fccf0d0f1f52c781361bd0149ef6c50df43e4","abstract_canon_sha256":"f550d20ed10538817400e7fce1b15072084bae35b7eb9b2256c0e3af3901f8fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:35.535911Z","signature_b64":"R39n/+S+WGUDgXdhuwSld731mpxuIANf5pWp18KbdEr4+sWLySd6A+EsKmTXHSaDtx6KhcnMVozVGA5EGeJgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dd99c2540b62bea0ec503a7531045253837f5a38f856e8bbd1531c7b5f46851","last_reissued_at":"2026-05-18T03:33:35.535116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:35.535116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ramsey number of the triangle and the cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Saxton, Gonzalo Fiz Pontiveros, Jozef Skokan, Robert Morris, Simon Griffiths","submitted_at":"2013-02-15T18:32:18Z","abstract_excerpt":"The Ramsey number r(K_3,Q_n) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K_N contains either a red n-dimensional hypercube, or a blue triangle. 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