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Let N_k(q,n) be the smallest integer N so that every q-coloring of the edges of the complete k-uniform hypergraph on N vertices contains a monochromatic monotone path of length n. While the study of N_k(q,n) for specific values of k and q goes back (implicitly) to the seminal 1935 paper of Erdos and Szekeres, the problem of bounding N_k(q,n) for arbitrary k and"},"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":"1206.4001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-18T17:43:40Z","cross_cats_sorted":[],"title_canon_sha256":"183c6e99e2ed982375abbf510736c1fc203ce01fcce9da5d7a059d4f7b686ac2","abstract_canon_sha256":"e6aba0a3f5d746e4374be309932dddd13c6ef0a96921d00adc28b0ec4fd319f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:18.179869Z","signature_b64":"J/abJPYrOHsFkJr9kBQ4AlscCzPHzA84334tsZk+PF6mlmY1AbrOL+IJWWWgw3ua81fKUNLdoyOY+Gnx2gZmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e5da03b6f27b0cf9dfec6ab37214ee14f8bb1120222e7d2391a923121ce0e4","last_reissued_at":"2026-05-18T03:53:18.179298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:18.179298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramsey Theory, Integer Partitions and a New Proof of the Erdos-Szekeres Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Shapira, Guy Moshkovitz","submitted_at":"2012-06-18T17:43:40Z","abstract_excerpt":"Let H be a k-uniform hypergraph whose vertices are the integers 1,...,N. 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