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They showed that if $H$ is a fixed $r$-uniform hypergraph that is not $r$-partite and the number of colors $k$ goes to infinity, $e^{\\Omega(\\sqrt{k})} \\le R_{\\ell} (H,k) \\le e^{O(k)}$. We prove that $R_{\\ell}(H,k) = e^{\\Theta(k)}$ if and only if $H$ is not $r$-partite."},"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":"2103.15175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-03-28T16:58:00Z","cross_cats_sorted":[],"title_canon_sha256":"f25d97c2a92db9d774b666d8b333e49bf3a82c10f1bec0cb47d91749d5835154","abstract_canon_sha256":"acf2033675584932822f3d422c996ef32d403a0581ce70452d0d79bc6206c74d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:50:48.166846Z","signature_b64":"9ApqlIeYdRUel3sgGTe5M6+cbkaREz9Xf08MjbQWoGG2w5Ep8RsmLAYJQlOFe++DjSHxJvDNPqP46QZw8SYDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8ef9b3421c9dc474cc7707a7f069b697a5c02ec14f654317d053b260a25a0ce","last_reissued_at":"2026-07-05T03:50:48.166285Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:50:48.166285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multicolor list Ramsey numbers grow exponentially","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jacob Fox, Max Wenqiang Xu, Sammy Luo, Xiaoyu He","submitted_at":"2021-03-28T16:58:00Z","abstract_excerpt":"The list Ramsey number $R_{\\ell}(H,k)$, recently introduced by Alon, Buci\\'c, Kalvari, Kuperwasser, and Szab\\'o, is a list-coloring variant of the classical Ramsey number. They showed that if $H$ is a fixed $r$-uniform hypergraph that is not $r$-partite and the number of colors $k$ goes to infinity, $e^{\\Omega(\\sqrt{k})} \\le R_{\\ell} (H,k) \\le e^{O(k)}$. 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