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In particular, this implies $\\lim_{n \\rightarrow \\infty} \\frac{\\tilde{r}(P_k, P_n)}{n} = \\frac{5}{3}$, whenever $10 \\le k=o(n)$, disproving a conjecture by Cyman, Dzido, Lapinskas and Lo."},"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":"2312.16628","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-12-27T16:26:46Z","cross_cats_sorted":[],"title_canon_sha256":"f3c1bd860d69d341a0515088311d606a8095539ad8e5d3486e3819639bfdfaf3","abstract_canon_sha256":"4a5c3ec8d7bb64e03035b35531f0a37c73285e547b04ed4866edca6ef600a49f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:54:06.061421Z","signature_b64":"Uz55ABe6gXmnhxeQll3IgWZMeaHL/VFTMRuLNGL883yMos69mPUPeJpJKVMncXl6QMdOCtW0MKlej2LYweYzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"291ce6c09a86364dd63d44d9700b13393c05ce6d8b8fad3a26808631bba6aac1","last_reissued_at":"2026-07-05T08:54:06.060912Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:54:06.060912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The asymptotic of off-diagonal online Ramsey numbers for paths","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adva Mond, Julien Portier","submitted_at":"2023-12-27T16:26:46Z","abstract_excerpt":"We prove that for every $k\\ge 10$, the online Ramsey number for paths $P_k$ and $P_n$ satisfies $\\tilde{r}(P_k,P_n) \\geq \\frac{5}{3}n + \\frac{k}{9} - 4$, matching up to a linear term in $k$ the upper bound recently obtained by Bednarska-Bzd{\\k{e}}ga. 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