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Each turn Builder picks an edge to build and Painter chooses whether that edge is red or blue, and Builder aims to create a red $K_m$ or blue $K_n$ in as few turns as possible. The restricted online Ramsey number $\\tilde{r}(m,n;N)$ is the minimum number of turns that Builder needs to guarantee her win in the restricted $(m,n;N)$-online Ramsey game. We show that if $N=r(n,n)$, \\[ \\tilde{r}(n,n;N)\\le \\binom{N}{2} - \\Omega(N\\log N), \\] motivated by a q"},"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":"1812.04131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-10T22:19:08Z","cross_cats_sorted":[],"title_canon_sha256":"934f4ec5a4d48db1fcb7898c481ea180daf15ad948bde3182984486b4f715144","abstract_canon_sha256":"81d6d5935c80bcc6c13e86b396dd13a7c55028a858833c30fc5c58ebc490e821"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:00.104136Z","signature_b64":"cj/mYx30UMc8A42LQyuyeA/5x+BH20dlDDa4JXSNZbxCoSNGhmB9CNI7puGj4+31IHEALwYnMrKbAuguUGyQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c14110adc594de0dea3d00ab65d9aa7df36fe4261b784f74ce720bb7547af31a","last_reissued_at":"2026-05-17T23:44:00.103546Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:00.103546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An upper bound for the restricted online Ramsey number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Gonzalez, Hanzhi Zheng, Xiaoyu He","submitted_at":"2018-12-10T22:19:08Z","abstract_excerpt":"The restricted $(m,n;N)$-online Ramsey game is a game played between two players, Builder and Painter. 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We show that if $N=r(n,n)$, \\[ \\tilde{r}(n,n;N)\\le \\binom{N}{2} - \\Omega(N\\log N), \\] motivated by a q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04131","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.04131","created_at":"2026-05-17T23:44:00.103634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04131v2","created_at":"2026-05-17T23:44:00.103634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04131","created_at":"2026-05-17T23:44:00.103634+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFARBLOFSTPA","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFARBLOFSTPA32R5","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFARBLOF","created_at":"2026-05-18T12:33:04.347982+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX","json":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX.json","graph_json":"https://pith.science/api/pith-number/YFARBLOFSTPA32R5ACVWLWNKPX/graph.json","events_json":"https://pith.science/api/pith-number/YFARBLOFSTPA32R5ACVWLWNKPX/events.json","paper":"https://pith.science/paper/YFARBLOF"},"agent_actions":{"view_html":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX","download_json":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX.json","view_paper":"https://pith.science/paper/YFARBLOF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04131&json=true","fetch_graph":"https://pith.science/api/pith-number/YFARBLOFSTPA32R5ACVWLWNKPX/graph.json","fetch_events":"https://pith.science/api/pith-number/YFARBLOFSTPA32R5ACVWLWNKPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX/action/storage_attestation","attest_author":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX/action/author_attestation","sign_citation":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX/action/citation_signature","submit_replication":"https://pith.science/pith/YFARBLOFSTPA32R5ACVWLWNKPX/action/replication_record"}},"created_at":"2026-05-17T23:44:00.103634+00:00","updated_at":"2026-05-17T23:44:00.103634+00:00"}