{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TN3YG3VDATI7NVDDENM5VWJE6V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a3a3d19899095f144ffc016c4401d4d1213cbb996eb755b4f0ca65008eb08eda","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T07:48:14Z","title_canon_sha256":"66f300fd20e34777f94b036bedb7104c1868c383dd7242a51baf893c5946ac19"},"schema_version":"1.0","source":{"id":"2605.22116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22116","created_at":"2026-05-22T01:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22116v1","created_at":"2026-05-22T01:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22116","created_at":"2026-05-22T01:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"TN3YG3VDATI7","created_at":"2026-05-22T01:04:26Z"},{"alias_kind":"pith_short_16","alias_value":"TN3YG3VDATI7NVDD","created_at":"2026-05-22T01:04:26Z"},{"alias_kind":"pith_short_8","alias_value":"TN3YG3VD","created_at":"2026-05-22T01:04:26Z"}],"graph_snapshots":[{"event_id":"sha256:c83ade7c7ee3b9ed8869a17136186ef5979e49b4ca54dc29d1f4661060c61e91","target":"graph","created_at":"2026-05-22T01:04:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.22116/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Ramsey number $\\mathrm{R}(G_1,G_2)$ is the smallest integer $N$ such that any red-blue coloring of the edges of the complete graph $K_N$ contains either a red copy of $G_1$ or a blue copy of $G_2$. In 2022, the third author and others gave lower and upper bounds of the Ramsey number $\\mathrm{R}(W_n,W_n)$, where $W_n$ is the wheel graph with $n$ vertices. In this paper, we improve their bounds by showing that $3n-2\\leq \\mathrm{R}(W_n,W_n)\\leq 6n-6$ for even $n\\geq 8$ and $2n\\leq \\mathrm{R}(W_n,W_n)\\leq \\frac{9n-7}{2}$ for odd $n\\geq 7$. Furthermore, we give recursive bounds for the $k$-colo","authors_text":"Maoxuan Li, Masaki Kashima, Yaping Mao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T07:48:14Z","title":"Diagonal Ramsey numbers for wheels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22116","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9b994b7952029bf8a0ced218fc9e4d4f9205181be038ca50eb73a211d5608977","target":"record","created_at":"2026-05-22T01:04:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a3a3d19899095f144ffc016c4401d4d1213cbb996eb755b4f0ca65008eb08eda","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T07:48:14Z","title_canon_sha256":"66f300fd20e34777f94b036bedb7104c1868c383dd7242a51baf893c5946ac19"},"schema_version":"1.0","source":{"id":"2605.22116","kind":"arxiv","version":1}},"canonical_sha256":"9b77836ea304d1f6d4632359dad924f55f282e3533fd8d32022f9f3fcd8a9a00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b77836ea304d1f6d4632359dad924f55f282e3533fd8d32022f9f3fcd8a9a00","first_computed_at":"2026-05-22T01:04:26.668530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:26.668530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1nO46zW/elL1IcYxG9/k78/J7fWeP/3PIJlBevJ0AH/QZUV5YEtFt0noTWcjnWpg3TIgssHoqQsjqlDsBfydDg==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:26.669256Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b994b7952029bf8a0ced218fc9e4d4f9205181be038ca50eb73a211d5608977","sha256:c83ade7c7ee3b9ed8869a17136186ef5979e49b4ca54dc29d1f4661060c61e91"],"state_sha256":"965c46e900dd079bb60216c10abed99bff964e802a0885bb6c8f9a5397bdaa9e"}