{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ORRNK73RSGZK7ASXHUYNPAYQXK","short_pith_number":"pith:ORRNK73R","schema_version":"1.0","canonical_sha256":"7462d57f7191b2af82573d30d78310babb1600931c82ae25da0230da7df73d0c","source":{"kind":"arxiv","id":"2608.01962","version":1},"attestation_state":"computed","paper":{"title":"New upper bound for multicolor Ramsey numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gang Yang, Yaping Mao","submitted_at":"2026-08-03T09:30:23Z","abstract_excerpt":"Let $R_r(k)$ denote the diagonal $r$-color graph Ramsey number. We prove that there exist absolute constants $c,K>0$ such that \\[\n  R_r(k)\\le\n  \\exp\\!\\left(-c\\frac{k}{r^2\\log^4(2r)}\\right)r^{rk} \\] for every $r\\ge2$ and every $k\\ge Kr^2\\log^6(2r)$. The proof combines a positive-coefficient root filter of variable order with a retained-spine refinement of the multicolor book method.b"},"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":"2608.01962","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-08-03T09:30:23Z","cross_cats_sorted":[],"title_canon_sha256":"503b630d7093fa122effcfab9203b5d9d38b6819605c8bc81615c4e659a883ef","abstract_canon_sha256":"e3cf3eb710c694690472d6cd8e140dcd95997c03ef3272c36a771c9a0ba1bfa2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:10:16.103502Z","signature_b64":"1cJpwDlJzLH2gteh1QOyDl3GSQ7vm7I+o/CsOwE8Pu+R5CoqmmWwKkg0xgG7LHmIUgcO7h7i+DgIFC2EmxK/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7462d57f7191b2af82573d30d78310babb1600931c82ae25da0230da7df73d0c","last_reissued_at":"2026-08-04T02:10:16.101751Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:10:16.101751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New upper bound for multicolor Ramsey numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gang Yang, Yaping Mao","submitted_at":"2026-08-03T09:30:23Z","abstract_excerpt":"Let $R_r(k)$ denote the diagonal $r$-color graph Ramsey number. We prove that there exist absolute constants $c,K>0$ such that \\[\n  R_r(k)\\le\n  \\exp\\!\\left(-c\\frac{k}{r^2\\log^4(2r)}\\right)r^{rk} \\] for every $r\\ge2$ and every $k\\ge Kr^2\\log^6(2r)$. The proof combines a positive-coefficient root filter of variable order with a retained-spine refinement of the multicolor book method.b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01962","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.01962/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.01962","created_at":"2026-08-04T02:10:16.103314+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.01962v1","created_at":"2026-08-04T02:10:16.103314+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01962","created_at":"2026-08-04T02:10:16.103314+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORRNK73RSGZK","created_at":"2026-08-04T02:10:16.103314+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORRNK73RSGZK7ASX","created_at":"2026-08-04T02:10:16.103314+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORRNK73R","created_at":"2026-08-04T02:10:16.103314+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/ORRNK73RSGZK7ASXHUYNPAYQXK","json":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK.json","graph_json":"https://pith.science/api/pith-number/ORRNK73RSGZK7ASXHUYNPAYQXK/graph.json","events_json":"https://pith.science/api/pith-number/ORRNK73RSGZK7ASXHUYNPAYQXK/events.json","paper":"https://pith.science/paper/ORRNK73R"},"agent_actions":{"view_html":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK","download_json":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK.json","view_paper":"https://pith.science/paper/ORRNK73R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.01962&json=true","fetch_graph":"https://pith.science/api/pith-number/ORRNK73RSGZK7ASXHUYNPAYQXK/graph.json","fetch_events":"https://pith.science/api/pith-number/ORRNK73RSGZK7ASXHUYNPAYQXK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK/action/storage_attestation","attest_author":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK/action/author_attestation","sign_citation":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK/action/citation_signature","submit_replication":"https://pith.science/pith/ORRNK73RSGZK7ASXHUYNPAYQXK/action/replication_record"}},"created_at":"2026-08-04T02:10:16.103314+00:00","updated_at":"2026-08-04T02:10:16.103314+00:00"}