{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:D5L7KBJTBA5MI24J27IP4KPG6T","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":"bd7916f4c8e82d8965789af76047746396e361ca30ea4db86590e875a7a1f7e7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-19T17:18:29Z","title_canon_sha256":"045eddb8f1b318fb86467e5b9a07d419952709f96d0419b68fc9c144f6ab12a3"},"schema_version":"1.0","source":{"id":"2505.13371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13371","created_at":"2026-07-05T11:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13371v1","created_at":"2026-07-05T11:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13371","created_at":"2026-07-05T11:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"D5L7KBJTBA5M","created_at":"2026-07-05T11:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"D5L7KBJTBA5MI24J","created_at":"2026-07-05T11:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"D5L7KBJT","created_at":"2026-07-05T11:05:29Z"}],"graph_snapshots":[{"event_id":"sha256:7458cd879d6d1a306b3a97c4651ced3cb8df38fe8a2f1fb7096e48edd07db792","target":"graph","created_at":"2026-07-05T11:05:29Z","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/2505.13371/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a new lower bound for the off-diagonal Ramsey numbers, \\[ R(3,k) \\geq \\bigg( \\frac{1}{3}+ o(1) \\bigg) \\frac{k^2}{\\log k }\\, , \\] thereby narrowing the gap between the upper and lower bounds to a factor of $3+o(1)$. This improves the best known lower bound of $(1/4+o(1))k^2/\\log k$ due, independently, to Bohman and Keevash, and Fiz Pontiveros, Griffiths and Morris, resulting from their celebrated analysis of the triangle-free process. As a consequence, we disprove a conjecture of Fiz Pontiveros, Griffiths and Morris that the constant $1/4$ is sharp.","authors_text":"Julian Sahasrabudhe, Marcelo Campos, Marcus Michelen, Matthew Jenssen","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-19T17:18:29Z","title":"A new lower bound for the Ramsey numbers $R(3,k)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13371","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:e507b15f6a846bc7ef411cc0e6ec737521c1f04296ab5984b61e60c1f211b76b","target":"record","created_at":"2026-07-05T11:05:29Z","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":"bd7916f4c8e82d8965789af76047746396e361ca30ea4db86590e875a7a1f7e7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-19T17:18:29Z","title_canon_sha256":"045eddb8f1b318fb86467e5b9a07d419952709f96d0419b68fc9c144f6ab12a3"},"schema_version":"1.0","source":{"id":"2505.13371","kind":"arxiv","version":1}},"canonical_sha256":"1f57f50533083ac46b89d7d0fe29e6f4d060f04178e07138af45625b562850c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f57f50533083ac46b89d7d0fe29e6f4d060f04178e07138af45625b562850c1","first_computed_at":"2026-07-05T11:05:29.080131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:29.080131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q0N1uuXVpwnKMN7sSyofGKhcX1Jp/MDyyuV2Xd7dbyqxeg2iXEh/J/MooFK6s+QXQeFESsnmwnqWsI/GMaOhCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:29.080612Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e507b15f6a846bc7ef411cc0e6ec737521c1f04296ab5984b61e60c1f211b76b","sha256:7458cd879d6d1a306b3a97c4651ced3cb8df38fe8a2f1fb7096e48edd07db792"],"state_sha256":"006bb7597b979460cc7dc015a1523a22dd73eff04a2e6d4d283422202723e197"}