{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:O2WAAIALZV7M7XYQVBPCHQY2MS","short_pith_number":"pith:O2WAAIAL","schema_version":"1.0","canonical_sha256":"76ac00200bcd7ecfdf10a85e23c31a649d909757d271a0fc5a65c7ea19b19892","source":{"kind":"arxiv","id":"2209.05147","version":2},"attestation_state":"computed","paper":{"title":"A new upper bound on the minimum degree of minimal Ramsey graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anurag Bishnoi, Thomas Lesgourgues","submitted_at":"2022-09-12T11:06:15Z","abstract_excerpt":"We prove that $s_r(K_{k+1}) = O(k^3 r^3 \\log^3 k)$, where $s_r(K_k)$ is the Ramsey parameter introduced by Burr, Erd\\H{o}s and Lov\\'{a}sz in 1976, which is defined as the smallest minimum degree of a graph $G$ such that any $r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no proper subgraph of $G$ has this property."},"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":"2209.05147","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-09-12T11:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"f31a8a0b8c0c88ec3dc3a83aaa705f2738dee1d5c80b860cf91c124477f47e4c","abstract_canon_sha256":"9f1ae0ce658fd85c394bd9d933332ee5f78e7fcf50490614b334d0c3c3de5693"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:42:20.363838Z","signature_b64":"69UwwAJ0/pYTlXcs6KjIg6M6sxu4ULNAQag9ag7nMQ4BrNu9nF4X8Rxvwe0GiqdmaR92q9oWPPztGEmGS3MwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76ac00200bcd7ecfdf10a85e23c31a649d909757d271a0fc5a65c7ea19b19892","last_reissued_at":"2026-07-05T08:42:20.363388Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:42:20.363388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new upper bound on the minimum degree of minimal Ramsey graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anurag Bishnoi, Thomas Lesgourgues","submitted_at":"2022-09-12T11:06:15Z","abstract_excerpt":"We prove that $s_r(K_{k+1}) = O(k^3 r^3 \\log^3 k)$, where $s_r(K_k)$ is the Ramsey parameter introduced by Burr, Erd\\H{o}s and Lov\\'{a}sz in 1976, which is defined as the smallest minimum degree of a graph $G$ such that any $r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no proper subgraph of $G$ has this property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.05147","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.05147/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":"2209.05147","created_at":"2026-07-05T08:42:20.363445+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.05147v2","created_at":"2026-07-05T08:42:20.363445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.05147","created_at":"2026-07-05T08:42:20.363445+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2WAAIALZV7M","created_at":"2026-07-05T08:42:20.363445+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2WAAIALZV7M7XYQ","created_at":"2026-07-05T08:42:20.363445+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2WAAIAL","created_at":"2026-07-05T08:42:20.363445+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/O2WAAIALZV7M7XYQVBPCHQY2MS","json":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS.json","graph_json":"https://pith.science/api/pith-number/O2WAAIALZV7M7XYQVBPCHQY2MS/graph.json","events_json":"https://pith.science/api/pith-number/O2WAAIALZV7M7XYQVBPCHQY2MS/events.json","paper":"https://pith.science/paper/O2WAAIAL"},"agent_actions":{"view_html":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS","download_json":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS.json","view_paper":"https://pith.science/paper/O2WAAIAL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.05147&json=true","fetch_graph":"https://pith.science/api/pith-number/O2WAAIALZV7M7XYQVBPCHQY2MS/graph.json","fetch_events":"https://pith.science/api/pith-number/O2WAAIALZV7M7XYQVBPCHQY2MS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS/action/storage_attestation","attest_author":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS/action/author_attestation","sign_citation":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS/action/citation_signature","submit_replication":"https://pith.science/pith/O2WAAIALZV7M7XYQVBPCHQY2MS/action/replication_record"}},"created_at":"2026-07-05T08:42:20.363445+00:00","updated_at":"2026-07-05T08:42:20.363445+00:00"}