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In this note we disprove this conjecture even if $v$ is replaced by a vertex set of size $\\mathcal{O}(\\log{\\lvert V(G)\\rvert})$. As a consequence, we answer in the negative a question of Harutyunyan, Le, Thomass\\'{e}, and Wu concerning the corresponding statement where the graph $G$ is replaced by another tournament, and disprove a relate"},"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":"2305.15585","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-05-24T21:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"d57432d30e99174bd914515871ccf79d7e9161c6b63d26e03b50eb05bdd9f017","abstract_canon_sha256":"bf3bd21add1b23e88f1c9b9ffd16d11fc76798e113032172b81e4628933e393c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:19:45.358429Z","signature_b64":"i2Kwl+zB/hk7n5n+QPzFWFdcbUAiaRWLlA3u0/1V3na/wTMKjTLcYFCDwygtCheiCL7CkaS8S+6x3UG5ftL8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"015d88e0daad6e7127af130d9098d9feeb7e45e266014cceeda60406b02add5d","last_reissued_at":"2026-07-05T07:19:45.357880Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:19:45.357880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chromatic number is not tournament-local","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ant\\'onio Gir\\~ao, Florian Lehner, Freddie Illingworth, Kevin Hendrey, Lukas Michel, Michael Savery, Raphael Steiner","submitted_at":"2023-05-24T21:41:18Z","abstract_excerpt":"Scott and Seymour conjectured the existence of a function $f \\colon \\mathbb{N} \\to \\mathbb{N}$ such that, for every graph $G$ and tournament $T$ on the same vertex set, $\\chi(G) \\geqslant f(k)$ implies that $\\chi(G[N_T^+(v)]) \\geqslant k$ for some vertex $v$. 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As a consequence, we answer in the negative a question of Harutyunyan, Le, Thomass\\'{e}, and Wu concerning the corresponding statement where the graph $G$ is replaced by another tournament, and disprove a relate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15585","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/2305.15585/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":"2305.15585","created_at":"2026-07-05T07:19:45.357951+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.15585v2","created_at":"2026-07-05T07:19:45.357951+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.15585","created_at":"2026-07-05T07:19:45.357951+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFOYRYG2VVXH","created_at":"2026-07-05T07:19:45.357951+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFOYRYG2VVXHCJ5P","created_at":"2026-07-05T07:19:45.357951+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFOYRYG2","created_at":"2026-07-05T07:19:45.357951+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/AFOYRYG2VVXHCJ5PCMGZBGGZ73","json":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73.json","graph_json":"https://pith.science/api/pith-number/AFOYRYG2VVXHCJ5PCMGZBGGZ73/graph.json","events_json":"https://pith.science/api/pith-number/AFOYRYG2VVXHCJ5PCMGZBGGZ73/events.json","paper":"https://pith.science/paper/AFOYRYG2"},"agent_actions":{"view_html":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73","download_json":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73.json","view_paper":"https://pith.science/paper/AFOYRYG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.15585&json=true","fetch_graph":"https://pith.science/api/pith-number/AFOYRYG2VVXHCJ5PCMGZBGGZ73/graph.json","fetch_events":"https://pith.science/api/pith-number/AFOYRYG2VVXHCJ5PCMGZBGGZ73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73/action/storage_attestation","attest_author":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73/action/author_attestation","sign_citation":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73/action/citation_signature","submit_replication":"https://pith.science/pith/AFOYRYG2VVXHCJ5PCMGZBGGZ73/action/replication_record"}},"created_at":"2026-07-05T07:19:45.357951+00:00","updated_at":"2026-07-05T07:19:45.357951+00:00"}