{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LAA75EDPLU4O4HBO4FWF7A4VWX","short_pith_number":"pith:LAA75EDP","schema_version":"1.0","canonical_sha256":"5801fe906f5d38ee1c2ee16c5f8395b5c65dfb2234dee53b2b8a1b77ec39e66a","source":{"kind":"arxiv","id":"2507.05641","version":2},"attestation_state":"computed","paper":{"title":"Off-Diagonal Ramsey Numbers for Linear Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hung-Hsun Hans Yu, Jiaxi Nie, Xiaoyu He, Yuval Wigderson","submitted_at":"2025-07-08T03:38:01Z","abstract_excerpt":"We study off-diagonal Ramsey numbers $r(H, K_n^{(k)})$ of $k$-uniform hypergraphs, where $H$ is a fixed linear $k$-uniform hypergraph and $K_n^{(k)}$ is complete on $n$ vertices. Recently, Conlon et al.\\ disproved the folklore conjecture that $r(H, K_n^{(3)})$ always grows polynomially in $n$. In this paper we show that much larger growth rates are possible in higher uniformity. In uniformity $k\\ge 4$, we prove that for any constant $C>0$, there exists a linear $k$-uniform hypergraph $H$ for which $$r(H,K_n^{(k)}) \\geq \\textup{twr}_{k-2}(2^{(\\log n)^C}).$$"},"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":"2507.05641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-08T03:38:01Z","cross_cats_sorted":[],"title_canon_sha256":"e075ef0540bed4243f406b0dbb6ee7a1dd275a5faaece6321a2bb5d379b89d80","abstract_canon_sha256":"35870cedbe1ba05f7e6d12cef8cf36049a7c1407e0a4158b8ca749a69f046fb8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:11.851848Z","signature_b64":"jlf3eCV6hqVk8T7IJUXojRXbCSPzqziaQvsqvVV6oP3QjNj5KB/uYU91OMqJB+OEb4g5dX1pzWP7DRYdF8LqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5801fe906f5d38ee1c2ee16c5f8395b5c65dfb2234dee53b2b8a1b77ec39e66a","last_reissued_at":"2026-07-05T11:34:11.851368Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:11.851368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Off-Diagonal Ramsey Numbers for Linear Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hung-Hsun Hans Yu, Jiaxi Nie, Xiaoyu He, Yuval Wigderson","submitted_at":"2025-07-08T03:38:01Z","abstract_excerpt":"We study off-diagonal Ramsey numbers $r(H, K_n^{(k)})$ of $k$-uniform hypergraphs, where $H$ is a fixed linear $k$-uniform hypergraph and $K_n^{(k)}$ is complete on $n$ vertices. Recently, Conlon et al.\\ disproved the folklore conjecture that $r(H, K_n^{(3)})$ always grows polynomially in $n$. In this paper we show that much larger growth rates are possible in higher uniformity. In uniformity $k\\ge 4$, we prove that for any constant $C>0$, there exists a linear $k$-uniform hypergraph $H$ for which $$r(H,K_n^{(k)}) \\geq \\textup{twr}_{k-2}(2^{(\\log n)^C}).$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05641","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/2507.05641/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":"2507.05641","created_at":"2026-07-05T11:34:11.851428+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.05641v2","created_at":"2026-07-05T11:34:11.851428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05641","created_at":"2026-07-05T11:34:11.851428+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAA75EDPLU4O","created_at":"2026-07-05T11:34:11.851428+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAA75EDPLU4O4HBO","created_at":"2026-07-05T11:34:11.851428+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAA75EDP","created_at":"2026-07-05T11:34:11.851428+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/LAA75EDPLU4O4HBO4FWF7A4VWX","json":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX.json","graph_json":"https://pith.science/api/pith-number/LAA75EDPLU4O4HBO4FWF7A4VWX/graph.json","events_json":"https://pith.science/api/pith-number/LAA75EDPLU4O4HBO4FWF7A4VWX/events.json","paper":"https://pith.science/paper/LAA75EDP"},"agent_actions":{"view_html":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX","download_json":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX.json","view_paper":"https://pith.science/paper/LAA75EDP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.05641&json=true","fetch_graph":"https://pith.science/api/pith-number/LAA75EDPLU4O4HBO4FWF7A4VWX/graph.json","fetch_events":"https://pith.science/api/pith-number/LAA75EDPLU4O4HBO4FWF7A4VWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX/action/storage_attestation","attest_author":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX/action/author_attestation","sign_citation":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX/action/citation_signature","submit_replication":"https://pith.science/pith/LAA75EDPLU4O4HBO4FWF7A4VWX/action/replication_record"}},"created_at":"2026-07-05T11:34:11.851428+00:00","updated_at":"2026-07-05T11:34:11.851428+00:00"}