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When $F_1=\\dots=F_s=F$, we write $\\mathcal{R}(F;s)=\\mathcal{R}(F_1,\\dots,F_s)$.\n  In this paper, we investigate when $\\mathcal{R}(H;s)\\subseteq\\mathcal{R}(Q_1,\\dots,Q_t)$ holds, where $H=H^{(r)}(n,p)$ is a random $r$-graph and $Q_1,\\dots,Q_t$ are fixed $r$-graphs. Our main result "},"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":"2605.28472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T13:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"136c516b5a091bc9d9935478ab7419dc324c996a88ddc0942a49433206f51aee","abstract_canon_sha256":"79126f23ff001172fb1699f2bb51b086fa66fc45a35b01de1e6f833fa41344a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:53.986950Z","signature_b64":"tSkROJv5tXK6W193b8qC2INNG+TGEGK35TQhtOwtM6E3G8E2GzoISVOCbblxAoVqn4guSW1oPRp9HFTR48ctAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b647c1e447468a4ab4821f4ef4a8d63556adf684f1783a680941fa026e635b6e","last_reissued_at":"2026-05-28T02:04:53.986520Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:53.986520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ramsey classes of random hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dingyuan Liu","submitted_at":"2026-05-27T13:37:27Z","abstract_excerpt":"Let $r,s,t\\geq2$ be integers. For $r$-graphs $G$ and $F_1,\\dots,F_s$, we write $G\\to(F_1,\\dots,F_s)$ if every $s$-edge-coloring of $G$ yields a monochromatic copy of $F_i$ in the $i$-th color for some $1\\leq i\\leq s$. Let $\\mathcal{R}(F_1,\\dots,F_s)$ denote the family of all $r$-graphs $G$ with $G\\to(F_1,\\dots,F_s)$. When $F_1=\\dots=F_s=F$, we write $\\mathcal{R}(F;s)=\\mathcal{R}(F_1,\\dots,F_s)$.\n  In this paper, we investigate when $\\mathcal{R}(H;s)\\subseteq\\mathcal{R}(Q_1,\\dots,Q_t)$ holds, where $H=H^{(r)}(n,p)$ is a random $r$-graph and $Q_1,\\dots,Q_t$ are fixed $r$-graphs. Our main result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28472","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/2605.28472/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":"2605.28472","created_at":"2026-05-28T02:04:53.986577+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.28472v1","created_at":"2026-05-28T02:04:53.986577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28472","created_at":"2026-05-28T02:04:53.986577+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZD4DZCHI2FE","created_at":"2026-05-28T02:04:53.986577+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZD4DZCHI2FEVNEC","created_at":"2026-05-28T02:04:53.986577+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZD4DZCH","created_at":"2026-05-28T02:04:53.986577+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/WZD4DZCHI2FEVNECD5HPJKGWGV","json":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV.json","graph_json":"https://pith.science/api/pith-number/WZD4DZCHI2FEVNECD5HPJKGWGV/graph.json","events_json":"https://pith.science/api/pith-number/WZD4DZCHI2FEVNECD5HPJKGWGV/events.json","paper":"https://pith.science/paper/WZD4DZCH"},"agent_actions":{"view_html":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV","download_json":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV.json","view_paper":"https://pith.science/paper/WZD4DZCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.28472&json=true","fetch_graph":"https://pith.science/api/pith-number/WZD4DZCHI2FEVNECD5HPJKGWGV/graph.json","fetch_events":"https://pith.science/api/pith-number/WZD4DZCHI2FEVNECD5HPJKGWGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV/action/storage_attestation","attest_author":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV/action/author_attestation","sign_citation":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV/action/citation_signature","submit_replication":"https://pith.science/pith/WZD4DZCHI2FEVNECD5HPJKGWGV/action/replication_record"}},"created_at":"2026-05-28T02:04:53.986577+00:00","updated_at":"2026-05-28T02:04:53.986577+00:00"}