{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DZVMDN57DB6VRIY3OEWYLCGQCQ","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":"20d247032bdb95f3e1d8900c69d350c712429615b9092e75be7ccfafbf3191ae","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T17:01:16Z","title_canon_sha256":"caa1c7daa1fa06b03b0f8785f0e044d7e55b9cbaa11b7eb80b6388e20d85576f"},"schema_version":"1.0","source":{"id":"2605.31546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31546","created_at":"2026-06-01T02:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31546v1","created_at":"2026-06-01T02:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31546","created_at":"2026-06-01T02:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"DZVMDN57DB6V","created_at":"2026-06-01T02:04:12Z"},{"alias_kind":"pith_short_16","alias_value":"DZVMDN57DB6VRIY3","created_at":"2026-06-01T02:04:12Z"},{"alias_kind":"pith_short_8","alias_value":"DZVMDN57","created_at":"2026-06-01T02:04:12Z"}],"graph_snapshots":[{"event_id":"sha256:d93f3d8bb33fc0c732d6055b4636f9b09063fa00cf9968399564eda141b2ab7b","target":"graph","created_at":"2026-06-01T02:04:12Z","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/2605.31546/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce weak and strong poset Ramsey-Tur\\'an numbers for $t$-chains in host poset families, focusing on the Boolean lattice family $\\mathcal{B}=\\{B_n:n\\ge 1\\}$. For any poset $P$, we show $\\operatorname{RT}(\\mathcal{B};n,P,l,t)\\le \\operatorname{RT}^{\\sharp}(\\mathcal{B};n,P,l,t)$, with equality when $P$ is a chain. In particular, for $t=1$, $\\operatorname{RT}(\\mathcal{B};n,C_k,l)=\\operatorname{RT}^{\\sharp}(\\mathcal{B};n,C_k,l)=(k-1)(l-1)$. We also give universal upper bounds for both versions. For fixed $k,l,t$ with $\\min\\{l-1,k-1\\}\\ge 1$, we prove $\\operatorname{RT}^{\\sharp}(\\mathcal{B};n","authors_text":"Gyula O.H. Katona, Yaping Mao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T17:01:16Z","title":"Ramsey-Tur\\'{a}n theory for partially-ordered sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31546","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:f5ffdef22b5044ea7b4cc52d720455e79f7bd8b109697248df393d1772d37141","target":"record","created_at":"2026-06-01T02:04:12Z","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":"20d247032bdb95f3e1d8900c69d350c712429615b9092e75be7ccfafbf3191ae","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T17:01:16Z","title_canon_sha256":"caa1c7daa1fa06b03b0f8785f0e044d7e55b9cbaa11b7eb80b6388e20d85576f"},"schema_version":"1.0","source":{"id":"2605.31546","kind":"arxiv","version":1}},"canonical_sha256":"1e6ac1b7bf187d58a31b712d8588d014286c0cfa35a1a87915eae8ce3e145fee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e6ac1b7bf187d58a31b712d8588d014286c0cfa35a1a87915eae8ce3e145fee","first_computed_at":"2026-06-01T02:04:12.067904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:04:12.067904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSu/GuHv0o5+ETstDf1J3LsYXH06qd9cE9afGikXps1zoUWiMaP7c2HpVgrPstwsN0pSF2a2L3Vvya1M4b52Dg==","signature_status":"signed_v1","signed_at":"2026-06-01T02:04:12.068761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5ffdef22b5044ea7b4cc52d720455e79f7bd8b109697248df393d1772d37141","sha256:d93f3d8bb33fc0c732d6055b4636f9b09063fa00cf9968399564eda141b2ab7b"],"state_sha256":"b73dd1f88fbc7124a80f1f90dfa57c619e1fb6a503cd9afbebfe112f2523e27b"}