{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARHTHCWYWHJWHRJRF6N7CHREVA","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":"26e305cd5f0978caa1fe750bfc7cca675fb6cf2fb22cf616e20ea08348ba5ff8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T12:02:15Z","title_canon_sha256":"9bd87be7b0315c1ec3fd65d3437951e542a8a250d17ef2bb155d468b07482630"},"schema_version":"1.0","source":{"id":"2606.02135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02135","created_at":"2026-06-02T02:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02135v1","created_at":"2026-06-02T02:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02135","created_at":"2026-06-02T02:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"ARHTHCWYWHJW","created_at":"2026-06-02T02:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"ARHTHCWYWHJWHRJR","created_at":"2026-06-02T02:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"ARHTHCWY","created_at":"2026-06-02T02:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:833febd83a3d90c9615f344cc8ab1e4920dd3444d38b893fa7bb47094a5f3a3b","target":"graph","created_at":"2026-06-02T02:05:07Z","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/2606.02135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We exhibit, in a systematic way, connections between hypergraph Tur\\'an problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Tur\\'an densities reduce to classical problems in extremal set theory, including the Erd\\H{o}s--Ko--Rado theorem, $L$-intersecting families, and the Erd\\H{o}s matching problem.","authors_text":"Ningyuan Yang, Tianming Zhu, Xizhi Liu, Yaobin Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T12:02:15Z","title":"Upper Bounds on Tur\\'an Densities via Extremal Set Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02135","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:cc125468a0b20d19b2bb6749d7965e5db086909138a23a686c8355806036d502","target":"record","created_at":"2026-06-02T02:05:07Z","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":"26e305cd5f0978caa1fe750bfc7cca675fb6cf2fb22cf616e20ea08348ba5ff8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T12:02:15Z","title_canon_sha256":"9bd87be7b0315c1ec3fd65d3437951e542a8a250d17ef2bb155d468b07482630"},"schema_version":"1.0","source":{"id":"2606.02135","kind":"arxiv","version":1}},"canonical_sha256":"044f338ad8b1d363c5312f9bf11e24a811afcf2caaeba8df16ee5f8ecf491a30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"044f338ad8b1d363c5312f9bf11e24a811afcf2caaeba8df16ee5f8ecf491a30","first_computed_at":"2026-06-02T02:05:07.442010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:05:07.442010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8CiZmVHjtZg1Lj1wGbJ5IvqpgNvz52MSy4UcxFRvJrngGsN3lhEOt8xFD510B5AbEYiQwNeeUG1/Nwwud1p2Dw==","signature_status":"signed_v1","signed_at":"2026-06-02T02:05:07.442431Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc125468a0b20d19b2bb6749d7965e5db086909138a23a686c8355806036d502","sha256:833febd83a3d90c9615f344cc8ab1e4920dd3444d38b893fa7bb47094a5f3a3b"],"state_sha256":"5f136b29464fe307896cef8c510f759a85bee3a6bb8053b76806fcc6fc51dd89"}