{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:63NOKYXDOYFHJDXRE6HVSVDZ22","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":"1f849014122c51ea949dfe9f8002e912dd8953ec44336d9944a9ca5dfce97164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-06T18:49:40Z","title_canon_sha256":"d64db19d44eac088072dffb99feb6cc824ab5f95345ff31e029898ce988e69f1"},"schema_version":"1.0","source":{"id":"1602.02289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02289","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02289v2","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02289","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"63NOKYXDOYFH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"63NOKYXDOYFHJDXR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"63NOKYXD","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:fb682117390b502046d48a4a3892d635cc941787323f5eb81a3c98af1abedb64","target":"graph","created_at":"2026-05-18T01:04:28Z","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"},"paper":{"abstract_excerpt":"We investigate extremal problems for quasirandom hypergraphs. We say that a $3$-uniform hypergraph $H=(V,E)$ is $(d,\\eta)$-quasirandom if for any subset $X\\subseteq V$ and every set of pairs $P\\subseteq V\\times V$ the number of pairs $(x,(y,z))\\in X\\times P$ with $\\{x,y,z\\}$ being a hyperedge of $H$ is in the interval $d|X||P|\\pm\\eta|V|^3$. We show that for any $\\varepsilon>0$ there exists $\\eta>0$ such that every sufficiently large $(1/2+\\varepsilon,\\eta)$-quasirandom hypergraph contains a tetrahedron, i.e., four vertices spanning all four hyperedges. A known random construction shows that th","authors_text":"Christian Reiher, Mathias Schacht, Vojt\\v{e}ch R\\\"odl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-06T18:49:40Z","title":"Embedding tetrahedra into quasirandom hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02289","kind":"arxiv","version":2},"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":"sha256:80c6e68f7cbc464d24e1c6323994a0aa2290f47df8bf398d294cf432ec8ade76","target":"record","created_at":"2026-05-18T01:04:28Z","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":"1f849014122c51ea949dfe9f8002e912dd8953ec44336d9944a9ca5dfce97164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-06T18:49:40Z","title_canon_sha256":"d64db19d44eac088072dffb99feb6cc824ab5f95345ff31e029898ce988e69f1"},"schema_version":"1.0","source":{"id":"1602.02289","kind":"arxiv","version":2}},"canonical_sha256":"f6dae562e3760a748ef1278f595479d6969c6b3ae3cdccbf7662a0d60da19870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6dae562e3760a748ef1278f595479d6969c6b3ae3cdccbf7662a0d60da19870","first_computed_at":"2026-05-18T01:04:28.105586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:28.105586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DPcxxP5+ZHFlvv0PkNXlvWmm30nqlLxDVoql0y7CPpuQQHNw4wf8KnR6JfV8Kw6n3bt/sL6ppjuTTBJx2wkPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:28.106336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80c6e68f7cbc464d24e1c6323994a0aa2290f47df8bf398d294cf432ec8ade76","sha256:fb682117390b502046d48a4a3892d635cc941787323f5eb81a3c98af1abedb64"],"state_sha256":"f02e689a753459bc14f078889219ed3706f2bf7e4291e1c518c927d78145458a"}