{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SAKCNZEJLDATVXDIDT5BXYPCI6","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":"d6b34d4c01c9e334f00493b1a503107098d59c0085d3366b783af3c6d987696b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-24T17:14:33Z","title_canon_sha256":"7f9df1d1ecfff352965fc7076e4255f0bb3981def85c6b6ed34c6ce87b945e65"},"schema_version":"1.0","source":{"id":"1607.07068","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07068","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07068v2","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07068","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"SAKCNZEJLDAT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SAKCNZEJLDATVXDI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SAKCNZEJ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:2665d7a8b44e555af80e4e9fc75e05dcc2dd7b813c644deba0f11b974b054a6e","target":"graph","created_at":"2026-05-17T23:52:19Z","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":"For a $k$-uniform hypergraph $F$ let $\\textrm{ex}(n,F)$ be the maximum number of edges of a $k$-uniform $n$-vertex hypergraph $H$ which contains no copy of $F$. Determining or estimating $\\textrm{ex}(n,F)$ is a classical and central problem in extremal combinatorics. While for $k=2$ this problem is well understood, due to the work of Tur\\'an and of Erd\\H{o}s and Stone, only very little is known for $k$-uniform hypergraphs for $k>2$. We focus on the case when $F$ is a $k$-uniform hypergraph with three edges on $k+1$ vertices. Already this very innocent (and maybe somewhat particular looking) pr","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":"2016-07-24T17:14:33Z","title":"On a generalisation of Mantel's theorem to uniformly dense hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07068","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":"sha256:5353cc67f4c319d98adadd52316c4be40c2e67637049041fdd536d81ffb1b2c3","target":"record","created_at":"2026-05-17T23:52:19Z","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":"d6b34d4c01c9e334f00493b1a503107098d59c0085d3366b783af3c6d987696b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-24T17:14:33Z","title_canon_sha256":"7f9df1d1ecfff352965fc7076e4255f0bb3981def85c6b6ed34c6ce87b945e65"},"schema_version":"1.0","source":{"id":"1607.07068","kind":"arxiv","version":2}},"canonical_sha256":"901426e48958c13adc681cfa1be1e2478436f29f7bcd50f8baeff034ed89cbd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"901426e48958c13adc681cfa1be1e2478436f29f7bcd50f8baeff034ed89cbd2","first_computed_at":"2026-05-17T23:52:19.183667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:19.183667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oZL/6p1hC4GL8OnzuoTcnPdpNbgBx5WL/PsMMbWhGbqMe3P1Yhvblghw14yhBhjb79nP4ch+txdsQAW8bnO/DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:19.184337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07068","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5353cc67f4c319d98adadd52316c4be40c2e67637049041fdd536d81ffb1b2c3","sha256:2665d7a8b44e555af80e4e9fc75e05dcc2dd7b813c644deba0f11b974b054a6e"],"state_sha256":"1e476fa7b2072ea28ad0d620a22c53683d11cec33d113fa183a1e274559f52f1"}