{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F7CXBOW7H57NB244PIDYICMLFA","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":"185a2be499372956d4a000e992279e932ad3dab4ec191746e3821a171e8cbab3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-03T23:15:54Z","title_canon_sha256":"d4835396c0a5f6e013023d41b82bc94cbe517d3365a0e62eab5f8a37daa82d1b"},"schema_version":"1.0","source":{"id":"1402.0544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0544","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0544v1","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0544","created_at":"2026-05-18T03:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"F7CXBOW7H57N","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F7CXBOW7H57NB244","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F7CXBOW7","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:4a16269d4fc1d5e733b14e91fd8d5cd06632a14d711b3a959d8d321b958da64b","target":"graph","created_at":"2026-05-18T03:00:14Z","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":"The expansion $G^+$ of a graph $G$ is the 3-uniform hypergraph obtained from $G$ by enlarging each edge of $G$ with a vertex disjoint from $V(G)$ such that distinct edges are enlarged by distinct vertices. Let ex$_r(n,F)$ denote the maximum number of edges in an $r$-uniform hypergraph with $n$ vertices not containing any copy of $F$. The authors \\cite{KMV} recently determined ex$_3(n,G^+)$ more generally, namely when $G$ is a path or cycle, thus settling conjectures of F\\\"uredi-Jiang \\cite{FJ} (for cycles) and F\\\"uredi-Jiang-Seiver \\cite{FJS} (for paths). Here we continue this project by deter","authors_text":"Alexandr Kostochka, Dhruv Mubayi, Jacques Verstraete","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-03T23:15:54Z","title":"Turan Problems and Shadows II: Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0544","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:fad23193ed387563e726d9aa6bdcbc12d275e24455b0f0ea0d92a86670a2c9af","target":"record","created_at":"2026-05-18T03:00:14Z","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":"185a2be499372956d4a000e992279e932ad3dab4ec191746e3821a171e8cbab3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-03T23:15:54Z","title_canon_sha256":"d4835396c0a5f6e013023d41b82bc94cbe517d3365a0e62eab5f8a37daa82d1b"},"schema_version":"1.0","source":{"id":"1402.0544","kind":"arxiv","version":1}},"canonical_sha256":"2fc570badf3f7ed0eb9c7a0784098b28238e73c17b205975fa3d1d4e59a3d829","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fc570badf3f7ed0eb9c7a0784098b28238e73c17b205975fa3d1d4e59a3d829","first_computed_at":"2026-05-18T03:00:14.039138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:14.039138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/DELVj5bI/wXeKs6jxUtOv3DuEwcL+s60cdu3cBiYPAfFlv4br3wzsG3yX6EUd7j/1eNtTj8SABJHNarPln+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:14.039901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fad23193ed387563e726d9aa6bdcbc12d275e24455b0f0ea0d92a86670a2c9af","sha256:4a16269d4fc1d5e733b14e91fd8d5cd06632a14d711b3a959d8d321b958da64b"],"state_sha256":"29201065498dcfa178abaa82bdf5275e007e034434bba61faa96fc0082559e18"}