{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FYFJTMOFDSNOFCRYZMFAPPZQKL","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":"fbb93e8dbdd3b964aa80ad097ef80ea0b5ef01ee543948457b8dcec95e14cf57","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-15T17:46:59Z","title_canon_sha256":"3c64d41d940502615f8f9bce50e2c5f51c85d2195235d7eb8ee44bc908279cb1"},"schema_version":"1.0","source":{"id":"1902.05903","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05903","created_at":"2026-07-05T00:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05903v4","created_at":"2026-07-05T00:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05903","created_at":"2026-07-05T00:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"FYFJTMOFDSNO","created_at":"2026-07-05T00:53:05Z"},{"alias_kind":"pith_short_16","alias_value":"FYFJTMOFDSNOFCRY","created_at":"2026-07-05T00:53:05Z"},{"alias_kind":"pith_short_8","alias_value":"FYFJTMOF","created_at":"2026-07-05T00:53:05Z"}],"graph_snapshots":[{"event_id":"sha256:df6d2687a3186e239383466bb0fea24ca090247b1556c1bd517a0b76af78ea6e","target":"graph","created_at":"2026-07-05T00:53:05Z","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/1902.05903/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For fixed integers $r\\ge 3,e\\ge 3,v\\ge r+1$, an $r$-uniform hypergraph is called $\\mathscr{G}_r(v,e)$-free if the union of any $e$ distinct edges contains at least $v+1$ vertices.\n  Brown, Erd\\H{o}s and S\\'{o}s showed that the maximum number of edges of such a hypergraph on $n$ vertices, denoted as $f_r(n,v,e)$, satisfies\n  $$\\Omega(n^{\\frac{er-v}{e-1}})=f_r(n,v,e)=\\mathcal{O}(n^{\\lceil\\frac{er-v}{e-1}\\rceil}).$$\n  For $e-1\\mid er-v$, the lower bound matches the upper bound up to a constant factor; whereas for $e-1\\nmid er-v$, in general it is a notoriously hard problem to determine the correc","authors_text":"Chong Shangguan, Itzhak Tamo","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-15T17:46:59Z","title":"Sparse Hypergraphs with Applications to Coding Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05903","kind":"arxiv","version":4},"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:b20268c698a09a4c8177cac31b21c33eafc2c9a356ada3e11d2b6daf5ca948b8","target":"record","created_at":"2026-07-05T00:53:05Z","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":"fbb93e8dbdd3b964aa80ad097ef80ea0b5ef01ee543948457b8dcec95e14cf57","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-15T17:46:59Z","title_canon_sha256":"3c64d41d940502615f8f9bce50e2c5f51c85d2195235d7eb8ee44bc908279cb1"},"schema_version":"1.0","source":{"id":"1902.05903","kind":"arxiv","version":4}},"canonical_sha256":"2e0a99b1c51c9ae28a38cb0a07bf3052c30182832749441087770996539bf70c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e0a99b1c51c9ae28a38cb0a07bf3052c30182832749441087770996539bf70c","first_computed_at":"2026-07-05T00:53:05.335119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:53:05.335119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkZW7CmGcE1kjYYXOWACc8Fbp7YSX+THM3Yl5MRSI0N56o0BqE1b6j9V9BbxqHzBrZYga2a1YLDstRETUYJ3Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:53:05.335620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05903","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b20268c698a09a4c8177cac31b21c33eafc2c9a356ada3e11d2b6daf5ca948b8","sha256:df6d2687a3186e239383466bb0fea24ca090247b1556c1bd517a0b76af78ea6e"],"state_sha256":"095c99bceed26365c775df158475a380a78405cad7d2c254a5b9978c02f3eadc"}