{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:G2HFUD3SL6XN2QBJ4EOHM3WR35","short_pith_number":"pith:G2HFUD3S","schema_version":"1.0","canonical_sha256":"368e5a0f725faedd4029e11c766ed1df56f577ba6ba439dd933adcbdedf551ef","source":{"kind":"arxiv","id":"1902.07614","version":2},"attestation_state":"computed","paper":{"title":"Proof of the Brown-Erd\\H{o}s-S\\'os conjecture in groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Mykhaylo Tyomkyn, Rajko Nenadov","submitted_at":"2019-02-20T16:02:05Z","abstract_excerpt":"The conjecture of Brown, Erd\\H{o}s and S\\'os from 1973 states that, for any $k \\ge 3$, if a $3$-uniform hypergraph $H$ with $n$ vertices does not contain a set of $k+3$ vertices spanning at least $k$ edges then it has $o(n^2)$ edges. The case $k=3$ of this conjecture is the celebrated $(6,3)$-theorem of Ruzsa and Szemer\\'edi which implies Roth's theorem on $3$-term arithmetic progressions in dense sets of integers. Solymosi observed that, in order to prove the conjecture, one can assume that $H$ consists of triples $(a, b, ab)$ of some finite quasigroup $\\Gamma$. Since this problem remains ope"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.07614","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-20T16:02:05Z","cross_cats_sorted":[],"title_canon_sha256":"1ef869ea1ce97cf6ba0caa6d32d3e152612091649738f798a2da8605f48ba898","abstract_canon_sha256":"34715ee8b07a802e504b24d6b5d9ad4daec9af8cd9b79b077d60241e1fef30b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:01.765805Z","signature_b64":"nvNpeK26CXOtCZBNNswBfIz9XPGKLQ3L3c47Ks8CxH9LO22B26MK0tUnd8njJyNkUDDOMtfwVhRl7wQd9JpwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"368e5a0f725faedd4029e11c766ed1df56f577ba6ba439dd933adcbdedf551ef","last_reissued_at":"2026-05-17T23:47:01.765000Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:01.765000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of the Brown-Erd\\H{o}s-S\\'os conjecture in groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Mykhaylo Tyomkyn, Rajko Nenadov","submitted_at":"2019-02-20T16:02:05Z","abstract_excerpt":"The conjecture of Brown, Erd\\H{o}s and S\\'os from 1973 states that, for any $k \\ge 3$, if a $3$-uniform hypergraph $H$ with $n$ vertices does not contain a set of $k+3$ vertices spanning at least $k$ edges then it has $o(n^2)$ edges. The case $k=3$ of this conjecture is the celebrated $(6,3)$-theorem of Ruzsa and Szemer\\'edi which implies Roth's theorem on $3$-term arithmetic progressions in dense sets of integers. Solymosi observed that, in order to prove the conjecture, one can assume that $H$ consists of triples $(a, b, ab)$ of some finite quasigroup $\\Gamma$. Since this problem remains ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07614","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.07614","created_at":"2026-05-17T23:47:01.765109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.07614v2","created_at":"2026-05-17T23:47:01.765109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07614","created_at":"2026-05-17T23:47:01.765109+00:00"},{"alias_kind":"pith_short_12","alias_value":"G2HFUD3SL6XN","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"G2HFUD3SL6XN2QBJ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"G2HFUD3S","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35","json":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35.json","graph_json":"https://pith.science/api/pith-number/G2HFUD3SL6XN2QBJ4EOHM3WR35/graph.json","events_json":"https://pith.science/api/pith-number/G2HFUD3SL6XN2QBJ4EOHM3WR35/events.json","paper":"https://pith.science/paper/G2HFUD3S"},"agent_actions":{"view_html":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35","download_json":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35.json","view_paper":"https://pith.science/paper/G2HFUD3S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.07614&json=true","fetch_graph":"https://pith.science/api/pith-number/G2HFUD3SL6XN2QBJ4EOHM3WR35/graph.json","fetch_events":"https://pith.science/api/pith-number/G2HFUD3SL6XN2QBJ4EOHM3WR35/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35/action/storage_attestation","attest_author":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35/action/author_attestation","sign_citation":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35/action/citation_signature","submit_replication":"https://pith.science/pith/G2HFUD3SL6XN2QBJ4EOHM3WR35/action/replication_record"}},"created_at":"2026-05-17T23:47:01.765109+00:00","updated_at":"2026-05-17T23:47:01.765109+00:00"}