{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SBLNSFBWY7AQY4LISD6RWJTHZY","short_pith_number":"pith:SBLNSFBW","schema_version":"1.0","canonical_sha256":"9056d91436c7c10c716890fd1b2667ce01eea5155beb1f85075e67f7fd9f7d9a","source":{"kind":"arxiv","id":"1901.09871","version":1},"attestation_state":"computed","paper":{"title":"The Brown-Erd\\H{o}s-S\\'os Conjecture in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ching Wong, Jozsef Solymosi","submitted_at":"2019-01-28T18:25:49Z","abstract_excerpt":"The Brown-Erd\\H{o}s-S\\'{o}s conjecture, one of the central conjectures in extremal combinatorics, states that for any integer $m\\geq 6,$ if a 3-uniform hypergraph on $n$ vertices contains no $m$ vertices spanning at least $m-3$ edges, then the number of edges is $o(n^2).$ We prove the conjecture for triple systems coming from finite abelian groups."},"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":"1901.09871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-28T18:25:49Z","cross_cats_sorted":[],"title_canon_sha256":"1e4734f859eb607445e70d144bf8194b9d47a9b79dea860e7d65bd128ee87d86","abstract_canon_sha256":"67b4f669e75f23a28f50c0fdfad768703558a19462a24da2db8010c68716186e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:23.624593Z","signature_b64":"X8sYu/fd6akvT59zt9bHoz8zXoBcihhCd1aRbIW4vceczo0EHhqpyGczSUM3mZmIDmWyc3QSaroixpo4vQSJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9056d91436c7c10c716890fd1b2667ce01eea5155beb1f85075e67f7fd9f7d9a","last_reissued_at":"2026-05-17T23:55:23.624203Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:23.624203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Brown-Erd\\H{o}s-S\\'os Conjecture in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ching Wong, Jozsef Solymosi","submitted_at":"2019-01-28T18:25:49Z","abstract_excerpt":"The Brown-Erd\\H{o}s-S\\'{o}s conjecture, one of the central conjectures in extremal combinatorics, states that for any integer $m\\geq 6,$ if a 3-uniform hypergraph on $n$ vertices contains no $m$ vertices spanning at least $m-3$ edges, then the number of edges is $o(n^2).$ We prove the conjecture for triple systems coming from finite abelian groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09871","kind":"arxiv","version":1},"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":"1901.09871","created_at":"2026-05-17T23:55:23.624264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.09871v1","created_at":"2026-05-17T23:55:23.624264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09871","created_at":"2026-05-17T23:55:23.624264+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBLNSFBWY7AQ","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBLNSFBWY7AQY4LI","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBLNSFBW","created_at":"2026-05-18T12:33:27.125529+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/SBLNSFBWY7AQY4LISD6RWJTHZY","json":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY.json","graph_json":"https://pith.science/api/pith-number/SBLNSFBWY7AQY4LISD6RWJTHZY/graph.json","events_json":"https://pith.science/api/pith-number/SBLNSFBWY7AQY4LISD6RWJTHZY/events.json","paper":"https://pith.science/paper/SBLNSFBW"},"agent_actions":{"view_html":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY","download_json":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY.json","view_paper":"https://pith.science/paper/SBLNSFBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.09871&json=true","fetch_graph":"https://pith.science/api/pith-number/SBLNSFBWY7AQY4LISD6RWJTHZY/graph.json","fetch_events":"https://pith.science/api/pith-number/SBLNSFBWY7AQY4LISD6RWJTHZY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY/action/storage_attestation","attest_author":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY/action/author_attestation","sign_citation":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY/action/citation_signature","submit_replication":"https://pith.science/pith/SBLNSFBWY7AQY4LISD6RWJTHZY/action/replication_record"}},"created_at":"2026-05-17T23:55:23.624264+00:00","updated_at":"2026-05-17T23:55:23.624264+00:00"}