{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LPMDZV3NJIOXKE4HXXGAPQITBQ","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":"3376228243aec6c14abda50c59e4b76e1f9540c2b4a9509b24399bc88138dc86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-01T12:36:30Z","title_canon_sha256":"20c4d3e1d465221c0209ddb2490adba9154bd2ddc59700c8a6d1e69a21bf487a"},"schema_version":"1.0","source":{"id":"1108.0297","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0297","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0297v2","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0297","created_at":"2026-05-18T03:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"LPMDZV3NJIOX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LPMDZV3NJIOXKE4H","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LPMDZV3N","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:69a2a28e536b30c1bab51b9febfc68d1b8201e8e4c8e2adc6102519a2d2f7d85","target":"graph","created_at":"2026-05-18T03:59:38Z","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":"Boros and Furedi (for d=2) and Barany (for abritrary d) proved that there exists a positive real number c_d such that for every set P of n points in R^d in general position, there exists a point of R^d contained in at least c_d n!/(d+1)!(n-d-1)! d-simplices with vertices at the points of P. Gromov improved the lower bound on c_d by topological means. Using methods from extremal combinatorics, we improve one of the quantities appearing in Gromov's approach and thereby provide a new stronger lower bound on c_d for arbitrary d. In particular, we improve the lower bound on c_3 from 0.06332 to more","authors_text":"Daniel Kral, Jean-Sebastien Sereni, Lukas Mach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-01T12:36:30Z","title":"A new lower bound based on Gromov's method of selecting heavily covered points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0297","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:cebba57c41b0f0c74d8ddeb325c4e22ee45174eb825a0bbe291f218fd5f6d34b","target":"record","created_at":"2026-05-18T03:59:38Z","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":"3376228243aec6c14abda50c59e4b76e1f9540c2b4a9509b24399bc88138dc86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-01T12:36:30Z","title_canon_sha256":"20c4d3e1d465221c0209ddb2490adba9154bd2ddc59700c8a6d1e69a21bf487a"},"schema_version":"1.0","source":{"id":"1108.0297","kind":"arxiv","version":2}},"canonical_sha256":"5bd83cd76d4a1d751387bdcc07c1130c2ee9a2fe9aa8ba559013e9cc7d62f5a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bd83cd76d4a1d751387bdcc07c1130c2ee9a2fe9aa8ba559013e9cc7d62f5a6","first_computed_at":"2026-05-18T03:59:38.158983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:38.158983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ctGomFZM8A5kAnt3UI0Xz1dL7ft+Y9cZ8cHVLz5/Gac6KdncZxd57gwUKoO16cLoyC/QqlxoA3SscDcciHyPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:38.159535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0297","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cebba57c41b0f0c74d8ddeb325c4e22ee45174eb825a0bbe291f218fd5f6d34b","sha256:69a2a28e536b30c1bab51b9febfc68d1b8201e8e4c8e2adc6102519a2d2f7d85"],"state_sha256":"75ebdd1cf4861ae00a58dbfb156a2343e2fc84a8144c64cc600e8419899359e1"}