{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RJ2DX2ZQOZYWHIZ2WNBXWYBE7K","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":"f473d70ea45aa522382508d457f660974ecc14b30cdad62f0b3ac5ea38cfbe7c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-06-12T06:04:00Z","title_canon_sha256":"b86fd542acc7408ad30ec1097df37a76cd43e6960eb08315f1d5b2d107ce6793"},"schema_version":"1.0","source":{"id":"0906.2262","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2262","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2262v2","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2262","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"RJ2DX2ZQOZYW","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RJ2DX2ZQOZYWHIZ2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RJ2DX2ZQ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:ccf8e68a33537b9a9e53e61e3819fb143ca5f524a071ee9ef34984d7d56a9042","target":"graph","created_at":"2026-05-18T03:15:21Z","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":"In this paper we consider families of compact convex sets in $\\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families.","authors_text":"R.N. Karasev","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-06-12T06:04:00Z","title":"Analogues of the central point theorem for families with $d$-intersection property in $\\mathbb R^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2262","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":"sha256:7e77f333e793e17f6a3df0a65913660cf8c598731f95cd24c87823d60bf14542","target":"record","created_at":"2026-05-18T03:15:21Z","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":"f473d70ea45aa522382508d457f660974ecc14b30cdad62f0b3ac5ea38cfbe7c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-06-12T06:04:00Z","title_canon_sha256":"b86fd542acc7408ad30ec1097df37a76cd43e6960eb08315f1d5b2d107ce6793"},"schema_version":"1.0","source":{"id":"0906.2262","kind":"arxiv","version":2}},"canonical_sha256":"8a743beb30767163a33ab3437b6024fab25da28ab231872a51eae05fa1a0ee25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a743beb30767163a33ab3437b6024fab25da28ab231872a51eae05fa1a0ee25","first_computed_at":"2026-05-18T03:15:21.290679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:21.290679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f0sQnqdBYR4q7ylX9N+RYGN98h9zygJZlyn/OHJgm4H2PM4g6sKxR/wJayYyoIPIveNAdtzROuSTYKyqWtIADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:21.291352Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2262","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e77f333e793e17f6a3df0a65913660cf8c598731f95cd24c87823d60bf14542","sha256:ccf8e68a33537b9a9e53e61e3819fb143ca5f524a071ee9ef34984d7d56a9042"],"state_sha256":"b63f69fe4a366bc57f0387d0d13e83b1f1b17ff57270dcda25db597f9da697a7"}