{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RJDFY5MHFGKE4WCOTS3FDRSNNE","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":"f83754610a4af4b55da8eafeef22fd21d5484322a45a7f340bd7bd40ad538a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-17T11:37:53Z","title_canon_sha256":"21c7ab0591128436fccee0223f567b3c23336849986364fb75c3b7ef67b20592"},"schema_version":"1.0","source":{"id":"1610.05053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05053","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05053v2","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05053","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"RJDFY5MHFGKE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RJDFY5MHFGKE4WCO","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RJDFY5MH","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:7503598393e7ce8ae1c9bdb8a99fb2a4e52ebc85927378f51e9cbc3bafb1933b","target":"graph","created_at":"2026-05-18T00:05:39Z","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":"Let $U_1,\\dots, U_{d+1}$ be $n$-element sets in $R^d$ and let $\\langle u_1,\\ldots,u_{d+1}\\rangle$ denote the convex hull of points $u_i$ in $U_i$ (for all $i$) which is a (possibly degenerate) simplex. Pach's selection theorem says that there are sets $Z_1 \\subset U_1,\\dots, Z_{d+1} \\subset U_{d+1}$ and a point $u$ in $R^d$ such that each $|Z_i| > c_1(d)n$ and $u$ belongs to $\\langle z_1,...,z_{d+1} \\rangle$ for every choice of $z_1$ in $Z_1,\\dots,z_{d+1}$ in $Z_{d+1}$. Here we show that this theorem does not admit a topological extension with linear size sets $Z_i$. However, there is a topolo","authors_text":"Eran Nevo, Imre B\\'ar\\'any, Martin Tancer, Roy Meshulam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-17T11:37:53Z","title":"Pach's selection theorem does not admit a topological extension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05053","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:c781724e7ca4b296cd15f160e041fc3c232ce39c67d7218c121103eae5f63802","target":"record","created_at":"2026-05-18T00:05:39Z","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":"f83754610a4af4b55da8eafeef22fd21d5484322a45a7f340bd7bd40ad538a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-17T11:37:53Z","title_canon_sha256":"21c7ab0591128436fccee0223f567b3c23336849986364fb75c3b7ef67b20592"},"schema_version":"1.0","source":{"id":"1610.05053","kind":"arxiv","version":2}},"canonical_sha256":"8a465c758729944e584e9cb651c64d693c9f8a1c7bcca581a26aabe11487b126","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a465c758729944e584e9cb651c64d693c9f8a1c7bcca581a26aabe11487b126","first_computed_at":"2026-05-18T00:05:39.921411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:39.921411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2DsTP9DsMa0fe4Rb/lYjTJlDCmGfoa5DxpNX1Erb6NxU12gE2WAYHYS46Upy/iwRZPMtwE3gWzivO+0QljbzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:39.921849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c781724e7ca4b296cd15f160e041fc3c232ce39c67d7218c121103eae5f63802","sha256:7503598393e7ce8ae1c9bdb8a99fb2a4e52ebc85927378f51e9cbc3bafb1933b"],"state_sha256":"42ace5fe56ae026cfb6ed94be3cc94a9ce035503acd0624d4251fadf8f188798"}