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Sober\\'{o}n and Strausz proved that there is always a $t$-tolerant Tverberg partition with $\\lceil n / (d+1)(t+1) \\rceil$ sets. However, so far no nontrivial algorithms for computing or approximating such partitions have been presented.\n  For $d \\leq 2$, we show that the Sober\\'{o}n-Strausz bound can be improved, and we show h"},"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":"1306.3452","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-06-14T16:47:36Z","cross_cats_sorted":[],"title_canon_sha256":"45f35e7035c77da835d55235685bd80b56fe7160f46e2b47f26bdde941679867","abstract_canon_sha256":"17a274bc41d4fc475ec26066327a0c49b79a67ac22f3820ecdcf5cfb20b97a07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:08.575240Z","signature_b64":"PnV7hEjrWlf84fNNfR2X1CzA8zg0BNNfDi92WYw3j3fx7j/nImGCVzS4I1Tfiq49WnuBwTZ8XdRiSRl19BquDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d737c8cd943c82593afefcae3508a348b0d4335e23db71b2119f521554595df8","last_reissued_at":"2026-05-18T02:02:08.574607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:08.574607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms for Tolerant Tverberg Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Wolfgang Mulzer, Yannik Stein","submitted_at":"2013-06-14T16:47:36Z","abstract_excerpt":"Let $P$ be a $d$-dimensional $n$-point set. A partition $T$ of $P$ is called a Tverberg partition if the convex hulls of all sets in $T$ intersect in at least one point. We say $T$ is $t$-tolerant if it remains a Tverberg partition after deleting any $t$ points from $P$. Sober\\'{o}n and Strausz proved that there is always a $t$-tolerant Tverberg partition with $\\lceil n / (d+1)(t+1) \\rceil$ sets. However, so far no nontrivial algorithms for computing or approximating such partitions have been presented.\n  For $d \\leq 2$, we show that the Sober\\'{o}n-Strausz bound can be improved, and we show h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3452","kind":"arxiv","version":3},"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":"1306.3452","created_at":"2026-05-18T02:02:08.574687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3452v3","created_at":"2026-05-18T02:02:08.574687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3452","created_at":"2026-05-18T02:02:08.574687+00:00"},{"alias_kind":"pith_short_12","alias_value":"2434RTMUHSBF","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"2434RTMUHSBFSOX6","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"2434RTMU","created_at":"2026-05-18T12:27:30.460161+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/2434RTMUHSBFSOX67SXDKCFDJC","json":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC.json","graph_json":"https://pith.science/api/pith-number/2434RTMUHSBFSOX67SXDKCFDJC/graph.json","events_json":"https://pith.science/api/pith-number/2434RTMUHSBFSOX67SXDKCFDJC/events.json","paper":"https://pith.science/paper/2434RTMU"},"agent_actions":{"view_html":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC","download_json":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC.json","view_paper":"https://pith.science/paper/2434RTMU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3452&json=true","fetch_graph":"https://pith.science/api/pith-number/2434RTMUHSBFSOX67SXDKCFDJC/graph.json","fetch_events":"https://pith.science/api/pith-number/2434RTMUHSBFSOX67SXDKCFDJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC/action/storage_attestation","attest_author":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC/action/author_attestation","sign_citation":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC/action/citation_signature","submit_replication":"https://pith.science/pith/2434RTMUHSBFSOX67SXDKCFDJC/action/replication_record"}},"created_at":"2026-05-18T02:02:08.574687+00:00","updated_at":"2026-05-18T02:02:08.574687+00:00"}