{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5KEYOHF4K5VPYLUSCYOTHRGGLP","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":"ae27c86cbfeb60d3eaccd49bb7604cd851bc2e3a1d74ce6065f1726086af9f87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-05-08T11:47:51Z","title_canon_sha256":"b1d637396217a65f5ea5d8cac259eee8d80145af6a380e41b2d3e0ddebed5125"},"schema_version":"1.0","source":{"id":"1405.1894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1894","created_at":"2026-05-18T02:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1894v1","created_at":"2026-05-18T02:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1894","created_at":"2026-05-18T02:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"5KEYOHF4K5VP","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5KEYOHF4K5VPYLUS","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5KEYOHF4","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:63653d1f35fabe924948de54e2ded0efe6c3737eb28e840222fff70ec7ecc7c6","target":"graph","created_at":"2026-05-18T02:52:15Z","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 $\\D$ be a set of $n$ pairwise disjoint unit balls in $\\R^d$ and $P$ the set of their center points. A hyperplane $\\Hy$ is an \\emph{$m$-separator} for $\\D$ if each closed halfspace bounded by $\\Hy$ contains at least $m$ points from $P$. This generalizes the notion of halving hyperplanes, which correspond to $n/2$-separators. The analogous notion for point sets has been well studied. Separators have various applications, for instance, in divide-and-conquer schemes. In such a scheme any ball that is intersected by the separating hyperplane may still interact with both sides of the partition. ","authors_text":"Michael Hoffmann, Tillmann Miltzow, Vincent Kusters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-05-08T11:47:51Z","title":"Halving Balls in Deterministic Linear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1894","kind":"arxiv","version":1},"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":"sha256:1a2744681bb7f9918c1f47a7fba0b8ecac76f7a8167c0cb56c16bfce7c139d79","target":"record","created_at":"2026-05-18T02:52:15Z","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":"ae27c86cbfeb60d3eaccd49bb7604cd851bc2e3a1d74ce6065f1726086af9f87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-05-08T11:47:51Z","title_canon_sha256":"b1d637396217a65f5ea5d8cac259eee8d80145af6a380e41b2d3e0ddebed5125"},"schema_version":"1.0","source":{"id":"1405.1894","kind":"arxiv","version":1}},"canonical_sha256":"ea89871cbc576afc2e92161d33c4c65be39a8a9b744a9aa86be9ea64cfd9ba1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea89871cbc576afc2e92161d33c4c65be39a8a9b744a9aa86be9ea64cfd9ba1d","first_computed_at":"2026-05-18T02:52:15.214051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:15.214051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E3KrmGjUFfBbPjBRDxIHC13QOe30zAVzudR27KokmPw1DzlBOkDX0EUIUIrqPiKPk6Efm+052KzZNWyYihlJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:15.214620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a2744681bb7f9918c1f47a7fba0b8ecac76f7a8167c0cb56c16bfce7c139d79","sha256:63653d1f35fabe924948de54e2ded0efe6c3737eb28e840222fff70ec7ecc7c6"],"state_sha256":"f8dd1e5705e0cc5aca7f83cf958f17816d21ffac4327289981d0a61d51550200"}