{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3EKCSV6JJJW2CUY4EVLTRXKEX6","short_pith_number":"pith:3EKCSV6J","schema_version":"1.0","canonical_sha256":"d9142957c94a6da1531c255738dd44bf8beb56165ea6e1c780ae1994578679dc","source":{"kind":"arxiv","id":"1001.1624","version":2},"attestation_state":"computed","paper":{"title":"On the boundedness of an iteration involving points on the hypersphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Thomas Binder, Thomas Martinetz","submitted_at":"2010-01-11T11:19:52Z","abstract_excerpt":"For a finite set of points $X$ on the unit hypersphere in $\\mathbb{R}^d$ we consider the iteration $u_{i+1}=u_i+\\chi_i$, where $\\chi_i$ is the point of $X$ farthest from $u_i$. Restricting to the case where the origin is contained in the convex hull of $X$ we study the maximal length of $u_i$. We give sharp upper bounds for the length of $u_i$ independently of $X$. Precisely, this upper bound is infinity for $d\\ge 3$ and $\\sqrt2$ for $d=2$."},"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":"1001.1624","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-01-11T11:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"15e511e28a53d1cf57ea315c0c73e1ca4e33542a07cbacfd24affd6b4cc40054","abstract_canon_sha256":"b4971aa653b37adbf93f17f20295f8b969845b596bcf3ffdcc8f113c4122df88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:56.586484Z","signature_b64":"jQ0XEr3o1YVaJB84onWETTLze225rujpbr/Xy4qnuHrOiTI2xgi1AWwTdq6+Z9vN7jJyT5AKmpeqTxOgj6sbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9142957c94a6da1531c255738dd44bf8beb56165ea6e1c780ae1994578679dc","last_reissued_at":"2026-05-18T03:28:56.585880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:56.585880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the boundedness of an iteration involving points on the hypersphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Thomas Binder, Thomas Martinetz","submitted_at":"2010-01-11T11:19:52Z","abstract_excerpt":"For a finite set of points $X$ on the unit hypersphere in $\\mathbb{R}^d$ we consider the iteration $u_{i+1}=u_i+\\chi_i$, where $\\chi_i$ is the point of $X$ farthest from $u_i$. Restricting to the case where the origin is contained in the convex hull of $X$ we study the maximal length of $u_i$. We give sharp upper bounds for the length of $u_i$ independently of $X$. Precisely, this upper bound is infinity for $d\\ge 3$ and $\\sqrt2$ for $d=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1624","kind":"arxiv","version":2},"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":"1001.1624","created_at":"2026-05-18T03:28:56.585964+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.1624v2","created_at":"2026-05-18T03:28:56.585964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1624","created_at":"2026-05-18T03:28:56.585964+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EKCSV6JJJW2","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EKCSV6JJJW2CUY4","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EKCSV6J","created_at":"2026-05-18T12:26:03.138858+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/3EKCSV6JJJW2CUY4EVLTRXKEX6","json":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6.json","graph_json":"https://pith.science/api/pith-number/3EKCSV6JJJW2CUY4EVLTRXKEX6/graph.json","events_json":"https://pith.science/api/pith-number/3EKCSV6JJJW2CUY4EVLTRXKEX6/events.json","paper":"https://pith.science/paper/3EKCSV6J"},"agent_actions":{"view_html":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6","download_json":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6.json","view_paper":"https://pith.science/paper/3EKCSV6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.1624&json=true","fetch_graph":"https://pith.science/api/pith-number/3EKCSV6JJJW2CUY4EVLTRXKEX6/graph.json","fetch_events":"https://pith.science/api/pith-number/3EKCSV6JJJW2CUY4EVLTRXKEX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/action/storage_attestation","attest_author":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/action/author_attestation","sign_citation":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/action/citation_signature","submit_replication":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/action/replication_record"}},"created_at":"2026-05-18T03:28:56.585964+00:00","updated_at":"2026-05-18T03:28:56.585964+00:00"}