{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3EKCSV6JJJW2CUY4EVLTRXKEX6","short_pith_number":"pith:3EKCSV6J","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"},"canonical_sha256":"d9142957c94a6da1531c255738dd44bf8beb56165ea6e1c780ae1994578679dc","source":{"kind":"arxiv","id":"1001.1624","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1624","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1624v2","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1624","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"3EKCSV6JJJW2","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3EKCSV6JJJW2CUY4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3EKCSV6J","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3EKCSV6JJJW2CUY4EVLTRXKEX6","target":"record","payload":{"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"},"canonical_sha256":"d9142957c94a6da1531c255738dd44bf8beb56165ea6e1c780ae1994578679dc","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"},"source_kind":"arxiv","source_id":"1001.1624","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubaFYkPVK+FEnBrSnTQcQJgjLBVFwlJpA5lDgumBvZe8bcxL9Cz+XwUgp6LNeuHVCYHbz3/FkVoSWvZUawCfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:40:57.584380Z"},"content_sha256":"defab613f30991057965d0a086b1d1a7eb2e5700848010aa3c67bd0d9010c862","schema_version":"1.0","event_id":"sha256:defab613f30991057965d0a086b1d1a7eb2e5700848010aa3c67bd0d9010c862"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3EKCSV6JJJW2CUY4EVLTRXKEX6","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfscA7Hs190RK5MY0+z6inDW5dUSL7XuOiqrrTVM0z5swgbnfBjgONyjd25HxhkeIA3T+dI3Fpja2+178djdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:40:57.584819Z"},"content_sha256":"7ef8cf67a4d18db5f8e0201721350f4f182af82396fdeec50f73f016ccc2f2c4","schema_version":"1.0","event_id":"sha256:7ef8cf67a4d18db5f8e0201721350f4f182af82396fdeec50f73f016ccc2f2c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/bundle.json","state_url":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T11:40:57Z","links":{"resolver":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6","bundle":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/bundle.json","state":"https://pith.science/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3EKCSV6JJJW2CUY4EVLTRXKEX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3EKCSV6JJJW2CUY4EVLTRXKEX6","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":"b4971aa653b37adbf93f17f20295f8b969845b596bcf3ffdcc8f113c4122df88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-01-11T11:19:52Z","title_canon_sha256":"15e511e28a53d1cf57ea315c0c73e1ca4e33542a07cbacfd24affd6b4cc40054"},"schema_version":"1.0","source":{"id":"1001.1624","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1624","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1624v2","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1624","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"3EKCSV6JJJW2","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3EKCSV6JJJW2CUY4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3EKCSV6J","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:7ef8cf67a4d18db5f8e0201721350f4f182af82396fdeec50f73f016ccc2f2c4","target":"graph","created_at":"2026-05-18T03:28:56Z","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":"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 $d=2$.","authors_text":"Thomas Binder, Thomas Martinetz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-01-11T11:19:52Z","title":"On the boundedness of an iteration involving points on the hypersphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1624","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:defab613f30991057965d0a086b1d1a7eb2e5700848010aa3c67bd0d9010c862","target":"record","created_at":"2026-05-18T03:28:56Z","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":"b4971aa653b37adbf93f17f20295f8b969845b596bcf3ffdcc8f113c4122df88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-01-11T11:19:52Z","title_canon_sha256":"15e511e28a53d1cf57ea315c0c73e1ca4e33542a07cbacfd24affd6b4cc40054"},"schema_version":"1.0","source":{"id":"1001.1624","kind":"arxiv","version":2}},"canonical_sha256":"d9142957c94a6da1531c255738dd44bf8beb56165ea6e1c780ae1994578679dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9142957c94a6da1531c255738dd44bf8beb56165ea6e1c780ae1994578679dc","first_computed_at":"2026-05-18T03:28:56.585880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:56.585880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQ0XEr3o1YVaJB84onWETTLze225rujpbr/Xy4qnuHrOiTI2xgi1AWwTdq6+Z9vN7jJyT5AKmpeqTxOgj6sbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:56.586484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1624","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:defab613f30991057965d0a086b1d1a7eb2e5700848010aa3c67bd0d9010c862","sha256:7ef8cf67a4d18db5f8e0201721350f4f182af82396fdeec50f73f016ccc2f2c4"],"state_sha256":"cb42adf02cc1d0b2409df66cd22bdd9a4fc7678ee82518bfbe4b9000298d7f67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0I1NmuvYWsMlYQ8xzqABaoQleZ2p+IduuophwrxiWQpxN5RjisyQXLcr7XkFgTPq2eWxUssHplt11mMdIWORDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T11:40:57.587478Z","bundle_sha256":"3d019bb9cd45de2c64ff9148f8c41a291006bd6c29306fd2014e19f0879d3854"}}