{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P2PEQNAH4WSBVIGB4C2WZJGUUI","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":"9fe8237c5662e88a2dc225f465240171605ddf21bb0bbe1884f0d392306e126a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-07-10T07:13:38Z","title_canon_sha256":"50bfd086808d230299cc168433bd3f344d47e644ddbd66ded6a5112c1bcc96c7"},"schema_version":"1.0","source":{"id":"1307.2700","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2700","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2700v4","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2700","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"pith_short_12","alias_value":"P2PEQNAH4WSB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P2PEQNAH4WSBVIGB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P2PEQNAH","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:57ba72339a5d49564f341155ebd74aeee945304e140d45854c4a9c315d643a66","target":"graph","created_at":"2026-05-18T03:07:03Z","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":"This paper presents a simple kinetic data structure for maintaining all the nearest neighbors of a set of $n$ moving points in $\\mathbb{R}^d$, where the trajectory of each point is an algebraic function of at most constant degree $s$. The approach is based on maintaining the edges of the Semi-Yao graph, a sparse graph whose edge set includes the pairs of nearest neighbors as a subset.\n  Our kinetic data structure (KDS) for maintaining all the nearest neighbors is deterministic. It processes $O(n^2\\beta_{2s+2}^2(n)\\log n)$ events with a total cost of $O(n^2\\beta_{2s+2}(n)\\log^{d+1} n)$. Here, $","authors_text":"Mohammad Ali Abam, Sue Whitesides, Valerie King, Zahed Rahmati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-07-10T07:13:38Z","title":"Kinetic Data Structures for the Semi-Yao Graph and All Nearest Neighbors in R^d"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2700","kind":"arxiv","version":4},"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":"sha256:60c0cfc2c41ec618e76020abc0b62810a2ecd42b034ce3ab32439359af997ef4","target":"record","created_at":"2026-05-18T03:07:03Z","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":"9fe8237c5662e88a2dc225f465240171605ddf21bb0bbe1884f0d392306e126a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-07-10T07:13:38Z","title_canon_sha256":"50bfd086808d230299cc168433bd3f344d47e644ddbd66ded6a5112c1bcc96c7"},"schema_version":"1.0","source":{"id":"1307.2700","kind":"arxiv","version":4}},"canonical_sha256":"7e9e483407e5a41aa0c1e0b56ca4d4a22f3a86768e6929e05e6ffb32f2e39332","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9e483407e5a41aa0c1e0b56ca4d4a22f3a86768e6929e05e6ffb32f2e39332","first_computed_at":"2026-05-18T03:07:03.669005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:03.669005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OP43SIsf9933spHUKsI9G9J5CjFIKD1uB6O5uDSnMBptEms7+atJLL6hfPVvSXDVoj6pRX+ZMmDEzAU7ZvxACA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:03.669441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2700","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60c0cfc2c41ec618e76020abc0b62810a2ecd42b034ce3ab32439359af997ef4","sha256:57ba72339a5d49564f341155ebd74aeee945304e140d45854c4a9c315d643a66"],"state_sha256":"5be2d4227abf891155028cb9560e6935b5389617bb710b187a0ec3be45a25fc4"}