{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EVAZ56HPF6OYEEWHYLISI7PKXU","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":"99cac792f33950f0414a72e68f417f23eb626d2ac6cca1fbe756aa1fcbd4008b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-08-05T19:55:58Z","title_canon_sha256":"d89f573edaec1414670b99c011c8626aeac0965de291b13cbd14362cdc90b038"},"schema_version":"1.0","source":{"id":"1008.1053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1053","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1053v1","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1053","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"EVAZ56HPF6OY","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EVAZ56HPF6OYEEWH","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EVAZ56HP","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:bc06852cb58a19afe8fbd1ca12e668d384e97f5890fa7552e26369efb4abe3bb","target":"graph","created_at":"2026-05-18T04:42:34Z","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":"Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations. We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We st","authors_text":"Boris Aronov, Ferran Hurtado, Muriel Dulieu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-08-05T19:55:58Z","title":"Witness (Delaunay) Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1053","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":"sha256:778a917e599c4e2a12a640b455f019d41f44fbc3966412782bbd7c4d40bd4b6d","target":"record","created_at":"2026-05-18T04:42:34Z","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":"99cac792f33950f0414a72e68f417f23eb626d2ac6cca1fbe756aa1fcbd4008b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-08-05T19:55:58Z","title_canon_sha256":"d89f573edaec1414670b99c011c8626aeac0965de291b13cbd14362cdc90b038"},"schema_version":"1.0","source":{"id":"1008.1053","kind":"arxiv","version":1}},"canonical_sha256":"25419ef8ef2f9d8212c7c2d1247deabd1493e2be5cbc581b52b1e57a293476bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25419ef8ef2f9d8212c7c2d1247deabd1493e2be5cbc581b52b1e57a293476bc","first_computed_at":"2026-05-18T04:42:34.692057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:34.692057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1E1wns7PKEL2gM9Xpwmh4aC9S1vtdSMCMEBQmo92IT0Cp8yOKEcnV4ulI7G8xfWpEgFGloysceaIp2doWKCfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:34.692633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:778a917e599c4e2a12a640b455f019d41f44fbc3966412782bbd7c4d40bd4b6d","sha256:bc06852cb58a19afe8fbd1ca12e668d384e97f5890fa7552e26369efb4abe3bb"],"state_sha256":"191c2dc203d593b24f60c384661ca20a4891eaa95330a8968dfd98a92f164acb"}