{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5KI6JYHND6V6Z3VJFFAOUEO6DV","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":"29be472727dd067c31b101b5c6a24cfa0f682afbd38a928783c5c263015c43ea","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-18T12:11:43Z","title_canon_sha256":"ec7fd7bae5782beca775cc9b2a2be3628c47702278ec457eb7c5f3ffc9166b4f"},"schema_version":"1.0","source":{"id":"1404.4757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4757","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4757v1","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4757","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"5KI6JYHND6V6","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5KI6JYHND6V6Z3VJ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5KI6JYHN","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:8993d76bd87b65949c22c2af26a5b5b6c128f8580b7eb0c8e911d0c10f4dc298","target":"graph","created_at":"2026-05-18T02:53:55Z","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":"Given any two vertices u, v of a random geometric graph, denote by d_E(u,v) their Euclidean distance and by d_G(u,v) their graph distance. The problem of finding upper bounds on d_G(u,v) in terms of d_E(u,v) has received a lot of attention in the literature. In this paper, we improve these upper bounds for values of r=omega(sqrt(log n)) (i.e. for r above the connectivity threshold). Our result also improves the best-known estimates on the diameter of random geometric graphs. We also provide a lower bound on d_G(u,v) in terms of d_E(u,v).","authors_text":"Dieter Mitsche, Guillem Perarnau, Josep D\\'iaz, Xavier P\\'erez-Gim\\'enez","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-18T12:11:43Z","title":"On the relation between graph distance and Euclidean distance in random geometric graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4757","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:fc59814d2afe8c0846b919f4ed6e4700dede7b3ba7f8864e07df8f5e5508742a","target":"record","created_at":"2026-05-18T02:53:55Z","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":"29be472727dd067c31b101b5c6a24cfa0f682afbd38a928783c5c263015c43ea","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-18T12:11:43Z","title_canon_sha256":"ec7fd7bae5782beca775cc9b2a2be3628c47702278ec457eb7c5f3ffc9166b4f"},"schema_version":"1.0","source":{"id":"1404.4757","kind":"arxiv","version":1}},"canonical_sha256":"ea91e4e0ed1fabeceea92940ea11de1d5757010829fa45379777577296591473","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea91e4e0ed1fabeceea92940ea11de1d5757010829fa45379777577296591473","first_computed_at":"2026-05-18T02:53:55.082044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:55.082044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DxDqKXxK9fPHyoEkQkXCNlEOBac5Tu4xxSjQge8r39ihksk8g1NP+EZciT/6n2ui/hK9av0kkDDe3LOQhN0NAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:55.082799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc59814d2afe8c0846b919f4ed6e4700dede7b3ba7f8864e07df8f5e5508742a","sha256:8993d76bd87b65949c22c2af26a5b5b6c128f8580b7eb0c8e911d0c10f4dc298"],"state_sha256":"b4ec28772fee04ee8a807003abcc915060432f08b1afc4038324beec8c11ae14"}