{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:677CGAS5CLYNKCYWL6PY7BUBF7","short_pith_number":"pith:677CGAS5","schema_version":"1.0","canonical_sha256":"f7fe23025d12f0d50b165f9f8f86812fdc418be095fb484d6f69fabab0fe9aae","source":{"kind":"arxiv","id":"1312.7170","version":1},"attestation_state":"computed","paper":{"title":"The acquaintance time of (percolated) random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Pawel Pralat, Tobias Muller","submitted_at":"2013-12-27T01:48:50Z","abstract_excerpt":"In this paper, we study the acquaintance time $\\AC(G)$ defined for a connected graph $G$. We focus on $\\G(n,r,p)$, a random subgraph of a random geometric graph in which $n$ vertices are chosen uniformly at random and independently from $[0,1]^2$, and two vertices are adjacent with probability $p$ if the Euclidean distance between them is at most $r$. We present asymptotic results for the acquaintance time of $\\G(n,r,p)$ for a wide range of $p=p(n)$ and $r=r(n)$. In particular, we show that with high probability $\\AC(G) = \\Theta(r^{-2})$ for $G \\in \\G(n,r,1)$, the \"ordinary\" random geometric g"},"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":"1312.7170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-27T01:48:50Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cb9e8d78dac5a1dc3093dc6cee2a314e0a75f7c91f58bafe940a5c7bdbdd0d7f","abstract_canon_sha256":"11cee4d01532cf0612f4d71961e7d251a15107c9850f2980cfd3e16b1d361027"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:45.600431Z","signature_b64":"Y9w1QXGCCzTfgtPQHHxE9MdDDdC8EHySR25ysrOMrxsZ33wh+uaYKspyN2Lcw3iWKTHfcUHTNEo7hZBMcvuvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7fe23025d12f0d50b165f9f8f86812fdc418be095fb484d6f69fabab0fe9aae","last_reissued_at":"2026-05-18T03:03:45.599821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:45.599821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The acquaintance time of (percolated) random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Pawel Pralat, Tobias Muller","submitted_at":"2013-12-27T01:48:50Z","abstract_excerpt":"In this paper, we study the acquaintance time $\\AC(G)$ defined for a connected graph $G$. We focus on $\\G(n,r,p)$, a random subgraph of a random geometric graph in which $n$ vertices are chosen uniformly at random and independently from $[0,1]^2$, and two vertices are adjacent with probability $p$ if the Euclidean distance between them is at most $r$. We present asymptotic results for the acquaintance time of $\\G(n,r,p)$ for a wide range of $p=p(n)$ and $r=r(n)$. In particular, we show that with high probability $\\AC(G) = \\Theta(r^{-2})$ for $G \\in \\G(n,r,1)$, the \"ordinary\" random geometric g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7170","kind":"arxiv","version":1},"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":"1312.7170","created_at":"2026-05-18T03:03:45.599930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7170v1","created_at":"2026-05-18T03:03:45.599930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7170","created_at":"2026-05-18T03:03:45.599930+00:00"},{"alias_kind":"pith_short_12","alias_value":"677CGAS5CLYN","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"677CGAS5CLYNKCYW","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"677CGAS5","created_at":"2026-05-18T12:27:36.564083+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/677CGAS5CLYNKCYWL6PY7BUBF7","json":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7.json","graph_json":"https://pith.science/api/pith-number/677CGAS5CLYNKCYWL6PY7BUBF7/graph.json","events_json":"https://pith.science/api/pith-number/677CGAS5CLYNKCYWL6PY7BUBF7/events.json","paper":"https://pith.science/paper/677CGAS5"},"agent_actions":{"view_html":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7","download_json":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7.json","view_paper":"https://pith.science/paper/677CGAS5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7170&json=true","fetch_graph":"https://pith.science/api/pith-number/677CGAS5CLYNKCYWL6PY7BUBF7/graph.json","fetch_events":"https://pith.science/api/pith-number/677CGAS5CLYNKCYWL6PY7BUBF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7/action/storage_attestation","attest_author":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7/action/author_attestation","sign_citation":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7/action/citation_signature","submit_replication":"https://pith.science/pith/677CGAS5CLYNKCYWL6PY7BUBF7/action/replication_record"}},"created_at":"2026-05-18T03:03:45.599930+00:00","updated_at":"2026-05-18T03:03:45.599930+00:00"}