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Let I_n(g) be the number of isolated vertices of (X_n,lambda_n,g_n) in some bounded Borel set K, where K has non-empty interior and boundary of Lebesgue measure zero. Roy and Sarkar [Phys. A 318 (2003), no. 1-2, 230-242] claim that (I_n(g) - E I_n(g)) / \\sqrt Var I_n(g) converges in distribution to a standard normal random variable. However, their proof has errors. We correct their proof and extend t"},"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":"1404.2096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-08T11:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"a27a4b56b0574691e2bea784d8569780149f7bfdcb9358a4604c0ab12982a8d6","abstract_canon_sha256":"e66617f6a4d53cf4b13f0624f95a84cfd24e4bd3ef528c7c0785c3232664e709"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:38.563241Z","signature_b64":"jk0+HuQ9v3dJFJlQQ4yRQWY7ravqXbwPSV73pq3qtjx1wy0m+NnNd4d6cnLLKSIm8VwyNyXOEGOG0db8nxxoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a066691bff12c498ce45923c26f502e54b473e0979e00430f8edcb49a13a6ce7","last_reissued_at":"2026-05-18T02:54:38.562810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:38.562810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On central limit theorems in the random connection model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ronald Meester, Tim van de Brug","submitted_at":"2014-04-08T11:54:40Z","abstract_excerpt":"Consider a sequence of Poisson random connection models (X_n,lambda_n,g_n) on R^d, where lambda_n / n^d \\to lambda > 0 and g_n(x) = g(nx) for some non-increasing, integrable connection function g. Let I_n(g) be the number of isolated vertices of (X_n,lambda_n,g_n) in some bounded Borel set K, where K has non-empty interior and boundary of Lebesgue measure zero. Roy and Sarkar [Phys. A 318 (2003), no. 1-2, 230-242] claim that (I_n(g) - E I_n(g)) / \\sqrt Var I_n(g) converges in distribution to a standard normal random variable. However, their proof has errors. We correct their proof and extend t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2096","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":"1404.2096","created_at":"2026-05-18T02:54:38.562871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2096v1","created_at":"2026-05-18T02:54:38.562871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2096","created_at":"2026-05-18T02:54:38.562871+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBTGSG77CLCJ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBTGSG77CLCJRTSF","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBTGSG77","created_at":"2026-05-18T12:28:52.271510+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/UBTGSG77CLCJRTSFSI6CN5IC4V","json":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V.json","graph_json":"https://pith.science/api/pith-number/UBTGSG77CLCJRTSFSI6CN5IC4V/graph.json","events_json":"https://pith.science/api/pith-number/UBTGSG77CLCJRTSFSI6CN5IC4V/events.json","paper":"https://pith.science/paper/UBTGSG77"},"agent_actions":{"view_html":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V","download_json":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V.json","view_paper":"https://pith.science/paper/UBTGSG77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2096&json=true","fetch_graph":"https://pith.science/api/pith-number/UBTGSG77CLCJRTSFSI6CN5IC4V/graph.json","fetch_events":"https://pith.science/api/pith-number/UBTGSG77CLCJRTSFSI6CN5IC4V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V/action/storage_attestation","attest_author":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V/action/author_attestation","sign_citation":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V/action/citation_signature","submit_replication":"https://pith.science/pith/UBTGSG77CLCJRTSFSI6CN5IC4V/action/replication_record"}},"created_at":"2026-05-18T02:54:38.562871+00:00","updated_at":"2026-05-18T02:54:38.562871+00:00"}