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Let $U$ be an open subset of open unit disk $\\mathbb D$ and ${\\mathcal X}_{\\infty}(rU)$ denote the number of points of ${\\mathcal X}_{\\infty}$ that fall in $rU$. 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Let $U$ be an open subset of open unit disk $\\mathbb D$ and ${\\mathcal X}_{\\infty}(rU)$ denote the number of points of ${\\mathcal X}_{\\infty}$ that fall in $rU$. Then, under some conditions on $U$, we show that $$ \\lim_{r\\to \\infty}\\frac{1}{r^4}\\log\\mathbb P[\\mathcal X_{\\infty}(rU)=0]=R_{\\emptyset}-R_{U}, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08363","kind":"arxiv","version":3},"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":"1604.08363","created_at":"2026-05-18T01:03:26.546089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.08363v3","created_at":"2026-05-18T01:03:26.546089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08363","created_at":"2026-05-18T01:03:26.546089+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYU3WSRW6BGS","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYU3WSRW6BGS4TTW","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYU3WSRW","created_at":"2026-05-18T12:30:07.202191+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/AYU3WSRW6BGS4TTWIRVQ47WGH6","json":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6.json","graph_json":"https://pith.science/api/pith-number/AYU3WSRW6BGS4TTWIRVQ47WGH6/graph.json","events_json":"https://pith.science/api/pith-number/AYU3WSRW6BGS4TTWIRVQ47WGH6/events.json","paper":"https://pith.science/paper/AYU3WSRW"},"agent_actions":{"view_html":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6","download_json":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6.json","view_paper":"https://pith.science/paper/AYU3WSRW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.08363&json=true","fetch_graph":"https://pith.science/api/pith-number/AYU3WSRW6BGS4TTWIRVQ47WGH6/graph.json","fetch_events":"https://pith.science/api/pith-number/AYU3WSRW6BGS4TTWIRVQ47WGH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6/action/storage_attestation","attest_author":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6/action/author_attestation","sign_citation":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6/action/citation_signature","submit_replication":"https://pith.science/pith/AYU3WSRW6BGS4TTWIRVQ47WGH6/action/replication_record"}},"created_at":"2026-05-18T01:03:26.546089+00:00","updated_at":"2026-05-18T01:03:26.546089+00:00"}