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We give an explicit formula for the mixed $(k,l)$-correlation function $\\rho_{k,l}:\\mathbb{R}^k\\times\\mathbb{C}_+^l \\to\\mathbb{R}_+$ between $k$ real and $l$ complex zeros of $G_n$."},"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":"1610.03610","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-12T06:37:07Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"4c042f0fc2c454f6acacc40b565f6351d25c590f74a9c568163ad5cc743915fe","abstract_canon_sha256":"7cb4ef061b41603a5aeb7823ae21cd9171f05d3093ed3e430f35f276369e4d45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:29.780729Z","signature_b64":"89RglQyaQEBw/uL2t3qT+72XDpZ+JfPE012xmM0dOaoK2YIlkNxrMeniZzOG7OyYjq5a1H+nTf5/Ex155WD+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24c8ffb3fa0d4cf157c32b98cb149ad6f8cd1d3cbf69e06f5420b66a2d971ab7","last_reissued_at":"2026-05-18T01:02:29.780203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:29.780203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlations between real and complex zeros of a random polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.PR","authors_text":"Denis Koleda, Dmitry Zaporozhets, Friedrich G\\\"otze","submitted_at":"2016-10-12T06:37:07Z","abstract_excerpt":"Consider a random polynomial $$ G(z):=\\xi_0+\\xi_1z+\\dots+\\xi_nz^n,\\quad z\\in\\mathbb{C}, $$ where $\\xi_0,\\xi_1,\\dots,\\xi_{n}$ are independent real-valued random variables with probability density functions $f_0,\\dots,f_n$. We give an explicit formula for the mixed $(k,l)$-correlation function $\\rho_{k,l}:\\mathbb{R}^k\\times\\mathbb{C}_+^l \\to\\mathbb{R}_+$ between $k$ real and $l$ complex zeros of $G_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03610","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":"1610.03610","created_at":"2026-05-18T01:02:29.780289+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.03610v1","created_at":"2026-05-18T01:02:29.780289+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03610","created_at":"2026-05-18T01:02:29.780289+00:00"},{"alias_kind":"pith_short_12","alias_value":"ETEP7M72BVGP","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"ETEP7M72BVGPCV6D","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"ETEP7M72","created_at":"2026-05-18T12:30:15.759754+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/ETEP7M72BVGPCV6DFOMMWFE223","json":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223.json","graph_json":"https://pith.science/api/pith-number/ETEP7M72BVGPCV6DFOMMWFE223/graph.json","events_json":"https://pith.science/api/pith-number/ETEP7M72BVGPCV6DFOMMWFE223/events.json","paper":"https://pith.science/paper/ETEP7M72"},"agent_actions":{"view_html":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223","download_json":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223.json","view_paper":"https://pith.science/paper/ETEP7M72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.03610&json=true","fetch_graph":"https://pith.science/api/pith-number/ETEP7M72BVGPCV6DFOMMWFE223/graph.json","fetch_events":"https://pith.science/api/pith-number/ETEP7M72BVGPCV6DFOMMWFE223/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/action/storage_attestation","attest_author":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/action/author_attestation","sign_citation":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/action/citation_signature","submit_replication":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/action/replication_record"}},"created_at":"2026-05-18T01:02:29.780289+00:00","updated_at":"2026-05-18T01:02:29.780289+00:00"}