{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ETEP7M72BVGPCV6DFOMMWFE223","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":"7cb4ef061b41603a5aeb7823ae21cd9171f05d3093ed3e430f35f276369e4d45","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-12T06:37:07Z","title_canon_sha256":"4c042f0fc2c454f6acacc40b565f6351d25c590f74a9c568163ad5cc743915fe"},"schema_version":"1.0","source":{"id":"1610.03610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03610","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03610v1","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03610","created_at":"2026-05-18T01:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"ETEP7M72BVGP","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ETEP7M72BVGPCV6D","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ETEP7M72","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:af544fc98b2357c64cd5007bf18486b606bc7299ba0bd7fde805fb8e0959a4b0","target":"graph","created_at":"2026-05-18T01:02:29Z","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":"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 $G_n$.","authors_text":"Denis Koleda, Dmitry Zaporozhets, Friedrich G\\\"otze","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-12T06:37:07Z","title":"Correlations between real and complex zeros of a random polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03610","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:c12796d6d0d473aa8d3264ad7ef56936993c7e563fb6bc5b29b435b11d637774","target":"record","created_at":"2026-05-18T01:02:29Z","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":"7cb4ef061b41603a5aeb7823ae21cd9171f05d3093ed3e430f35f276369e4d45","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-12T06:37:07Z","title_canon_sha256":"4c042f0fc2c454f6acacc40b565f6351d25c590f74a9c568163ad5cc743915fe"},"schema_version":"1.0","source":{"id":"1610.03610","kind":"arxiv","version":1}},"canonical_sha256":"24c8ffb3fa0d4cf157c32b98cb149ad6f8cd1d3cbf69e06f5420b66a2d971ab7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24c8ffb3fa0d4cf157c32b98cb149ad6f8cd1d3cbf69e06f5420b66a2d971ab7","first_computed_at":"2026-05-18T01:02:29.780203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:29.780203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"89RglQyaQEBw/uL2t3qT+72XDpZ+JfPE012xmM0dOaoK2YIlkNxrMeniZzOG7OyYjq5a1H+nTf5/Ex155WD+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:29.780729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c12796d6d0d473aa8d3264ad7ef56936993c7e563fb6bc5b29b435b11d637774","sha256:af544fc98b2357c64cd5007bf18486b606bc7299ba0bd7fde805fb8e0959a4b0"],"state_sha256":"bada665f5e23ae2c592bc5d107d11698c5a89dd50e3eac310680217f2f613658"}