{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ETEP7M72BVGPCV6DFOMMWFE223","short_pith_number":"pith:ETEP7M72","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"},"canonical_sha256":"24c8ffb3fa0d4cf157c32b98cb149ad6f8cd1d3cbf69e06f5420b66a2d971ab7","source":{"kind":"arxiv","id":"1610.03610","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ETEP7M72BVGPCV6DFOMMWFE223","target":"record","payload":{"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"},"canonical_sha256":"24c8ffb3fa0d4cf157c32b98cb149ad6f8cd1d3cbf69e06f5420b66a2d971ab7","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"},"source_kind":"arxiv","source_id":"1610.03610","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvncxRiKPbeWwLjR7nrhGnmINemySX1lCXCbat9ncRFkVuUG6WW/a9/CcTfs1NQs0Qz+uZQ/2ZzZIhvalvxJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:19:13.601166Z"},"content_sha256":"c12796d6d0d473aa8d3264ad7ef56936993c7e563fb6bc5b29b435b11d637774","schema_version":"1.0","event_id":"sha256:c12796d6d0d473aa8d3264ad7ef56936993c7e563fb6bc5b29b435b11d637774"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ETEP7M72BVGPCV6DFOMMWFE223","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XozWSiQEb3W1gXhYLIigMV+LA2rbb1c1a9JeaTl9htJgA9wLtys0OPnn+FYvSEEbgiLmyuzikB9q66yC+lKPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:19:13.601865Z"},"content_sha256":"af544fc98b2357c64cd5007bf18486b606bc7299ba0bd7fde805fb8e0959a4b0","schema_version":"1.0","event_id":"sha256:af544fc98b2357c64cd5007bf18486b606bc7299ba0bd7fde805fb8e0959a4b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/bundle.json","state_url":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ETEP7M72BVGPCV6DFOMMWFE223/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T17:19:13Z","links":{"resolver":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223","bundle":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/bundle.json","state":"https://pith.science/pith/ETEP7M72BVGPCV6DFOMMWFE223/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ETEP7M72BVGPCV6DFOMMWFE223/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IVZa8VA3TGXAgZjodq8ON2t85ZGLYH73KE/VlIHJqt3hRjyBowcUTOxOMbu5awIwsp7UTaN7mdzwAQhpITpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:19:13.605210Z","bundle_sha256":"2f080548d4d65e89386e8899b39a558ff8d8c61382bb5fb499a312760c048f48"}}