{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LU67OLWY54BCNY6XQJNILX3ZWE","short_pith_number":"pith:LU67OLWY","schema_version":"1.0","canonical_sha256":"5d3df72ed8ef0226e3d7825a85df79b1139f5140152ad1da30aebea06cf62d9f","source":{"kind":"arxiv","id":"1307.4357","version":3},"attestation_state":"computed","paper":{"title":"Local universality of zeroes of random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Terence Tao, Van Vu","submitted_at":"2013-07-16T17:48:19Z","abstract_excerpt":"In this paper, we establish some local universality results concerning the correlation functions of the zeroes of random polynomials with independent coefficients. More precisely, consider two random polynomials $f =\\sum_{i=1}^n c_i \\xi_i z^i$ and $\\tilde f =\\sum_{i=1}^n c_i \\tilde \\xi_i z^i$, where the $\\xi_i$ and $\\tilde \\xi_i$ are iid random variables that match moments to second order, the coefficients $c_i$ are deterministic, and the degree parameter $n$ is large. Our results show, under some light conditions on the coefficients\n  $c_i$ and the tails of $\\xi_i, \\tilde \\xi_i$, that the cor"},"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":"1307.4357","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T17:48:19Z","cross_cats_sorted":[],"title_canon_sha256":"de17924b9e4af9b974a1979eb8f7fcdf443308f8e8bcad9589de2166a24be3e9","abstract_canon_sha256":"a85a9c44f97e9e1e20e3676de292d31dad358fd139d921b291156924f375c561"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:56.071893Z","signature_b64":"7udt9J4kLMj19UPn+gdzW0QEPD4AmIT2c3V+GqadrhYW2m8SSnvlprqVWI2ppbd35c8vq0HDKg6KJ7Ky5TwpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d3df72ed8ef0226e3d7825a85df79b1139f5140152ad1da30aebea06cf62d9f","last_reissued_at":"2026-05-18T02:52:56.071335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:56.071335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local universality of zeroes of random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Terence Tao, Van Vu","submitted_at":"2013-07-16T17:48:19Z","abstract_excerpt":"In this paper, we establish some local universality results concerning the correlation functions of the zeroes of random polynomials with independent coefficients. More precisely, consider two random polynomials $f =\\sum_{i=1}^n c_i \\xi_i z^i$ and $\\tilde f =\\sum_{i=1}^n c_i \\tilde \\xi_i z^i$, where the $\\xi_i$ and $\\tilde \\xi_i$ are iid random variables that match moments to second order, the coefficients $c_i$ are deterministic, and the degree parameter $n$ is large. Our results show, under some light conditions on the coefficients\n  $c_i$ and the tails of $\\xi_i, \\tilde \\xi_i$, that the cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4357","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":"1307.4357","created_at":"2026-05-18T02:52:56.071436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4357v3","created_at":"2026-05-18T02:52:56.071436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4357","created_at":"2026-05-18T02:52:56.071436+00:00"},{"alias_kind":"pith_short_12","alias_value":"LU67OLWY54BC","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LU67OLWY54BCNY6X","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LU67OLWY","created_at":"2026-05-18T12:27:51.066281+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/LU67OLWY54BCNY6XQJNILX3ZWE","json":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE.json","graph_json":"https://pith.science/api/pith-number/LU67OLWY54BCNY6XQJNILX3ZWE/graph.json","events_json":"https://pith.science/api/pith-number/LU67OLWY54BCNY6XQJNILX3ZWE/events.json","paper":"https://pith.science/paper/LU67OLWY"},"agent_actions":{"view_html":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE","download_json":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE.json","view_paper":"https://pith.science/paper/LU67OLWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4357&json=true","fetch_graph":"https://pith.science/api/pith-number/LU67OLWY54BCNY6XQJNILX3ZWE/graph.json","fetch_events":"https://pith.science/api/pith-number/LU67OLWY54BCNY6XQJNILX3ZWE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE/action/storage_attestation","attest_author":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE/action/author_attestation","sign_citation":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE/action/citation_signature","submit_replication":"https://pith.science/pith/LU67OLWY54BCNY6XQJNILX3ZWE/action/replication_record"}},"created_at":"2026-05-18T02:52:56.071436+00:00","updated_at":"2026-05-18T02:52:56.071436+00:00"}