{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UZWA6BUEXBJSAOT2CL6SP2DO6Q","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":"3aa6a0724836f8742a2a35533468791c45abdd1c14da28d170c886413beee3a9","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-19T17:08:20Z","title_canon_sha256":"ac5aa5a8199f6f7971a6ddc89ea23c81831cf3dc4f8550732201eba734142afb"},"schema_version":"1.0","source":{"id":"1207.4734","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4734","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4734v2","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4734","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"UZWA6BUEXBJS","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UZWA6BUEXBJSAOT2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UZWA6BUE","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:ad9ad08463a86342aadcbc967a3336b683bd8f9c469f8eb33c2548a2e86d18cd","target":"graph","created_at":"2026-05-18T01:23:45Z","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":"We study the asymptotics of correlations and nearest neighbor spacings between zeros and holomorphic critical points of $p_N$, a degree N Hermitian Gaussian random polynomial in the sense of Shiffman and Zeldtich, as N goes to infinity. By holomorphic critical point we mean a solution to the equation $\\frac{d}{dz}p_N(z)=0.$ Our principal result is an explicit asymptotic formula for the local scaling limit of $\\E{Z_{p_N}\\wedge C_{p_N}},$ the expected joint intensity of zeros and critical points, around any point on the Riemann sphere. Here $Z_{p_N}$ and $C_{p_N}$ are the currents of integration","authors_text":"Boris Hanin","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-19T17:08:20Z","title":"Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4734","kind":"arxiv","version":2},"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:b216230901b258e86cd97d61b14207e7c542b94ff74097a3d8c44d922a9b9474","target":"record","created_at":"2026-05-18T01:23:45Z","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":"3aa6a0724836f8742a2a35533468791c45abdd1c14da28d170c886413beee3a9","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-19T17:08:20Z","title_canon_sha256":"ac5aa5a8199f6f7971a6ddc89ea23c81831cf3dc4f8550732201eba734142afb"},"schema_version":"1.0","source":{"id":"1207.4734","kind":"arxiv","version":2}},"canonical_sha256":"a66c0f0684b853203a7a12fd27e86ef43b1fa46fb8a9674e83f1fe07035d9f8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a66c0f0684b853203a7a12fd27e86ef43b1fa46fb8a9674e83f1fe07035d9f8d","first_computed_at":"2026-05-18T01:23:45.719180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:45.719180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QtSpglZCCYXYKug0b+ZPQXQVmafulGIIqkwvvxrC5nZFEVzneB/q1MCEAncReuALy7gItGkypixYQ1Ue0nBaBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:45.720135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4734","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b216230901b258e86cd97d61b14207e7c542b94ff74097a3d8c44d922a9b9474","sha256:ad9ad08463a86342aadcbc967a3336b683bd8f9c469f8eb33c2548a2e86d18cd"],"state_sha256":"02351e6e2ac3a5b34f8985676895b1edbd475d0d3da33c56ccc4f8e794ddff6b"}