{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6B5KULGONAFZQEBWYZJSKPIZ74","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":"0cf9ad1ab1d0d08bddd4834e9021402a8d0841849947c9725353680658492c75","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-02T23:10:15Z","title_canon_sha256":"f32689df071d4e00ecf858dff9ea8a7f9443344095ff26ad672edb6a02429b21"},"schema_version":"1.0","source":{"id":"1710.00937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00937","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00937v1","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00937","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"6B5KULGONAFZ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6B5KULGONAFZQEBW","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6B5KULGO","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:2570fc654e2b9d17092a035740e701b78edb83e722c2a3f19b9c9e3513eebff6","target":"graph","created_at":"2026-05-18T00:33:47Z","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 consider the zero distribution of random polynomials of the form $P_n(z) = \\sum_{k=0}^n a_k B_k(z)$, where $\\{a_k\\}_{k=0}^{\\infty}$ are non-trivial i.i.d. complex random variables with mean $0$ and finite variance. Polynomials $\\{B_k\\}_{k=0}^{\\infty}$ are selected from a standard basis such as Szeg\\H{o}, Bergman, or Faber polynomials associated with a Jordan domain $G$ whose boundary is $C^{2, \\alpha}$ smooth. We show that the zero counting measures of $P_n$ converge almost surely to the equilibrium measure on the boundary of $G$. We also show that if $\\{a_k\\}_{k=0}^{\\infty}$ are i.i.d. ran","authors_text":"Igor Pritsker, Koushik Ramachandran","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-02T23:10:15Z","title":"Natural boundary and zero distribution of random polynomials in smooth domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00937","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":"sha256:4a328eea92bb1c5b27e45dc15ea800b299b4a8029a81d809191ece1ccda0e91a","target":"record","created_at":"2026-05-18T00:33:47Z","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":"0cf9ad1ab1d0d08bddd4834e9021402a8d0841849947c9725353680658492c75","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-02T23:10:15Z","title_canon_sha256":"f32689df071d4e00ecf858dff9ea8a7f9443344095ff26ad672edb6a02429b21"},"schema_version":"1.0","source":{"id":"1710.00937","kind":"arxiv","version":1}},"canonical_sha256":"f07aaa2cce680b981036c653253d19ff3d1106432718c4139265539163d70a80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f07aaa2cce680b981036c653253d19ff3d1106432718c4139265539163d70a80","first_computed_at":"2026-05-18T00:33:47.447633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:47.447633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2G/fNPvUErxvImw8AyCp6AWjEoHL/ocaq0fcNtwsvyrHb3QNl9c7r7Gs4GpdExChgtjLYtzuHSdWgZcmUlrJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:47.448104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a328eea92bb1c5b27e45dc15ea800b299b4a8029a81d809191ece1ccda0e91a","sha256:2570fc654e2b9d17092a035740e701b78edb83e722c2a3f19b9c9e3513eebff6"],"state_sha256":"53b28c22fa475e7ae6247c22ab4665917bc980a89472aa95e849c0faa651522b"}