{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:4TASBKQEO22HTSII7WAJ4JVENE","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":"b1bb1baead6895b2072022e53f72c378fb67e31ddd9a08633272ce3a2d97d1a6","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.PR","submitted_at":"2003-10-19T23:09:43Z","title_canon_sha256":"98b645904eb648ce310a3add40881eff34c624cfa7619c378a37fc5de027e8be"},"schema_version":"1.0","source":{"id":"math/0310297","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0310297","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0310297v4","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310297","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"4TASBKQEO22H","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"4TASBKQEO22HTSII","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"4TASBKQE","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:63dfc2a90864c9b751f2221815a7cce271ea9765da8b07aebc22840d226ccf6b","target":"graph","created_at":"2026-05-18T04:08:43Z","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 the zero set of the random power series f(z)=sum a_n z^n with i.i.d. complex Gaussian coefficients a_n. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the Bergman kernel. We show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent {0,1}-valued random variables X_k, where P(X_k=1)=r^{2k}. Moreover, the set of absolute values of the zeros of f has the same distribution as the set {U_k^{1/2k}} where the U_k are i.i.d. random variables uniform in ","authors_text":"Balint Virag, Yuval Peres","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2003-10-19T23:09:43Z","title":"Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310297","kind":"arxiv","version":4},"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":"sha256:0018e38894efb37a9fd1a60d99e69cdda2535b08f7b7d0a800ad99b0b9104577","target":"record","created_at":"2026-05-18T04:08:43Z","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":"b1bb1baead6895b2072022e53f72c378fb67e31ddd9a08633272ce3a2d97d1a6","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.PR","submitted_at":"2003-10-19T23:09:43Z","title_canon_sha256":"98b645904eb648ce310a3add40881eff34c624cfa7619c378a37fc5de027e8be"},"schema_version":"1.0","source":{"id":"math/0310297","kind":"arxiv","version":4}},"canonical_sha256":"e4c120aa0476b479c908fd809e26a4691b1e770169187b741244d6235447f5f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4c120aa0476b479c908fd809e26a4691b1e770169187b741244d6235447f5f7","first_computed_at":"2026-05-18T04:08:43.031821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:43.031821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kt+veiQNdWS0vF+y1DD4nkPHJc4zefUv7MQcWAvH3Htsht4+NDw3bj3Nat4atT2HQ+EKCTsIj8gRztPckzfgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:43.032526Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0310297","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0018e38894efb37a9fd1a60d99e69cdda2535b08f7b7d0a800ad99b0b9104577","sha256:63dfc2a90864c9b751f2221815a7cce271ea9765da8b07aebc22840d226ccf6b"],"state_sha256":"1fdacab03f172fee02bba83aa59a249af0e3e8caa8313196cf5cd9a964242321"}