{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OTDGYCNSOQKCCE7WX7KTGMQ7SY","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":"f4fcbae6e3055a7d5dc52f5c93bf9c3b32b4bab32dd47efcd27e7bb4dbbc1768","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-05-28T18:30:24Z","title_canon_sha256":"ef4be6494df9033d4865eb253d453c8aa2da699d40cb4241b2addefeae552d4a"},"schema_version":"1.0","source":{"id":"1105.5734","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5734","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5734v2","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5734","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"OTDGYCNSOQKC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OTDGYCNSOQKCCE7W","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OTDGYCNS","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:f120c07f44a0db5a64383b599e260b22c8d6f33a62e36922ed11cdbcfa382baf","target":"graph","created_at":"2026-05-18T04:20:49Z","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 hole probability of Gaussian entire functions. More specifically, we work with entire functions in Taylor series form with i.i.d complex Gaussian random variables and arbitrary non-random coefficients. A hole is the event where the function has no zeros in a disc of radius r. We find exact asymptotics for the rate of decay of the hole probability for large values of r, outside a small exceptional set. The exceptional set depends only on the non-random coefficients. We assume no regularity conditions on the non-random coefficients.","authors_text":"Alon Nishry","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-05-28T18:30:24Z","title":"Hole Probability for Entire Functions represented by Gaussian Taylor Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5734","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:d07e25980870f9baf4ee408c06cd70b842820c59bbbbf1fd777070060ad8a6ec","target":"record","created_at":"2026-05-18T04:20:49Z","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":"f4fcbae6e3055a7d5dc52f5c93bf9c3b32b4bab32dd47efcd27e7bb4dbbc1768","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-05-28T18:30:24Z","title_canon_sha256":"ef4be6494df9033d4865eb253d453c8aa2da699d40cb4241b2addefeae552d4a"},"schema_version":"1.0","source":{"id":"1105.5734","kind":"arxiv","version":2}},"canonical_sha256":"74c66c09b274142113f6bfd533321f9617f18170fe657d432970cdd50471ad42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74c66c09b274142113f6bfd533321f9617f18170fe657d432970cdd50471ad42","first_computed_at":"2026-05-18T04:20:49.408247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:49.408247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"66V6GhQtzVuAqHk5aLsVZybqFH9fcCPIzxhgAENIcIPkRtX6lqR7mX2kZaSPIsmegOjG/qrGJ9nN/cOxbir3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:49.408853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5734","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d07e25980870f9baf4ee408c06cd70b842820c59bbbbf1fd777070060ad8a6ec","sha256:f120c07f44a0db5a64383b599e260b22c8d6f33a62e36922ed11cdbcfa382baf"],"state_sha256":"e962c7b68c1637c3097bc854cff9763979b0f0bb2fac166b436a7bd5bf8fe4d8"}