{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZHOBH6DMYRRKFJ34JLXWVZINH6","short_pith_number":"pith:ZHOBH6DM","canonical_record":{"source":{"id":"1409.2736","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-09T13:51:01Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"2cad145560f3969813e6f78dd42e4299bd8045f592eccd27ea0d823cf31b50c1","abstract_canon_sha256":"b3c1a0113a0c0784f3cb8b6f1196a2706b1338be05de855b5dd99f7617c5f44b"},"schema_version":"1.0"},"canonical_sha256":"c9dc13f86cc462a2a77c4aef6ae50d3f9ffeb498594e3526905435237a63b15b","source":{"kind":"arxiv","id":"1409.2736","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2736","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2736v3","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2736","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZHOBH6DMYRRK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZHOBH6DMYRRKFJ34","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZHOBH6DM","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZHOBH6DMYRRKFJ34JLXWVZINH6","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2736","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-09T13:51:01Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"2cad145560f3969813e6f78dd42e4299bd8045f592eccd27ea0d823cf31b50c1","abstract_canon_sha256":"b3c1a0113a0c0784f3cb8b6f1196a2706b1338be05de855b5dd99f7617c5f44b"},"schema_version":"1.0"},"canonical_sha256":"c9dc13f86cc462a2a77c4aef6ae50d3f9ffeb498594e3526905435237a63b15b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:12.581223Z","signature_b64":"LG0PInPLoD+rqujCKmJ4yRqyeUXCggQ8+/Q2m+LqIqXmiGdfGEkVSHi6MguE02SWS0+hGM4qyBzIK2B8yiQLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9dc13f86cc462a2a77c4aef6ae50d3f9ffeb498594e3526905435237a63b15b","last_reissued_at":"2026-05-18T01:23:12.580728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:12.580728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2736","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4X6SreEVQo1zNtu7p5M5DQ1BtIAu+UNRj/8l6pp7hIByHTWxzd7QFMEy/5SJnfa0WwzuVeCEOhAOItpaQywCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:22:46.518978Z"},"content_sha256":"d10ddd562b7badf40589c5a2df13452a844ccb3cdba6d1216d8027e440d3dea8","schema_version":"1.0","event_id":"sha256:d10ddd562b7badf40589c5a2df13452a844ccb3cdba6d1216d8027e440d3dea8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZHOBH6DMYRRKFJ34JLXWVZINH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entire functions of exponential type represented by pseudo-random and random Taylor series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Alexander Borichev, Alon Nishry, Mikhail Sodin","submitted_at":"2014-09-09T13:51:01Z","abstract_excerpt":"We study the influence of the multipliers $\\xi (n)$ on the angular distribution of zeroes of the Taylor series \\[ F_\\xi (z) = \\sum_{n\\ge 0} \\xi (n) \\frac{z^n}{n!}\\,. \\] We show that the distribution of zeroes of $ F_\\xi $ is governed by certain autocorrelations of the sequence $ \\xi $. Using this guiding principle, we consider several examples of random and pseudo-random sequences $\\xi$ and, in particular, answer some questions posed by Chen and Littlewood in 1967.\n  As a by-product we show that if $\\xi$ is a stationary random integer-valued sequence, then either it is periodic, or its spectra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2736","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IVSdE9GwFvCQftYEzbw2ATn456DEH3t1v2cdB2zfWRn1HX9CwH/P9N91Hs/QU7cXVsmJ5kH9SAs9by5GEZIaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:22:46.519334Z"},"content_sha256":"df6121260197e4be9c592d62fcce730677711aa5fcf94b3aae499d9f836febba","schema_version":"1.0","event_id":"sha256:df6121260197e4be9c592d62fcce730677711aa5fcf94b3aae499d9f836febba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6/bundle.json","state_url":"https://pith.science/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T10:22:46Z","links":{"resolver":"https://pith.science/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6","bundle":"https://pith.science/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6/bundle.json","state":"https://pith.science/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHOBH6DMYRRKFJ34JLXWVZINH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZHOBH6DMYRRKFJ34JLXWVZINH6","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":"b3c1a0113a0c0784f3cb8b6f1196a2706b1338be05de855b5dd99f7617c5f44b","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-09T13:51:01Z","title_canon_sha256":"2cad145560f3969813e6f78dd42e4299bd8045f592eccd27ea0d823cf31b50c1"},"schema_version":"1.0","source":{"id":"1409.2736","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2736","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2736v3","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2736","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZHOBH6DMYRRK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZHOBH6DMYRRKFJ34","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZHOBH6DM","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:df6121260197e4be9c592d62fcce730677711aa5fcf94b3aae499d9f836febba","target":"graph","created_at":"2026-05-18T01:23:12Z","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 influence of the multipliers $\\xi (n)$ on the angular distribution of zeroes of the Taylor series \\[ F_\\xi (z) = \\sum_{n\\ge 0} \\xi (n) \\frac{z^n}{n!}\\,. \\] We show that the distribution of zeroes of $ F_\\xi $ is governed by certain autocorrelations of the sequence $ \\xi $. Using this guiding principle, we consider several examples of random and pseudo-random sequences $\\xi$ and, in particular, answer some questions posed by Chen and Littlewood in 1967.\n  As a by-product we show that if $\\xi$ is a stationary random integer-valued sequence, then either it is periodic, or its spectra","authors_text":"Alexander Borichev, Alon Nishry, Mikhail Sodin","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-09T13:51:01Z","title":"Entire functions of exponential type represented by pseudo-random and random Taylor series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2736","kind":"arxiv","version":3},"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:d10ddd562b7badf40589c5a2df13452a844ccb3cdba6d1216d8027e440d3dea8","target":"record","created_at":"2026-05-18T01:23:12Z","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":"b3c1a0113a0c0784f3cb8b6f1196a2706b1338be05de855b5dd99f7617c5f44b","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-09T13:51:01Z","title_canon_sha256":"2cad145560f3969813e6f78dd42e4299bd8045f592eccd27ea0d823cf31b50c1"},"schema_version":"1.0","source":{"id":"1409.2736","kind":"arxiv","version":3}},"canonical_sha256":"c9dc13f86cc462a2a77c4aef6ae50d3f9ffeb498594e3526905435237a63b15b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9dc13f86cc462a2a77c4aef6ae50d3f9ffeb498594e3526905435237a63b15b","first_computed_at":"2026-05-18T01:23:12.580728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:12.580728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LG0PInPLoD+rqujCKmJ4yRqyeUXCggQ8+/Q2m+LqIqXmiGdfGEkVSHi6MguE02SWS0+hGM4qyBzIK2B8yiQLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:12.581223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2736","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d10ddd562b7badf40589c5a2df13452a844ccb3cdba6d1216d8027e440d3dea8","sha256:df6121260197e4be9c592d62fcce730677711aa5fcf94b3aae499d9f836febba"],"state_sha256":"6f679d04ffdef75cea2102d7b601c7327b90c3adcc4c7b45fdbaf27f3eae6920"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYskeh5FiLY2UeM9BSZENcp3GaohZA8lfxkv74eK5OOmJoUpIQ2wEm5wmKNmoXCnjbDA70MMJJo/hhQNSUc7Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:22:46.521262Z","bundle_sha256":"5a944660a94b497fd7bd6d0d812842334d262283e68e2e99e2e32f1f169b2cfb"}}