{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NVUORV7AS4NRF43AVNIAY7JY5Q","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":"6af11bc0e4baebe0f47e123633e890f53d95c30e1176739487671ff98413c4b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T18:35:26Z","title_canon_sha256":"cf96b1f9a1a7730e6961b366ea831fc1925a4c224c886ebe94c475d14a086292"},"schema_version":"1.0","source":{"id":"1601.05740","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05740","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05740v2","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05740","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"NVUORV7AS4NR","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NVUORV7AS4NRF43A","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NVUORV7A","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:879e48f6339d5063f96976b542ef153a1a6a9ff17ca8324354a212b84e9c29e2","target":"graph","created_at":"2026-05-18T01:14:52Z","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 a random trigonometric polynomial $X_n: \\mathbb R \\to \\mathbb R$ of the form $$ X_n(t) = \\sum_{k=1}^n \\left( \\xi_k \\sin (kt) + \\eta_k \\cos (kt)\\right), $$ where $(\\xi_1,\\eta_1),(\\xi_2,\\eta_2),\\ldots$ are independent identically distributed bivariate real random vectors with zero mean and unit covariance matrix. Let $(s_n)_{n\\in\\mathbb N}$ be any sequence of real numbers. We prove that as $n\\to\\infty$, the number of real zeros of $X_n$ in the interval $[s_n+a/n, s_n+ b/n]$ converges in distribution to the number of zeros in the interval $[a,b]$ of a stationary, zero-mean Gaussian proce","authors_text":"Alexander Iksanov, Alexander Marynych, Zakhar Kabluchko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T18:35:26Z","title":"Local universality for real roots of random trigonometric polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05740","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":"sha256:022702c8230c1129b58a887482d5dd5851599c449d2fa7632584f2e7d11e9ca7","target":"record","created_at":"2026-05-18T01:14:52Z","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":"6af11bc0e4baebe0f47e123633e890f53d95c30e1176739487671ff98413c4b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-21T18:35:26Z","title_canon_sha256":"cf96b1f9a1a7730e6961b366ea831fc1925a4c224c886ebe94c475d14a086292"},"schema_version":"1.0","source":{"id":"1601.05740","kind":"arxiv","version":2}},"canonical_sha256":"6d68e8d7e0971b12f360ab500c7d38ec21b9c47cd310916153ed3c77c5618715","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d68e8d7e0971b12f360ab500c7d38ec21b9c47cd310916153ed3c77c5618715","first_computed_at":"2026-05-18T01:14:52.554581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:52.554581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H+/yuYa/G97Qo6M/q3jHEv+KfhFZSFq5BUXxi/igfZFCCQWO8YJjWQmHODRxYIXOb74iPOB9sousTKbwdcGEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:52.555201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05740","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:022702c8230c1129b58a887482d5dd5851599c449d2fa7632584f2e7d11e9ca7","sha256:879e48f6339d5063f96976b542ef153a1a6a9ff17ca8324354a212b84e9c29e2"],"state_sha256":"6b68beaecda82434fb83153e4a5235eca451466f875f9ea4062cf4631f4585bf"}