{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RPA4RJJBORUKWODL5MOBXODWQJ","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":"8d31462c88582cb61e4b26a21737e0b2db66b46a39fc34fb266d374012e8531a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-21T09:58:58Z","title_canon_sha256":"11121cda54cdbc2fc24c73a4f94fff88ba9f451f888a918b93e67c1d8a7a9bad"},"schema_version":"1.0","source":{"id":"1707.06819","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06819","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06819v1","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06819","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"RPA4RJJBORUK","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RPA4RJJBORUKWODL","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RPA4RJJB","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:9e6fe0bc4832ac8961888f5c42689dda706b6a0f023fbda34a071584a2323b3a","target":"graph","created_at":"2026-05-18T00:39:51Z","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 probability distributions of values in the complex plane attained by Fourier sums of the form \\sum_{j=1}^n a_j exp(-2\\pi i j nu) /sqrt{n} when the frequency nu is drawn uniformly at random from an interval of length 1. If the coefficients a_j are i.i.d. drawn with finite third moment, the distance of these distributions to an isotropic two-dimensional Gaussian on C converges in probability to zero for any pseudometric on the set of distributions for which the distance between empirical distributions and the underlying distribution converges to zero in probability.","authors_text":"Dominik Janzing, Michel Besserve, Naji Shajarisales","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-21T09:58:58Z","title":"A central limit like theorem for Fourier sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06819","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:fe2751ea3128367b575f33f145babb37595229c2853b92d531d402165ac6db0f","target":"record","created_at":"2026-05-18T00:39:51Z","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":"8d31462c88582cb61e4b26a21737e0b2db66b46a39fc34fb266d374012e8531a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-21T09:58:58Z","title_canon_sha256":"11121cda54cdbc2fc24c73a4f94fff88ba9f451f888a918b93e67c1d8a7a9bad"},"schema_version":"1.0","source":{"id":"1707.06819","kind":"arxiv","version":1}},"canonical_sha256":"8bc1c8a5217468ab386beb1c1bb87682787390571d127d89553e070d9d4273c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bc1c8a5217468ab386beb1c1bb87682787390571d127d89553e070d9d4273c5","first_computed_at":"2026-05-18T00:39:51.502777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:51.502777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XzK6lsJ4a8ApMj7XKuia2HQbjoXixb8cAlwkqefFSge5mRqDhnQ75CpwUFUG0T9N1HkRpY/16yff2PVt2K1qAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:51.503533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06819","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe2751ea3128367b575f33f145babb37595229c2853b92d531d402165ac6db0f","sha256:9e6fe0bc4832ac8961888f5c42689dda706b6a0f023fbda34a071584a2323b3a"],"state_sha256":"b1501b8ae6f08eb12474c8ddb37f9d8dcb4a5bdf439cd13ba70f3c84140bde84"}