{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CM3Y5G3I2LR4JBVVBQBZZYVJQI","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":"38c6735b2d63b755b5bce8ae1dfeba26b9da645ed343853d0c5f1240e995806f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-01-09T19:50:58Z","title_canon_sha256":"750600f9386d86c3849a30015d914f65622b69d7040f8f11c34b4cf4df6beb85"},"schema_version":"1.0","source":{"id":"1501.02247","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02247","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02247v4","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02247","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"CM3Y5G3I2LR4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CM3Y5G3I2LR4JBVV","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CM3Y5G3I","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:d3c5471135fcf19fe729a9d8b407f54d5d673256a8297e7129a03f1e12fa3a4c","target":"graph","created_at":"2026-05-18T01:12:43Z","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":"The Karhunen-Lo\\`eve expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on R^d displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d=1. Several properties of this new distribution are obtained. Specifically, its series representation in terms of independent chi-squared random variables is given, the asymptotic behavior of the eigenvalues, its L\\`evy-Khintchine representation, as well as its membership ","authors_text":"M.D. Ruiz-Medina, M.S. Taqqu, N.N. Leonenko","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-01-09T19:50:58Z","title":"Rosenblatt distribution subordinated to gaussian random fields with long-range dependence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02247","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:e511ba28d103b39e33270e9493a18dd47165a6fa12926a4ceacf90cca62147b0","target":"record","created_at":"2026-05-18T01:12:43Z","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":"38c6735b2d63b755b5bce8ae1dfeba26b9da645ed343853d0c5f1240e995806f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-01-09T19:50:58Z","title_canon_sha256":"750600f9386d86c3849a30015d914f65622b69d7040f8f11c34b4cf4df6beb85"},"schema_version":"1.0","source":{"id":"1501.02247","kind":"arxiv","version":4}},"canonical_sha256":"13378e9b68d2e3c486b50c039ce2a98214a7ef8d3ec11c0425fb3ae83a05874c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13378e9b68d2e3c486b50c039ce2a98214a7ef8d3ec11c0425fb3ae83a05874c","first_computed_at":"2026-05-18T01:12:43.510797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:43.510797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZnbYQkmXklvE2YVgfoPXehmyM0780KuF4aGoLtXX8J8BlVkOsSXRgs1kupdHv+Q/P+kaWcKGwkR2xGbA5/QeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:43.511153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02247","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e511ba28d103b39e33270e9493a18dd47165a6fa12926a4ceacf90cca62147b0","sha256:d3c5471135fcf19fe729a9d8b407f54d5d673256a8297e7129a03f1e12fa3a4c"],"state_sha256":"8144389b570fdabe4163bdc455383aa5dd010f79111194e800802914fba3973d"}