{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GZ6XFKAFCIZ43ICK6ZK4FHZQ75","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":"5ffb327fcd4f9d6ae46dfa92acde1fe479d6c28d2c7400e12c7b42fc69f744d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T16:59:46Z","title_canon_sha256":"de0e254dd1401587044e4005f5fc3b7d15ea0aa6641f2c51e4b0cf9f064e88ed"},"schema_version":"1.0","source":{"id":"1501.05574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05574","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05574v2","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05574","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"GZ6XFKAFCIZ4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GZ6XFKAFCIZ43ICK","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GZ6XFKAF","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:a037196ef8ae5737c90f159e972ec7e5902042f091422195e4778df576776ad9","target":"graph","created_at":"2026-05-18T02:17:33Z","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":"\\noindent The paper establishes weak convergence in $C[0,1]$ of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both central and non-central functional limit theorems are obtained.","authors_text":"Mamikon S. Ginovyan, Murad S. Taqqu, Shuyang Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T16:59:46Z","title":"Functional Limit Theorems for Toeplitz Quadratic Functionals of Continuous time Gaussian Stationary Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05574","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":"sha256:48962b9e566ce0791d117e4a72d34792759badca223141487da5779e334ba850","target":"record","created_at":"2026-05-18T02:17:33Z","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":"5ffb327fcd4f9d6ae46dfa92acde1fe479d6c28d2c7400e12c7b42fc69f744d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-22T16:59:46Z","title_canon_sha256":"de0e254dd1401587044e4005f5fc3b7d15ea0aa6641f2c51e4b0cf9f064e88ed"},"schema_version":"1.0","source":{"id":"1501.05574","kind":"arxiv","version":2}},"canonical_sha256":"367d72a8051233cda04af655c29f30ff7f1c28b7f655df505cb21085db765187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"367d72a8051233cda04af655c29f30ff7f1c28b7f655df505cb21085db765187","first_computed_at":"2026-05-18T02:17:33.225377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:33.225377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jzwc9CKARTK3YIYRS7rvTpfvAUb8QCN4gu3RidqrDesQNxbWCx8/1cz3vqtF5y2A3ILTZfXovgwaSnNMtJVFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:33.226071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48962b9e566ce0791d117e4a72d34792759badca223141487da5779e334ba850","sha256:a037196ef8ae5737c90f159e972ec7e5902042f091422195e4778df576776ad9"],"state_sha256":"0c89f33ec85622de7d089723a785fca3df48657a2292fd204a54c03a22449d94"}