{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z6YB6ICSV3S6RYRJDP3Z6L6642","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":"f56a966d44d0660de6b3873a2adbfe72e601a8c97a5ee65b3ec4ec5111f4fab7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T02:27:49Z","title_canon_sha256":"12139860d4af58569911844c6b1668f2c7983bc712df6116bfa46b1e4133bcbe"},"schema_version":"1.0","source":{"id":"1409.1646","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1646","created_at":"2026-05-18T00:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1646v3","created_at":"2026-05-18T00:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1646","created_at":"2026-05-18T00:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"Z6YB6ICSV3S6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z6YB6ICSV3S6RYRJ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z6YB6ICS","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:a223a124ccb1f0333abbfdd8f0c67256e0d0d57382955263c00868358c048ad8","target":"graph","created_at":"2026-05-18T00:13:22Z","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":"Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process","authors_text":"Guangjun Shen, Hongshuai Dai, Lingtao Kong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T02:27:49Z","title":"Limit theorems for functionals of Gaussian vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1646","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:e72ac33b9fdda877c42b8183e1b03e58780e7ac71d0af6330dcb150ec8492394","target":"record","created_at":"2026-05-18T00:13:22Z","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":"f56a966d44d0660de6b3873a2adbfe72e601a8c97a5ee65b3ec4ec5111f4fab7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T02:27:49Z","title_canon_sha256":"12139860d4af58569911844c6b1668f2c7983bc712df6116bfa46b1e4133bcbe"},"schema_version":"1.0","source":{"id":"1409.1646","kind":"arxiv","version":3}},"canonical_sha256":"cfb01f2052aee5e8e2291bf79f2fdee6b8a4e801cc94ef903c944a0faf3ed784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfb01f2052aee5e8e2291bf79f2fdee6b8a4e801cc94ef903c944a0faf3ed784","first_computed_at":"2026-05-18T00:13:22.349731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:22.349731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m7ShvXJKi9fQPiflQmsg+1qr9Js4biJiA/6iQYUWiXlj64CNu2NxuQgrDwI47bp9PISipuRS3SyqmxUCDw8fAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:22.350384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1646","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e72ac33b9fdda877c42b8183e1b03e58780e7ac71d0af6330dcb150ec8492394","sha256:a223a124ccb1f0333abbfdd8f0c67256e0d0d57382955263c00868358c048ad8"],"state_sha256":"7ed14bbe33427aa4ebe5eda0f872be3ef29ff8fdc7d1086ccc76b2f715211bd7"}