{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EOIMEVCERDKKEQAALPMBMNWGHL","short_pith_number":"pith:EOIMEVCE","schema_version":"1.0","canonical_sha256":"2390c2544488d4a240005bd81636c63ae23cd4f918f7ca980432fcad545ddcf5","source":{"kind":"arxiv","id":"1205.4172","version":2},"attestation_state":"computed","paper":{"title":"Variance of partial sums of stationary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"George Deligiannidis, Sergey Utev","submitted_at":"2012-05-18T15:07:26Z","abstract_excerpt":"Let $X_1,X_2,\\ldots$ be a centred sequence of weakly stationary random variables with spectral measure $F$ and partial sums $S_n=X_1+\\cdots+X_n$. We show that $\\operatorname {var}(S_n)$ is regularly varying of index $\\gamma$ at infinity, if and only if $G(x):=\\int_{-x}^xF(\\mathrm {d}x)$ is regularly varying of index $2-\\gamma$ at the origin ($0<\\gamma<2$)."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.4172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-18T15:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"2cee909f31b6f9f4fb13e054e1a5c3664fc052859a506f34e841338871040f9c","abstract_canon_sha256":"b7198a600c399dd8f61fd85459ea3a386ff9fe71ed6914e5f86f624d2b92e56a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:00.231515Z","signature_b64":"UGtooVswF+t0xK68quTuY1RBQp5BDBIFigV6GIckb4qXoNBKv9JJwPlo94U2eulCCMJoya/jctZQffan2FllCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2390c2544488d4a240005bd81636c63ae23cd4f918f7ca980432fcad545ddcf5","last_reissued_at":"2026-05-18T03:10:00.230967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:00.230967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variance of partial sums of stationary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"George Deligiannidis, Sergey Utev","submitted_at":"2012-05-18T15:07:26Z","abstract_excerpt":"Let $X_1,X_2,\\ldots$ be a centred sequence of weakly stationary random variables with spectral measure $F$ and partial sums $S_n=X_1+\\cdots+X_n$. We show that $\\operatorname {var}(S_n)$ is regularly varying of index $\\gamma$ at infinity, if and only if $G(x):=\\int_{-x}^xF(\\mathrm {d}x)$ is regularly varying of index $2-\\gamma$ at the origin ($0<\\gamma<2$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4172","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.4172","created_at":"2026-05-18T03:10:00.231043+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4172v2","created_at":"2026-05-18T03:10:00.231043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4172","created_at":"2026-05-18T03:10:00.231043+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOIMEVCERDKK","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOIMEVCERDKKEQAA","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOIMEVCE","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL","json":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL.json","graph_json":"https://pith.science/api/pith-number/EOIMEVCERDKKEQAALPMBMNWGHL/graph.json","events_json":"https://pith.science/api/pith-number/EOIMEVCERDKKEQAALPMBMNWGHL/events.json","paper":"https://pith.science/paper/EOIMEVCE"},"agent_actions":{"view_html":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL","download_json":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL.json","view_paper":"https://pith.science/paper/EOIMEVCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4172&json=true","fetch_graph":"https://pith.science/api/pith-number/EOIMEVCERDKKEQAALPMBMNWGHL/graph.json","fetch_events":"https://pith.science/api/pith-number/EOIMEVCERDKKEQAALPMBMNWGHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL/action/storage_attestation","attest_author":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL/action/author_attestation","sign_citation":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL/action/citation_signature","submit_replication":"https://pith.science/pith/EOIMEVCERDKKEQAALPMBMNWGHL/action/replication_record"}},"created_at":"2026-05-18T03:10:00.231043+00:00","updated_at":"2026-05-18T03:10:00.231043+00:00"}