{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SDTZBJ6JOF25MDQETCRKPKIUPG","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":"cb39d10c59c3a3b16a893b4f40f744bd3287da0e48b6a89b9ba0d5f47e905eef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-08T20:05:17Z","title_canon_sha256":"e91ba1af0fc308e73d9caf0d7a7cd5d10536e6208af0e1af9105024a5010efb9"},"schema_version":"1.0","source":{"id":"1012.1842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1842","created_at":"2026-05-18T04:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1842v1","created_at":"2026-05-18T04:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1842","created_at":"2026-05-18T04:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"SDTZBJ6JOF25","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SDTZBJ6JOF25MDQE","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SDTZBJ6J","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:2372450298f23379e8f1791d0f1930273ffae2c46ef1af530ce0ea6bc7ff8513","target":"graph","created_at":"2026-05-18T04:33:51Z","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":"In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced $\\rho'$-mixing condition.","authors_text":"Cristina Tone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-08T20:05:17Z","title":"Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1842","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":"sha256:58defa3fd078da2dc543723359f2ba4c33f50105b2f57c71459fdf88af3e8774","target":"record","created_at":"2026-05-18T04:33:51Z","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":"cb39d10c59c3a3b16a893b4f40f744bd3287da0e48b6a89b9ba0d5f47e905eef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-08T20:05:17Z","title_canon_sha256":"e91ba1af0fc308e73d9caf0d7a7cd5d10536e6208af0e1af9105024a5010efb9"},"schema_version":"1.0","source":{"id":"1012.1842","kind":"arxiv","version":1}},"canonical_sha256":"90e790a7c97175d60e0498a2a7a914799ed9a6de7b58e9b2d530df4e3e6bad21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90e790a7c97175d60e0498a2a7a914799ed9a6de7b58e9b2d530df4e3e6bad21","first_computed_at":"2026-05-18T04:33:51.176236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:51.176236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xrugQEvts9lIcBYZL9xIbrcHo/mVXOboE/QHOqmRGlTP/YRNGn2t9ISwxFptlCy133i+N980McxBkBzZFsqvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:51.176872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58defa3fd078da2dc543723359f2ba4c33f50105b2f57c71459fdf88af3e8774","sha256:2372450298f23379e8f1791d0f1930273ffae2c46ef1af530ce0ea6bc7ff8513"],"state_sha256":"659ff7f7c12e480c856f14ad92e8dd086495fd490ec1448202b3a63cb301e69d"}