{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RGYSA4WINZIGPN5WX4FGXRQMID","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":"6a0fc6305e2a1a486d3f0a981c795c59ac6cd52694b4afd70ac3f39b32bf1a2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-03T18:54:28Z","title_canon_sha256":"02d26422d1144548dff8dd1e67975115dd8b577d3620018fcd17bac0af5070a2"},"schema_version":"1.0","source":{"id":"1706.00991","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00991","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00991v3","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00991","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"RGYSA4WINZIG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RGYSA4WINZIGPN5W","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RGYSA4WI","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:272d7553b30b56408c00f4e55131ed569b567ec1a417aa2514a3f2f0470159ac","target":"graph","created_at":"2026-05-18T00:03:29Z","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 Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. An upper bound for a new class of random fields is obtained here by induction in dimension.\n  Version 3.\n  Sect 1. Stationarity, being not essential in the proofs, is removed from the definitions and the main result formulation.\n  Sect. 2. $[C,2C]$ instead of $[C_1,2C_1]$ before Prop. 2.6; $ a\\ge1$ instead of $a\\ge C/C_1$ in the last proof; Remark 2.5 added; supremum over shifts in (2.2) (formerly (2.3)","authors_text":"Boris Tsirelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-03T18:54:28Z","title":"Linear response and moderate deviations: hierarchical approach. II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00991","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:ca70bd0ba659f7360dfcaafecec365a3c221c14d834c38d8091a780f54aa0a55","target":"record","created_at":"2026-05-18T00:03:29Z","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":"6a0fc6305e2a1a486d3f0a981c795c59ac6cd52694b4afd70ac3f39b32bf1a2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-03T18:54:28Z","title_canon_sha256":"02d26422d1144548dff8dd1e67975115dd8b577d3620018fcd17bac0af5070a2"},"schema_version":"1.0","source":{"id":"1706.00991","kind":"arxiv","version":3}},"canonical_sha256":"89b12072c86e5067b7b6bf0a6bc60c40d3dfc0821f94cf014dd10631bf639948","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89b12072c86e5067b7b6bf0a6bc60c40d3dfc0821f94cf014dd10631bf639948","first_computed_at":"2026-05-18T00:03:29.676800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:29.676800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ALF2ahk/wdqeuGfw4DoApfkSaq677qe23c/eNcFZaXCDb306bI+u/fQvqq8w/0IVqkZ3AD+PI6EcRNgBHNwLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:29.677501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00991","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca70bd0ba659f7360dfcaafecec365a3c221c14d834c38d8091a780f54aa0a55","sha256:272d7553b30b56408c00f4e55131ed569b567ec1a417aa2514a3f2f0470159ac"],"state_sha256":"288fecbff2a1e3f87071ea8bb8bfe1e07cacb82542531ae6433d66ffd83607fe"}