{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:FSNA6VR76YVGXQJMQLOXO6GDEE","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":"ad23805bef4a998be91b20ba9c9c022377115e81ad6621318b346d32d5925b64","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2006-08-13T07:41:16Z","title_canon_sha256":"83c5025fdd426e0713d72a84bbf98c33eea5eb333da478e85fe97327b29b4c4a"},"schema_version":"1.0","source":{"id":"math/0608311","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608311","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608311v3","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608311","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"FSNA6VR76YVG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"FSNA6VR76YVGXQJM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"FSNA6VR7","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:a0f5b34a6984ffc92e013cf384a4ad5585476942edec618a71ab87c799c0c10f","target":"graph","created_at":"2026-05-18T01:05:22Z","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":"For arrays $(S_{i,j})_{1\\leq i\\leq j}$ of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process $(S_{1,n})_{n=1}^{\\infty}$ can be bounded in terms of a measure of the ``mean subadditivity'' of the process $(S_{i,j})_{1\\leq i\\leq j}$. We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon--MacMillan--Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.","authors_text":"Michael Hochman","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2006-08-13T07:41:16Z","title":"Upcrossing inequalities for stationary sequences and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608311","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":"sha256:906273b1c8996dccdaacb9765a50f77cd38ef1e0457ac4a4f09bddddd9d3e818","target":"record","created_at":"2026-05-18T01:05:22Z","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":"ad23805bef4a998be91b20ba9c9c022377115e81ad6621318b346d32d5925b64","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2006-08-13T07:41:16Z","title_canon_sha256":"83c5025fdd426e0713d72a84bbf98c33eea5eb333da478e85fe97327b29b4c4a"},"schema_version":"1.0","source":{"id":"math/0608311","kind":"arxiv","version":3}},"canonical_sha256":"2c9a0f563ff62a6bc12c82dd7778c3211ad7fb724a9e4e8fad560985eb833da7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c9a0f563ff62a6bc12c82dd7778c3211ad7fb724a9e4e8fad560985eb833da7","first_computed_at":"2026-05-18T01:05:22.605875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.605875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l9QMK6zyUWWQ5g+9Y/ifWUyJafyxqy6LzsllOmcH5zCSDxwV0LHp184yLpCZ4AljFC5D3+/V1ktXSW+bPT7xAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.606275Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608311","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:906273b1c8996dccdaacb9765a50f77cd38ef1e0457ac4a4f09bddddd9d3e818","sha256:a0f5b34a6984ffc92e013cf384a4ad5585476942edec618a71ab87c799c0c10f"],"state_sha256":"feb46700a1b95153618134d5ffdd26c1b8a9d06daba78beddedd9b590bd853b3"}