{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OV4SHSPISVKEJTECCWG3I5SM4I","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":"5cb60b79a752b414660273af11aef7c1512e9a0c72080c0f8d9567f6e9ccbfa0","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-03T11:08:18Z","title_canon_sha256":"81ba5f5aa9e33e6b0c5a2b16dc98d0c95fd16e53f316d6d636d040ad927a3793"},"schema_version":"1.0","source":{"id":"2502.01244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01244","created_at":"2026-07-05T10:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01244v1","created_at":"2026-07-05T10:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01244","created_at":"2026-07-05T10:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"OV4SHSPISVKE","created_at":"2026-07-05T10:08:44Z"},{"alias_kind":"pith_short_16","alias_value":"OV4SHSPISVKEJTEC","created_at":"2026-07-05T10:08:44Z"},{"alias_kind":"pith_short_8","alias_value":"OV4SHSPI","created_at":"2026-07-05T10:08:44Z"}],"graph_snapshots":[{"event_id":"sha256:d7b6a49ee970b49d3a4ebe97df8261e5ab1695c8798d8cd5bfab69bdb94161e7","target":"graph","created_at":"2026-07-05T10:08:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.01244/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach leverages the coin-betting framework, and inherits several favourable characteristics of coin-betting methods. In particular, for each point in the domain of the mean function, we obtain anytime-valid confidence intervals that are numerically tight and adapt to the variance of the observations. To derive uniform confidence bands, we employ a continuous union ","authors_text":"Eugenio Clerico, Hamish E Flynn, Patrick Rebeschini","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-03T11:08:18Z","title":"Uniform mean estimation for monotonic processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01244","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":"sha256:6e8b0e501edb4eb794106ca73973dfc579cf04d3609e871030debd6a45701309","target":"record","created_at":"2026-07-05T10:08:44Z","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":"5cb60b79a752b414660273af11aef7c1512e9a0c72080c0f8d9567f6e9ccbfa0","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-03T11:08:18Z","title_canon_sha256":"81ba5f5aa9e33e6b0c5a2b16dc98d0c95fd16e53f316d6d636d040ad927a3793"},"schema_version":"1.0","source":{"id":"2502.01244","kind":"arxiv","version":1}},"canonical_sha256":"757923c9e8955444cc82158db4764ce23c4e1872ccba6053d3fd1d40b06b7510","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"757923c9e8955444cc82158db4764ce23c4e1872ccba6053d3fd1d40b06b7510","first_computed_at":"2026-07-05T10:08:44.750447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:08:44.750447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b7bZwtLh9YqrxlDtvJVOgMz41vRlryNYKd2/eghbXW2bPl0XnEkw265ragBFS+3vhlnNXc1czOmgZzjpVEC8Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:08:44.750958Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.01244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e8b0e501edb4eb794106ca73973dfc579cf04d3609e871030debd6a45701309","sha256:d7b6a49ee970b49d3a4ebe97df8261e5ab1695c8798d8cd5bfab69bdb94161e7"],"state_sha256":"14173ecd8e8671236767f343e768666dcf7aca43b262fd02416e30a2855b5fcc"}