{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OV4SHSPISVKEJTECCWG3I5SM4I","short_pith_number":"pith:OV4SHSPI","canonical_record":{"source":{"id":"2502.01244","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-03T11:08:18Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"81ba5f5aa9e33e6b0c5a2b16dc98d0c95fd16e53f316d6d636d040ad927a3793","abstract_canon_sha256":"5cb60b79a752b414660273af11aef7c1512e9a0c72080c0f8d9567f6e9ccbfa0"},"schema_version":"1.0"},"canonical_sha256":"757923c9e8955444cc82158db4764ce23c4e1872ccba6053d3fd1d40b06b7510","source":{"kind":"arxiv","id":"2502.01244","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OV4SHSPISVKEJTECCWG3I5SM4I","target":"record","payload":{"canonical_record":{"source":{"id":"2502.01244","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-03T11:08:18Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"81ba5f5aa9e33e6b0c5a2b16dc98d0c95fd16e53f316d6d636d040ad927a3793","abstract_canon_sha256":"5cb60b79a752b414660273af11aef7c1512e9a0c72080c0f8d9567f6e9ccbfa0"},"schema_version":"1.0"},"canonical_sha256":"757923c9e8955444cc82158db4764ce23c4e1872ccba6053d3fd1d40b06b7510","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:44.750958Z","signature_b64":"b7bZwtLh9YqrxlDtvJVOgMz41vRlryNYKd2/eghbXW2bPl0XnEkw265ragBFS+3vhlnNXc1czOmgZzjpVEC8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"757923c9e8955444cc82158db4764ce23c4e1872ccba6053d3fd1d40b06b7510","last_reissued_at":"2026-07-05T10:08:44.750447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:44.750447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.01244","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQzJ8lfFe5ndH7a6hygBWFsqdcW+Jsi3pQUgqvKfXwpMQUiD/r8ZXSuXfYUpOiDMLLpT4zejmDrvMpNAR83IBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:30:14.609816Z"},"content_sha256":"6e8b0e501edb4eb794106ca73973dfc579cf04d3609e871030debd6a45701309","schema_version":"1.0","event_id":"sha256:6e8b0e501edb4eb794106ca73973dfc579cf04d3609e871030debd6a45701309"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OV4SHSPISVKEJTECCWG3I5SM4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform mean estimation for monotonic processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eugenio Clerico, Hamish E Flynn, Patrick Rebeschini","submitted_at":"2025-02-03T11:08:18Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01244","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01244/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1YOpDPPHxXgIYrapMB0pw9HrSLU9bnfCTKdMZrRDRoyTTCDbuunAN3E4+P/prH1WfcTrGAi4XBQBPKVGNXzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:30:14.610320Z"},"content_sha256":"d7b6a49ee970b49d3a4ebe97df8261e5ab1695c8798d8cd5bfab69bdb94161e7","schema_version":"1.0","event_id":"sha256:d7b6a49ee970b49d3a4ebe97df8261e5ab1695c8798d8cd5bfab69bdb94161e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OV4SHSPISVKEJTECCWG3I5SM4I/bundle.json","state_url":"https://pith.science/pith/OV4SHSPISVKEJTECCWG3I5SM4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OV4SHSPISVKEJTECCWG3I5SM4I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T22:30:14Z","links":{"resolver":"https://pith.science/pith/OV4SHSPISVKEJTECCWG3I5SM4I","bundle":"https://pith.science/pith/OV4SHSPISVKEJTECCWG3I5SM4I/bundle.json","state":"https://pith.science/pith/OV4SHSPISVKEJTECCWG3I5SM4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OV4SHSPISVKEJTECCWG3I5SM4I/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkmqHi6k6f+v0QzCHU/8UDfzaKi3X5tU7R08lqzY8tVbuqHa+mNUjbWNUkwa38g9XePegnxsXvRETs7+EpSiCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T22:30:14.615086Z","bundle_sha256":"c178c09342cede0ee80cef421e60c6f92babecbafada4fbcca279535453d3e2a"}}