{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5FCKYSQHEHCUCVWMEZBAYNOK3J","short_pith_number":"pith:5FCKYSQH","canonical_record":{"source":{"id":"1510.04351","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2015-10-14T23:42:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6d1635207ebd06b9cf666bf5faa1118194f9ebfcb46d997ed7b70351a828a677","abstract_canon_sha256":"04ff314eb7b6cfa063d4188b2c4c0a0be9584ab233cc0846cc4c5efa5604ac74"},"schema_version":"1.0"},"canonical_sha256":"e944ac4a0721c54156cc26420c35cada53ba08041497a2c3665b66005832fc78","source":{"kind":"arxiv","id":"1510.04351","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04351","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04351v3","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04351","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"5FCKYSQHEHCU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5FCKYSQHEHCUCVWM","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5FCKYSQH","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5FCKYSQHEHCUCVWMEZBAYNOK3J","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04351","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2015-10-14T23:42:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6d1635207ebd06b9cf666bf5faa1118194f9ebfcb46d997ed7b70351a828a677","abstract_canon_sha256":"04ff314eb7b6cfa063d4188b2c4c0a0be9584ab233cc0846cc4c5efa5604ac74"},"schema_version":"1.0"},"canonical_sha256":"e944ac4a0721c54156cc26420c35cada53ba08041497a2c3665b66005832fc78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:43.761184Z","signature_b64":"ScAOznwjiYszVDCETwKN1Nws4Ypa7fxq4j7Qs9PP0yGewlxcF8zC+EYLwaKFbcEEy9q48cZtqH/c/HccS1XJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e944ac4a0721c54156cc26420c35cada53ba08041497a2c3665b66005832fc78","last_reissued_at":"2026-05-18T01:11:43.760851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:43.760851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04351","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jo/8BqRMJ/QbJbLiCjWJehJn+Jy+Y4W5jvDuXDI+KymglsIndrgrVKVtjNgEUQJiYxVS8O7oxCNetppqQUtBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T06:03:20.860849Z"},"content_sha256":"48b3a151554aba83a24c795f12161b706ccf059674d34df056524c4f748caba0","schema_version":"1.0","event_id":"sha256:48b3a151554aba83a24c795f12161b706ccf059674d34df056524c4f748caba0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5FCKYSQHEHCUCVWMEZBAYNOK3J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stopping time property of thresholds of Storey-type FDR procedures","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"R.W. Doerge, Xiongzhi Chen","submitted_at":"2015-10-14T23:42:56Z","abstract_excerpt":"For multiple testing, we introduce Storey-type FDR procedures and the concept of \"regular estimator of the proportion of true nulls\". We show that the rejection threshold of a Storey-type FDR procedure is a stopping time with respect to the backward filtration generated by the p-values and that a Storey-type FDR estimator at this rejection threshold equals the pre-specified FDR level, when the estimator of the proportion of true nulls is regular. These results hold regardless of the dependence among or the types of distributions of the p-values. They directly imply that a Storey-type FDR proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04351","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:11:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fd8ZI17GdO8OgpZJvX455/aYMN7qjrgtsbBhT1D6xm6OhRt81ljLuC+CmF5Yc9mmNFlGbSUqtnJw6Ud9JkZjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T06:03:20.861184Z"},"content_sha256":"48795ac35bed8a5321cc0d3bf90661663359492b670c4721da14dba93e9715fb","schema_version":"1.0","event_id":"sha256:48795ac35bed8a5321cc0d3bf90661663359492b670c4721da14dba93e9715fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J/bundle.json","state_url":"https://pith.science/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J/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":"2026-06-28T06:03:20Z","links":{"resolver":"https://pith.science/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J","bundle":"https://pith.science/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J/bundle.json","state":"https://pith.science/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FCKYSQHEHCUCVWMEZBAYNOK3J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5FCKYSQHEHCUCVWMEZBAYNOK3J","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":"04ff314eb7b6cfa063d4188b2c4c0a0be9584ab233cc0846cc4c5efa5604ac74","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2015-10-14T23:42:56Z","title_canon_sha256":"6d1635207ebd06b9cf666bf5faa1118194f9ebfcb46d997ed7b70351a828a677"},"schema_version":"1.0","source":{"id":"1510.04351","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04351","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04351v3","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04351","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"5FCKYSQHEHCU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5FCKYSQHEHCUCVWM","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5FCKYSQH","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:48795ac35bed8a5321cc0d3bf90661663359492b670c4721da14dba93e9715fb","target":"graph","created_at":"2026-05-18T01:11:43Z","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 multiple testing, we introduce Storey-type FDR procedures and the concept of \"regular estimator of the proportion of true nulls\". We show that the rejection threshold of a Storey-type FDR procedure is a stopping time with respect to the backward filtration generated by the p-values and that a Storey-type FDR estimator at this rejection threshold equals the pre-specified FDR level, when the estimator of the proportion of true nulls is regular. These results hold regardless of the dependence among or the types of distributions of the p-values. They directly imply that a Storey-type FDR proce","authors_text":"R.W. Doerge, Xiongzhi Chen","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2015-10-14T23:42:56Z","title":"Stopping time property of thresholds of Storey-type FDR procedures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04351","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":"sha256:48b3a151554aba83a24c795f12161b706ccf059674d34df056524c4f748caba0","target":"record","created_at":"2026-05-18T01:11:43Z","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":"04ff314eb7b6cfa063d4188b2c4c0a0be9584ab233cc0846cc4c5efa5604ac74","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2015-10-14T23:42:56Z","title_canon_sha256":"6d1635207ebd06b9cf666bf5faa1118194f9ebfcb46d997ed7b70351a828a677"},"schema_version":"1.0","source":{"id":"1510.04351","kind":"arxiv","version":3}},"canonical_sha256":"e944ac4a0721c54156cc26420c35cada53ba08041497a2c3665b66005832fc78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e944ac4a0721c54156cc26420c35cada53ba08041497a2c3665b66005832fc78","first_computed_at":"2026-05-18T01:11:43.760851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:43.760851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ScAOznwjiYszVDCETwKN1Nws4Ypa7fxq4j7Qs9PP0yGewlxcF8zC+EYLwaKFbcEEy9q48cZtqH/c/HccS1XJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:43.761184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04351","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48b3a151554aba83a24c795f12161b706ccf059674d34df056524c4f748caba0","sha256:48795ac35bed8a5321cc0d3bf90661663359492b670c4721da14dba93e9715fb"],"state_sha256":"f3bc7f00774e82a76a150222544cc0952d05048962ae8d22097ca8e40ce2a4d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8CgwfWXNsVrQIfkOCRqwmQ7Bn0b660fWM6DI1VjI/kgxWutPLhfWX8dvPgH65VcSE+sNNoWVmqc7XFqEzZ49DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T06:03:20.863043Z","bundle_sha256":"0cf4e6d06e849d03b7a577d92bf45ce6223a074fb15a751c31e400d3ca874cf2"}}