{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:C7BXYLH37MBKWU5S6QMVGCCIRB","short_pith_number":"pith:C7BXYLH3","canonical_record":{"source":{"id":"2105.09032","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2021-05-19T09:56:42Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1a81e97a4d7d7678717a3d3e77442a4eff93fb43f7ac1635aa7eaf5a544efa58","abstract_canon_sha256":"76e3c9009ca8adbef0a0851c8a90db84f2a627ecee830eca97edd428f627e069"},"schema_version":"1.0"},"canonical_sha256":"17c37c2cfbfb02ab53b2f41953084888714c5be0bf4691e9f475fed25d29443b","source":{"kind":"arxiv","id":"2105.09032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.09032","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"2105.09032v1","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.09032","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"C7BXYLH37MBK","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"pith_short_16","alias_value":"C7BXYLH37MBKWU5S","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"pith_short_8","alias_value":"C7BXYLH3","created_at":"2026-07-05T02:41:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:C7BXYLH37MBKWU5S6QMVGCCIRB","target":"record","payload":{"canonical_record":{"source":{"id":"2105.09032","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2021-05-19T09:56:42Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1a81e97a4d7d7678717a3d3e77442a4eff93fb43f7ac1635aa7eaf5a544efa58","abstract_canon_sha256":"76e3c9009ca8adbef0a0851c8a90db84f2a627ecee830eca97edd428f627e069"},"schema_version":"1.0"},"canonical_sha256":"17c37c2cfbfb02ab53b2f41953084888714c5be0bf4691e9f475fed25d29443b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:41:36.469974Z","signature_b64":"xhVO1nfJCVVhpXzZmX9/7Jy2ZO7BtL5OOU1CGUoKWkzusp1gyx6jg3AIWAlbU+IIWoM1KsDxbPlt/p0q0IT7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17c37c2cfbfb02ab53b2f41953084888714c5be0bf4691e9f475fed25d29443b","last_reissued_at":"2026-07-05T02:41:36.469586Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:41:36.469586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.09032","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":"2026-07-05T02:41:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pq3ShfbDHd53vF+xBeAzTQ46tnNpnWlh64NdkML76avLMWSCn8QyfCEoIMqHD+LNTUNWTmBfPULOvC4C8oBNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:42:56.415788Z"},"content_sha256":"6fe071551304da87510bf67cc04d82a75798d419c307e4f96e63c367beefbec1","schema_version":"1.0","event_id":"sha256:6fe071551304da87510bf67cc04d82a75798d419c307e4f96e63c367beefbec1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:C7BXYLH37MBKWU5S6QMVGCCIRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Testing partial conjunction hypotheses under dependency, with applications to meta-analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marina Bogomolov","submitted_at":"2021-05-19T09:56:42Z","abstract_excerpt":"In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of discovering groups containing $u$ or more signals with group-level false discovery rate (FDR) control. This goal can be addressed by multiple testing of partial conjunction hypotheses with a parameter $u,$ which reduce to global null hypotheses for $u=1.$ We consider the case where the partial conjunction $p$-values are combinations of within-group $p$-values, and obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.09032","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/2105.09032/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":"2026-07-05T02:41:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8jJgY/udnotMb+M9FEF5Hcr6e25EpVpwUenZPA/7mIB80weLsQxHef3k0qw9Hd9Ez4CrWpUU7pgX85X1LN3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:42:56.416437Z"},"content_sha256":"0f4eb23c163210d32bbfb2be837a4e037eba7925b56609631947a7f0a701f69b","schema_version":"1.0","event_id":"sha256:0f4eb23c163210d32bbfb2be837a4e037eba7925b56609631947a7f0a701f69b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C7BXYLH37MBKWU5S6QMVGCCIRB/bundle.json","state_url":"https://pith.science/pith/C7BXYLH37MBKWU5S6QMVGCCIRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C7BXYLH37MBKWU5S6QMVGCCIRB/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":"2026-08-11T16:42:56Z","links":{"resolver":"https://pith.science/pith/C7BXYLH37MBKWU5S6QMVGCCIRB","bundle":"https://pith.science/pith/C7BXYLH37MBKWU5S6QMVGCCIRB/bundle.json","state":"https://pith.science/pith/C7BXYLH37MBKWU5S6QMVGCCIRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C7BXYLH37MBKWU5S6QMVGCCIRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:C7BXYLH37MBKWU5S6QMVGCCIRB","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":"76e3c9009ca8adbef0a0851c8a90db84f2a627ecee830eca97edd428f627e069","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2021-05-19T09:56:42Z","title_canon_sha256":"1a81e97a4d7d7678717a3d3e77442a4eff93fb43f7ac1635aa7eaf5a544efa58"},"schema_version":"1.0","source":{"id":"2105.09032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.09032","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"2105.09032v1","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.09032","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"C7BXYLH37MBK","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"pith_short_16","alias_value":"C7BXYLH37MBKWU5S","created_at":"2026-07-05T02:41:36Z"},{"alias_kind":"pith_short_8","alias_value":"C7BXYLH3","created_at":"2026-07-05T02:41:36Z"}],"graph_snapshots":[{"event_id":"sha256:0f4eb23c163210d32bbfb2be837a4e037eba7925b56609631947a7f0a701f69b","target":"graph","created_at":"2026-07-05T02:41:36Z","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/2105.09032/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of discovering groups containing $u$ or more signals with group-level false discovery rate (FDR) control. This goal can be addressed by multiple testing of partial conjunction hypotheses with a parameter $u,$ which reduce to global null hypotheses for $u=1.$ We consider the case where the partial conjunction $p$-values are combinations of within-group $p$-values, and obt","authors_text":"Marina Bogomolov","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2021-05-19T09:56:42Z","title":"Testing partial conjunction hypotheses under dependency, with applications to meta-analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.09032","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":"sha256:6fe071551304da87510bf67cc04d82a75798d419c307e4f96e63c367beefbec1","target":"record","created_at":"2026-07-05T02:41:36Z","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":"76e3c9009ca8adbef0a0851c8a90db84f2a627ecee830eca97edd428f627e069","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2021-05-19T09:56:42Z","title_canon_sha256":"1a81e97a4d7d7678717a3d3e77442a4eff93fb43f7ac1635aa7eaf5a544efa58"},"schema_version":"1.0","source":{"id":"2105.09032","kind":"arxiv","version":1}},"canonical_sha256":"17c37c2cfbfb02ab53b2f41953084888714c5be0bf4691e9f475fed25d29443b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17c37c2cfbfb02ab53b2f41953084888714c5be0bf4691e9f475fed25d29443b","first_computed_at":"2026-07-05T02:41:36.469586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:41:36.469586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xhVO1nfJCVVhpXzZmX9/7Jy2ZO7BtL5OOU1CGUoKWkzusp1gyx6jg3AIWAlbU+IIWoM1KsDxbPlt/p0q0IT7Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:41:36.469974Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.09032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe071551304da87510bf67cc04d82a75798d419c307e4f96e63c367beefbec1","sha256:0f4eb23c163210d32bbfb2be837a4e037eba7925b56609631947a7f0a701f69b"],"state_sha256":"89055db5ceeedec3c374a84c29041103d9917fe49ceadf2e85cca3cf7b72b64f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLONlgmT2bpHOa9+am4qj1dsfvj1sGf3boBHHTYrzg/FJ8B7Er4QcIwTX5XZWAdhrza51YnTG7gGwGtLU1/NBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:42:56.423254Z","bundle_sha256":"ae84e8ceff32cec224309af6eb9aa17628fe4f271efa54c85d8d7c1a10cb460e"}}