{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LD665ZZPFACGHGBUTYVRRDBGGJ","short_pith_number":"pith:LD665ZZP","canonical_record":{"source":{"id":"2504.00856","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2025-04-01T14:45:49Z","cross_cats_sorted":[],"title_canon_sha256":"590f2aab2f3a893375ee111939fce0b2c504dc7493c19cbd10d89e269d7d214b","abstract_canon_sha256":"c75baf73fb6addb062c612c3d71554dbec3531958f39c65d53daf5f70a785509"},"schema_version":"1.0"},"canonical_sha256":"58fdeee72f28046398349e2b188c263251eb890a1edf958f87ea8320325015ca","source":{"kind":"arxiv","id":"2504.00856","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.00856","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"2504.00856v4","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.00856","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"LD665ZZPFACG","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_16","alias_value":"LD665ZZPFACGHGBU","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_8","alias_value":"LD665ZZP","created_at":"2026-06-25T00:18:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LD665ZZPFACGHGBUTYVRRDBGGJ","target":"record","payload":{"canonical_record":{"source":{"id":"2504.00856","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2025-04-01T14:45:49Z","cross_cats_sorted":[],"title_canon_sha256":"590f2aab2f3a893375ee111939fce0b2c504dc7493c19cbd10d89e269d7d214b","abstract_canon_sha256":"c75baf73fb6addb062c612c3d71554dbec3531958f39c65d53daf5f70a785509"},"schema_version":"1.0"},"canonical_sha256":"58fdeee72f28046398349e2b188c263251eb890a1edf958f87ea8320325015ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T00:18:11.071841Z","signature_b64":"wpgArXfQEgw6an3vjwwGhWRQfwftp1lZBWAV2YfLw+F5c4LScnmPkuGHyCUOZOR0L3O3s1YF9eiGC57fqefdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58fdeee72f28046398349e2b188c263251eb890a1edf958f87ea8320325015ca","last_reissued_at":"2026-06-25T00:18:11.071411Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T00:18:11.071411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.00856","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-25T00:18:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pPrl8irC5e2JtodOBmULTnlC3Nq0QJWmS9I3WeErSIaAGYJD8/7EqRo4KEJKNz5Ep1m+zpROCPncHJM8r2vpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T05:07:32.771584Z"},"content_sha256":"14d615247b2be61341188c156df1840abcc43bb18d7aa69b3fbfec28fe515076","schema_version":"1.0","event_id":"sha256:14d615247b2be61341188c156df1840abcc43bb18d7aa69b3fbfec28fe515076"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LD665ZZPFACGHGBUTYVRRDBGGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group Sequential Design with Posterior and Posterior Predictive Probabilities","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Luke Hagar, Marina B. Klein, Shirin Golchi","submitted_at":"2025-04-01T14:45:49Z","abstract_excerpt":"Group sequential designs drive innovation in clinical, industrial, and corporate settings. Early stopping for failure in sequential designs conserves experimental resources, whereas early stopping for success accelerates access to improved interventions. Bayesian decision procedures provide a formal and intuitive framework for early stopping using posterior and posterior predictive probabilities. Design parameters including decision thresholds and sample sizes are chosen to control the error probabilities associated with the sequential decision process. These choices are routinely made based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.00856","kind":"arxiv","version":4},"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/2504.00856/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":"2026-06-25T00:18:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wSoyO3Q5bEkKbHUWYb2M048RLoEnAN39e+gh2DL2SKqFQfHAZ8S07DwsmP+cBVy5cAM1IDEm2erK4sNqYqveBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T05:07:32.772721Z"},"content_sha256":"e352727e9160187d3e97532dd1cc72dd0e7c9282132d0387c96df8b3dd2a503c","schema_version":"1.0","event_id":"sha256:e352727e9160187d3e97532dd1cc72dd0e7c9282132d0387c96df8b3dd2a503c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LD665ZZPFACGHGBUTYVRRDBGGJ/bundle.json","state_url":"https://pith.science/pith/LD665ZZPFACGHGBUTYVRRDBGGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LD665ZZPFACGHGBUTYVRRDBGGJ/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":"2026-08-22T05:07:32Z","links":{"resolver":"https://pith.science/pith/LD665ZZPFACGHGBUTYVRRDBGGJ","bundle":"https://pith.science/pith/LD665ZZPFACGHGBUTYVRRDBGGJ/bundle.json","state":"https://pith.science/pith/LD665ZZPFACGHGBUTYVRRDBGGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LD665ZZPFACGHGBUTYVRRDBGGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LD665ZZPFACGHGBUTYVRRDBGGJ","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":"c75baf73fb6addb062c612c3d71554dbec3531958f39c65d53daf5f70a785509","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2025-04-01T14:45:49Z","title_canon_sha256":"590f2aab2f3a893375ee111939fce0b2c504dc7493c19cbd10d89e269d7d214b"},"schema_version":"1.0","source":{"id":"2504.00856","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.00856","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"2504.00856v4","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.00856","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"LD665ZZPFACG","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_16","alias_value":"LD665ZZPFACGHGBU","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_8","alias_value":"LD665ZZP","created_at":"2026-06-25T00:18:11Z"}],"graph_snapshots":[{"event_id":"sha256:e352727e9160187d3e97532dd1cc72dd0e7c9282132d0387c96df8b3dd2a503c","target":"graph","created_at":"2026-06-25T00:18:11Z","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/2504.00856/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Group sequential designs drive innovation in clinical, industrial, and corporate settings. Early stopping for failure in sequential designs conserves experimental resources, whereas early stopping for success accelerates access to improved interventions. Bayesian decision procedures provide a formal and intuitive framework for early stopping using posterior and posterior predictive probabilities. Design parameters including decision thresholds and sample sizes are chosen to control the error probabilities associated with the sequential decision process. These choices are routinely made based o","authors_text":"Luke Hagar, Marina B. Klein, Shirin Golchi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2025-04-01T14:45:49Z","title":"Group Sequential Design with Posterior and Posterior Predictive Probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.00856","kind":"arxiv","version":4},"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":"sha256:14d615247b2be61341188c156df1840abcc43bb18d7aa69b3fbfec28fe515076","target":"record","created_at":"2026-06-25T00:18:11Z","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":"c75baf73fb6addb062c612c3d71554dbec3531958f39c65d53daf5f70a785509","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2025-04-01T14:45:49Z","title_canon_sha256":"590f2aab2f3a893375ee111939fce0b2c504dc7493c19cbd10d89e269d7d214b"},"schema_version":"1.0","source":{"id":"2504.00856","kind":"arxiv","version":4}},"canonical_sha256":"58fdeee72f28046398349e2b188c263251eb890a1edf958f87ea8320325015ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58fdeee72f28046398349e2b188c263251eb890a1edf958f87ea8320325015ca","first_computed_at":"2026-06-25T00:18:11.071411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T00:18:11.071411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wpgArXfQEgw6an3vjwwGhWRQfwftp1lZBWAV2YfLw+F5c4LScnmPkuGHyCUOZOR0L3O3s1YF9eiGC57fqefdBA==","signature_status":"signed_v1","signed_at":"2026-06-25T00:18:11.071841Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.00856","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14d615247b2be61341188c156df1840abcc43bb18d7aa69b3fbfec28fe515076","sha256:e352727e9160187d3e97532dd1cc72dd0e7c9282132d0387c96df8b3dd2a503c"],"state_sha256":"63e9655b816a5e8c8f7a4300728611ae81a1d1f83ffcc5b70aeab93381e0bfe8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"seclY86s/Jc54M2iZ27jdOR8gSDcsFD0NrcSMr33mRGv9GqlG0jor3OSEZcoasBGBmu5qZ0IKXh1MyYrsXtwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T05:07:32.778595Z","bundle_sha256":"e3bd4b351ec125676e8718fe46ec2fa014cb167b99723321afeafadd5b25ca0f"}}