{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JN73UGMM3LE5UKTC4SZQZV7TMD","short_pith_number":"pith:JN73UGMM","canonical_record":{"source":{"id":"1106.2790","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-06-14T19:13:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"dd058f7c9b1622f91bf9c0743ec25b620580351963e14b320573609bf42e533c","abstract_canon_sha256":"644dfb937426a42b8b9c9c7dfde170dc1396a1fdf8fab707f3147a3bef617e63"},"schema_version":"1.0"},"canonical_sha256":"4b7fba198cdac9da2a62e4b30cd7f360eba2a8229ffaae22afd1daaf11a76587","source":{"kind":"arxiv","id":"1106.2790","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2790","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2790v2","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2790","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"JN73UGMM3LE5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JN73UGMM3LE5UKTC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JN73UGMM","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JN73UGMM3LE5UKTC4SZQZV7TMD","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2790","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-06-14T19:13:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"dd058f7c9b1622f91bf9c0743ec25b620580351963e14b320573609bf42e533c","abstract_canon_sha256":"644dfb937426a42b8b9c9c7dfde170dc1396a1fdf8fab707f3147a3bef617e63"},"schema_version":"1.0"},"canonical_sha256":"4b7fba198cdac9da2a62e4b30cd7f360eba2a8229ffaae22afd1daaf11a76587","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:06.996125Z","signature_b64":"cDrG6dTYTtzJQBxHTU9PNcec2aMvMj5dgH9luH77qW0YQrdyDkSQhDyWJO/F9jjjJ/FbNbLM0Z3sIXw6JUFHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7fba198cdac9da2a62e4b30cd7f360eba2a8229ffaae22afd1daaf11a76587","last_reissued_at":"2026-05-18T03:04:06.995695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:06.995695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2790","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQd3anKLbOARr7N5zW/CdyXrgISR1uiw7dOI5nzQ0hSAC0oiF87psuUyslON0Y6NjvV3hz5xzyakOUi3nK1kAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:21:59.386903Z"},"content_sha256":"6f52ea17cf3260e7f0656f708d68b7a0841dbeee54fd078f5de2b3855b22136f","schema_version":"1.0","event_id":"sha256:6f52ea17cf3260e7f0656f708d68b7a0841dbeee54fd078f5de2b3855b22136f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JN73UGMM3LE5UKTC4SZQZV7TMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sequential Analysis of Cox Model under Response Dependent Allocation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Gongjun Xu, Xiaolong Luo, Zhiliang Ying","submitted_at":"2011-06-14T19:13:06Z","abstract_excerpt":"Sellke and Siegmund (1983) developed the Brownian approximation to the Cox partial likelihood score as a process of calendar time, laying the foundation for group sequential analysis of survival studies. We extend their results to cover situations in which treatment allocations may depend on observed outcomes. The new development makes use of the entry time and calendar time along with the corresponding $\\sigma$-filtrations to handle the natural information accumulation. Large sample properties are established under suitable regularity conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2790","kind":"arxiv","version":2},"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":"2026-05-18T03:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwC0+kmJa7HKijYvxK2ZhOmiktz2ceRo/BhU5D2wEqzMfTLJ/AbEJCk6WSS05w4/DJT+nWXvw38aJz2PUYx7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:21:59.387247Z"},"content_sha256":"d20961f2a8f8eaf199bdeaeb9045f467ffe83fc1bf8f02da6319bcaf7f364ae0","schema_version":"1.0","event_id":"sha256:d20961f2a8f8eaf199bdeaeb9045f467ffe83fc1bf8f02da6319bcaf7f364ae0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JN73UGMM3LE5UKTC4SZQZV7TMD/bundle.json","state_url":"https://pith.science/pith/JN73UGMM3LE5UKTC4SZQZV7TMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JN73UGMM3LE5UKTC4SZQZV7TMD/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":"2026-06-01T05:21:59Z","links":{"resolver":"https://pith.science/pith/JN73UGMM3LE5UKTC4SZQZV7TMD","bundle":"https://pith.science/pith/JN73UGMM3LE5UKTC4SZQZV7TMD/bundle.json","state":"https://pith.science/pith/JN73UGMM3LE5UKTC4SZQZV7TMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JN73UGMM3LE5UKTC4SZQZV7TMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JN73UGMM3LE5UKTC4SZQZV7TMD","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":"644dfb937426a42b8b9c9c7dfde170dc1396a1fdf8fab707f3147a3bef617e63","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-06-14T19:13:06Z","title_canon_sha256":"dd058f7c9b1622f91bf9c0743ec25b620580351963e14b320573609bf42e533c"},"schema_version":"1.0","source":{"id":"1106.2790","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2790","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2790v2","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2790","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"JN73UGMM3LE5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JN73UGMM3LE5UKTC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JN73UGMM","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:d20961f2a8f8eaf199bdeaeb9045f467ffe83fc1bf8f02da6319bcaf7f364ae0","target":"graph","created_at":"2026-05-18T03:04:06Z","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":"Sellke and Siegmund (1983) developed the Brownian approximation to the Cox partial likelihood score as a process of calendar time, laying the foundation for group sequential analysis of survival studies. We extend their results to cover situations in which treatment allocations may depend on observed outcomes. The new development makes use of the entry time and calendar time along with the corresponding $\\sigma$-filtrations to handle the natural information accumulation. Large sample properties are established under suitable regularity conditions.","authors_text":"Gongjun Xu, Xiaolong Luo, Zhiliang Ying","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-06-14T19:13:06Z","title":"Sequential Analysis of Cox Model under Response Dependent Allocation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2790","kind":"arxiv","version":2},"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":"sha256:6f52ea17cf3260e7f0656f708d68b7a0841dbeee54fd078f5de2b3855b22136f","target":"record","created_at":"2026-05-18T03:04:06Z","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":"644dfb937426a42b8b9c9c7dfde170dc1396a1fdf8fab707f3147a3bef617e63","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-06-14T19:13:06Z","title_canon_sha256":"dd058f7c9b1622f91bf9c0743ec25b620580351963e14b320573609bf42e533c"},"schema_version":"1.0","source":{"id":"1106.2790","kind":"arxiv","version":2}},"canonical_sha256":"4b7fba198cdac9da2a62e4b30cd7f360eba2a8229ffaae22afd1daaf11a76587","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7fba198cdac9da2a62e4b30cd7f360eba2a8229ffaae22afd1daaf11a76587","first_computed_at":"2026-05-18T03:04:06.995695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:06.995695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDrG6dTYTtzJQBxHTU9PNcec2aMvMj5dgH9luH77qW0YQrdyDkSQhDyWJO/F9jjjJ/FbNbLM0Z3sIXw6JUFHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:06.996125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2790","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f52ea17cf3260e7f0656f708d68b7a0841dbeee54fd078f5de2b3855b22136f","sha256:d20961f2a8f8eaf199bdeaeb9045f467ffe83fc1bf8f02da6319bcaf7f364ae0"],"state_sha256":"50aa3f648c41aae93d8f3edd5f9169c32716836d1e4fba583b2b932dacdb7362"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o7uU5xGAYtnpIGbkR3o+HsLzdZgoFbMWhHM45IDOXTCK3sSjwMkz6p2bGjtaffRLc/Y1EbgTxXRRbj3GamS7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:21:59.389444Z","bundle_sha256":"cdaae8528b3ab3387307aa9db48696638bcd4ed8a661b08566c2f05b4c741619"}}