{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:H4PTM4NEDJNWCYGBJ4O4EKY5M6","short_pith_number":"pith:H4PTM4NE","canonical_record":{"source":{"id":"1011.5775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-26T13:02:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f1cd8b2927c6f2220605e64e5dc0f1d3d5158aeab52cf241a7bc54c77537544e","abstract_canon_sha256":"e37cce2018f57cce648260ea3e8eb1dd7e558e230614757289b8c67bb3bdd5ed"},"schema_version":"1.0"},"canonical_sha256":"3f1f3671a41a5b6160c14f1dc22b1d6796dc080eb8ffbebe7d535b80bc1bc2d2","source":{"kind":"arxiv","id":"1011.5775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5775","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5775v1","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5775","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"H4PTM4NEDJNW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H4PTM4NEDJNWCYGB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H4PTM4NE","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:H4PTM4NEDJNWCYGBJ4O4EKY5M6","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-26T13:02:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f1cd8b2927c6f2220605e64e5dc0f1d3d5158aeab52cf241a7bc54c77537544e","abstract_canon_sha256":"e37cce2018f57cce648260ea3e8eb1dd7e558e230614757289b8c67bb3bdd5ed"},"schema_version":"1.0"},"canonical_sha256":"3f1f3671a41a5b6160c14f1dc22b1d6796dc080eb8ffbebe7d535b80bc1bc2d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:38.503272Z","signature_b64":"itcUfBJBhM4w7QXJLqnyt6nEvtR5Vy2/BUtK+VO0IGiM4w2j9RCKsU1etxkHjwQ0Dacy0f6hr0988A+TxrD0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f1f3671a41a5b6160c14f1dc22b1d6796dc080eb8ffbebe7d535b80bc1bc2d2","last_reissued_at":"2026-05-18T04:34:38.502815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:38.502815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5775","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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VCDlKRMXzOal+8nIdlM7p4rMxAXyQtPby3IPdeUhaHDL0e0VlfUwneNC6v5KNuZB7n87+XcBGn0s073YrFzeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T02:21:44.687289Z"},"content_sha256":"74b4827be61c3cd6d9fce982f8b364070ef8e27f12127ff959fd94131429e175","schema_version":"1.0","event_id":"sha256:74b4827be61c3cd6d9fce982f8b364070ef8e27f12127ff959fd94131429e175"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:H4PTM4NEDJNWCYGBJ4O4EKY5M6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate saddlepoint approximations in tail probability and conditional inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jixin Li, John Kolassa","submitted_at":"2010-11-26T13:02:13Z","abstract_excerpt":"We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant generating function. The method is applied to some examples, including a real data set from a case-control study of endometrial cancer. The method contains less terms and is easier to implement than existing methods, while showing an accuracy comparable to those methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5775","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":""},"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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJ+DxL0HwbhhGlDcS+Ume9p++1CbHjZuMeLtsTGf8dajggFvLnPmmcisrekxsElR6WQT+rgkxoQtvwl2+UDYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T02:21:44.687746Z"},"content_sha256":"a5fe055d4438c626a60c368b741aa0d31305f3067c83342f5495ff9cddff1b97","schema_version":"1.0","event_id":"sha256:a5fe055d4438c626a60c368b741aa0d31305f3067c83342f5495ff9cddff1b97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6/bundle.json","state_url":"https://pith.science/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6/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":"2026-07-05T02:21:44Z","links":{"resolver":"https://pith.science/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6","bundle":"https://pith.science/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6/bundle.json","state":"https://pith.science/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4PTM4NEDJNWCYGBJ4O4EKY5M6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:H4PTM4NEDJNWCYGBJ4O4EKY5M6","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":"e37cce2018f57cce648260ea3e8eb1dd7e558e230614757289b8c67bb3bdd5ed","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-26T13:02:13Z","title_canon_sha256":"f1cd8b2927c6f2220605e64e5dc0f1d3d5158aeab52cf241a7bc54c77537544e"},"schema_version":"1.0","source":{"id":"1011.5775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5775","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5775v1","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5775","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"H4PTM4NEDJNW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H4PTM4NEDJNWCYGB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H4PTM4NE","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:a5fe055d4438c626a60c368b741aa0d31305f3067c83342f5495ff9cddff1b97","target":"graph","created_at":"2026-05-18T04:34:38Z","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":"We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant generating function. The method is applied to some examples, including a real data set from a case-control study of endometrial cancer. The method contains less terms and is easier to implement than existing methods, while showing an accuracy comparable to those methods.","authors_text":"Jixin Li, John Kolassa","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-26T13:02:13Z","title":"Multivariate saddlepoint approximations in tail probability and conditional inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5775","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":"sha256:74b4827be61c3cd6d9fce982f8b364070ef8e27f12127ff959fd94131429e175","target":"record","created_at":"2026-05-18T04:34:38Z","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":"e37cce2018f57cce648260ea3e8eb1dd7e558e230614757289b8c67bb3bdd5ed","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-11-26T13:02:13Z","title_canon_sha256":"f1cd8b2927c6f2220605e64e5dc0f1d3d5158aeab52cf241a7bc54c77537544e"},"schema_version":"1.0","source":{"id":"1011.5775","kind":"arxiv","version":1}},"canonical_sha256":"3f1f3671a41a5b6160c14f1dc22b1d6796dc080eb8ffbebe7d535b80bc1bc2d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f1f3671a41a5b6160c14f1dc22b1d6796dc080eb8ffbebe7d535b80bc1bc2d2","first_computed_at":"2026-05-18T04:34:38.502815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:38.502815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"itcUfBJBhM4w7QXJLqnyt6nEvtR5Vy2/BUtK+VO0IGiM4w2j9RCKsU1etxkHjwQ0Dacy0f6hr0988A+TxrD0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:38.503272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74b4827be61c3cd6d9fce982f8b364070ef8e27f12127ff959fd94131429e175","sha256:a5fe055d4438c626a60c368b741aa0d31305f3067c83342f5495ff9cddff1b97"],"state_sha256":"593a0fa0c6fd86c1f94d70e229ebb05f75fa53a4762d91dbb1a1499a1bf0649f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFBJn6cvQUoPT4t9q+vNmNjPUvt0TaSvCYCYhkxpDQvwQd5pTa7A4EfWn9HoqhsvLpQR3K3MzDTjR2un2e5MDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T02:21:44.689742Z","bundle_sha256":"69b4eb81ffc32ac744efdfeb06ba967782c53ad60199136d003d2abed9762350"}}