{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6LVROTJITJTJOBGK3SEFRBRJAS","short_pith_number":"pith:6LVROTJI","canonical_record":{"source":{"id":"1207.5654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-24T10:49:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a48384640a8001f74fbb4a7da144ed82c9c30e718b237af2028a8eeebe8e6ba2","abstract_canon_sha256":"89fc4098a1e5eef6c1ccefba0d9403d4075e98c20c9f91af4f22a1670e8f669a"},"schema_version":"1.0"},"canonical_sha256":"f2eb174d289a669704cadc88588629048108833835bbf8bf9b79f6df32ad7911","source":{"kind":"arxiv","id":"1207.5654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5654","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5654v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5654","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"6LVROTJITJTJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LVROTJITJTJOBGK","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LVROTJI","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6LVROTJITJTJOBGK3SEFRBRJAS","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-24T10:49:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a48384640a8001f74fbb4a7da144ed82c9c30e718b237af2028a8eeebe8e6ba2","abstract_canon_sha256":"89fc4098a1e5eef6c1ccefba0d9403d4075e98c20c9f91af4f22a1670e8f669a"},"schema_version":"1.0"},"canonical_sha256":"f2eb174d289a669704cadc88588629048108833835bbf8bf9b79f6df32ad7911","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:11.728754Z","signature_b64":"LOC4CoIOI/wNPTUnFM1flk3lgc5LBwDlgnHLvoogSvWecEImllFymzI39i1kFVxthi1nkdt1q0RmU24e2gY2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2eb174d289a669704cadc88588629048108833835bbf8bf9b79f6df32ad7911","last_reissued_at":"2026-05-18T03:50:11.727997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:11.727997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5654","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":"2026-05-18T03:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LZa2DhNYvkITL95di9v4UXfGDFr0x2OQMVOZMdMC/I3qdtdLSSABIglgqF9Uy+/7/lytoIJOaaB6fFmm9ZcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:07:27.195621Z"},"content_sha256":"4f8c480e6a12287df57ab803ff6ae890168db8d42a2ab7d4e41e0cfae2483285","schema_version":"1.0","event_id":"sha256:4f8c480e6a12287df57ab803ff6ae890168db8d42a2ab7d4e41e0cfae2483285"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6LVROTJITJTJOBGK3SEFRBRJAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of rejective sampling inclusion probabilities and application to high order correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anne Ruiz-Gazen, H\\'el\\`ene Boistard, Hendrik P. Lopuha\\\"a","submitted_at":"2012-07-24T10:49:34Z","abstract_excerpt":"This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by H\\'ajek (1964) and H\\'ajek (1981) and making the remainder term more precise. Following H\\'ajek (1981), the proof is based on Edgeworth expansions. The main result is applied to derive bounds on higher order correlations, which are needed for the consistency and asymptotic normality of several complex estimators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5654","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":"2026-05-18T03:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mymE1miTh7/I6HlGPK3bYxA+Jn4twFVafpAbD+/zKDWX/5Qs9GnbFml2nxdKcKY3ymkFsQZ0DQyW7DWjkqwTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:07:27.195978Z"},"content_sha256":"541052205718dd65e4ea602f17a9bad49d6509684ddb594fa138c341ad809320","schema_version":"1.0","event_id":"sha256:541052205718dd65e4ea602f17a9bad49d6509684ddb594fa138c341ad809320"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LVROTJITJTJOBGK3SEFRBRJAS/bundle.json","state_url":"https://pith.science/pith/6LVROTJITJTJOBGK3SEFRBRJAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LVROTJITJTJOBGK3SEFRBRJAS/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":"2026-06-21T18:07:27Z","links":{"resolver":"https://pith.science/pith/6LVROTJITJTJOBGK3SEFRBRJAS","bundle":"https://pith.science/pith/6LVROTJITJTJOBGK3SEFRBRJAS/bundle.json","state":"https://pith.science/pith/6LVROTJITJTJOBGK3SEFRBRJAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LVROTJITJTJOBGK3SEFRBRJAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6LVROTJITJTJOBGK3SEFRBRJAS","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":"89fc4098a1e5eef6c1ccefba0d9403d4075e98c20c9f91af4f22a1670e8f669a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-24T10:49:34Z","title_canon_sha256":"a48384640a8001f74fbb4a7da144ed82c9c30e718b237af2028a8eeebe8e6ba2"},"schema_version":"1.0","source":{"id":"1207.5654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5654","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5654v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5654","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"6LVROTJITJTJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LVROTJITJTJOBGK","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LVROTJI","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:541052205718dd65e4ea602f17a9bad49d6509684ddb594fa138c341ad809320","target":"graph","created_at":"2026-05-18T03:50:11Z","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"},"paper":{"abstract_excerpt":"This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by H\\'ajek (1964) and H\\'ajek (1981) and making the remainder term more precise. Following H\\'ajek (1981), the proof is based on Edgeworth expansions. The main result is applied to derive bounds on higher order correlations, which are needed for the consistency and asymptotic normality of several complex estimators.","authors_text":"Anne Ruiz-Gazen, H\\'el\\`ene Boistard, Hendrik P. Lopuha\\\"a","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-24T10:49:34Z","title":"Approximation of rejective sampling inclusion probabilities and application to high order correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5654","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":"sha256:4f8c480e6a12287df57ab803ff6ae890168db8d42a2ab7d4e41e0cfae2483285","target":"record","created_at":"2026-05-18T03:50:11Z","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":"89fc4098a1e5eef6c1ccefba0d9403d4075e98c20c9f91af4f22a1670e8f669a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-24T10:49:34Z","title_canon_sha256":"a48384640a8001f74fbb4a7da144ed82c9c30e718b237af2028a8eeebe8e6ba2"},"schema_version":"1.0","source":{"id":"1207.5654","kind":"arxiv","version":1}},"canonical_sha256":"f2eb174d289a669704cadc88588629048108833835bbf8bf9b79f6df32ad7911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2eb174d289a669704cadc88588629048108833835bbf8bf9b79f6df32ad7911","first_computed_at":"2026-05-18T03:50:11.727997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:11.727997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LOC4CoIOI/wNPTUnFM1flk3lgc5LBwDlgnHLvoogSvWecEImllFymzI39i1kFVxthi1nkdt1q0RmU24e2gY2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:11.728754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f8c480e6a12287df57ab803ff6ae890168db8d42a2ab7d4e41e0cfae2483285","sha256:541052205718dd65e4ea602f17a9bad49d6509684ddb594fa138c341ad809320"],"state_sha256":"9636e9fe789bab5333bc4c1e847d330bb05444f35b55c31d92bbb5a86a2d52d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rGRBYGuOe5Z3pIfh0nPEE8dBaar5OxyH+u2pZyaDtdr2rg3mrV8ZIdCjIrisRaQdMNQ1O0RKr5wZ9FdhcKxIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T18:07:27.198015Z","bundle_sha256":"f38c02af36ab4b4406d9143f5266c2b095146ccf4a45b6817caaa3cfb0354012"}}