{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KU6GWWPVFEIFRKLMTOK5VJZ3D4","short_pith_number":"pith:KU6GWWPV","canonical_record":{"source":{"id":"1607.04430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-15T09:31:18Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c204b4242b40d6456331a1182c1a1202052ab87024e5f8d4d544a0a7b6d7fcdb","abstract_canon_sha256":"7d057d66721efb3dec3bf6fd9a1d791e348f2288b12728c5a92d366ebe88ed90"},"schema_version":"1.0"},"canonical_sha256":"553c6b59f5291058a96c9b95daa73b1f1d75277e807ff1fb1f1693d763f9b676","source":{"kind":"arxiv","id":"1607.04430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04430","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04430v2","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04430","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"KU6GWWPVFEIF","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KU6GWWPVFEIFRKLM","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KU6GWWPV","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KU6GWWPVFEIFRKLMTOK5VJZ3D4","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-15T09:31:18Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c204b4242b40d6456331a1182c1a1202052ab87024e5f8d4d544a0a7b6d7fcdb","abstract_canon_sha256":"7d057d66721efb3dec3bf6fd9a1d791e348f2288b12728c5a92d366ebe88ed90"},"schema_version":"1.0"},"canonical_sha256":"553c6b59f5291058a96c9b95daa73b1f1d75277e807ff1fb1f1693d763f9b676","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:43.887853Z","signature_b64":"JCcSfP5IFagts1JTJxPrCRz7jB5lBbRvj9ogv1OVJwfAdnx8bHkF6Y/xDrrK9DMaOuEJblLkqtrOj+hK4AKeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"553c6b59f5291058a96c9b95daa73b1f1d75277e807ff1fb1f1693d763f9b676","last_reissued_at":"2026-05-18T00:57:43.887457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:43.887457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04430","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":"2026-05-18T00:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWvRV78Qp8kVz3xTFnWsVXtoi5DftwktZTauvRWZSmMiYGhetCdGb6FTGVoonW23X3uvXE+cNdrlFmn6sRveDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:26:22.955235Z"},"content_sha256":"0812a8fb8c09090bb20613975df9f634c54fb90e75f5e17743a81ce591bc3a0a","schema_version":"1.0","event_id":"sha256:0812a8fb8c09090bb20613975df9f634c54fb90e75f5e17743a81ce591bc3a0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KU6GWWPVFEIFRKLMTOK5VJZ3D4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Empirical Beta Copula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Hideatsu Tsukahara, Johan Segers, Masaaki Sibuya","submitted_at":"2016-07-15T09:31:18Z","abstract_excerpt":"Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This idea can be regarded as a variant on Baker's [J. Multivariate Anal. 99 (2008) 2312--2327] copula construction and leads to the definition of the empirical beta copula. The latter turns out to be a particular case of the empirical Bernstein copula, the degrees of all Bernstein polynomials being equal to the sample size.\n  Necessary and sufficient conditions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04430","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":"2026-05-18T00:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4PjKGmAwNrO/0Y4pTikMMEIz7FUFB+1OPNbFDzlmWWT1GZMpQeluTf073qOiSX0cHNQoLJSYNBP0cN6NeEVnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:26:22.955610Z"},"content_sha256":"ecf9a6a22ee625790d8d4cd19524fca2c2a2aaa498bf45c0d8e6ce93eefa8987","schema_version":"1.0","event_id":"sha256:ecf9a6a22ee625790d8d4cd19524fca2c2a2aaa498bf45c0d8e6ce93eefa8987"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4/bundle.json","state_url":"https://pith.science/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4/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":"2026-06-01T10:26:22Z","links":{"resolver":"https://pith.science/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4","bundle":"https://pith.science/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4/bundle.json","state":"https://pith.science/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KU6GWWPVFEIFRKLMTOK5VJZ3D4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KU6GWWPVFEIFRKLMTOK5VJZ3D4","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":"7d057d66721efb3dec3bf6fd9a1d791e348f2288b12728c5a92d366ebe88ed90","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-15T09:31:18Z","title_canon_sha256":"c204b4242b40d6456331a1182c1a1202052ab87024e5f8d4d544a0a7b6d7fcdb"},"schema_version":"1.0","source":{"id":"1607.04430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04430","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04430v2","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04430","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"KU6GWWPVFEIF","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KU6GWWPVFEIFRKLM","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KU6GWWPV","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:ecf9a6a22ee625790d8d4cd19524fca2c2a2aaa498bf45c0d8e6ce93eefa8987","target":"graph","created_at":"2026-05-18T00:57:43Z","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":"Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This idea can be regarded as a variant on Baker's [J. Multivariate Anal. 99 (2008) 2312--2327] copula construction and leads to the definition of the empirical beta copula. The latter turns out to be a particular case of the empirical Bernstein copula, the degrees of all Bernstein polynomials being equal to the sample size.\n  Necessary and sufficient conditions ","authors_text":"Hideatsu Tsukahara, Johan Segers, Masaaki Sibuya","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-15T09:31:18Z","title":"The Empirical Beta Copula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04430","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":"sha256:0812a8fb8c09090bb20613975df9f634c54fb90e75f5e17743a81ce591bc3a0a","target":"record","created_at":"2026-05-18T00:57:43Z","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":"7d057d66721efb3dec3bf6fd9a1d791e348f2288b12728c5a92d366ebe88ed90","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-15T09:31:18Z","title_canon_sha256":"c204b4242b40d6456331a1182c1a1202052ab87024e5f8d4d544a0a7b6d7fcdb"},"schema_version":"1.0","source":{"id":"1607.04430","kind":"arxiv","version":2}},"canonical_sha256":"553c6b59f5291058a96c9b95daa73b1f1d75277e807ff1fb1f1693d763f9b676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"553c6b59f5291058a96c9b95daa73b1f1d75277e807ff1fb1f1693d763f9b676","first_computed_at":"2026-05-18T00:57:43.887457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:43.887457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JCcSfP5IFagts1JTJxPrCRz7jB5lBbRvj9ogv1OVJwfAdnx8bHkF6Y/xDrrK9DMaOuEJblLkqtrOj+hK4AKeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:43.887853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0812a8fb8c09090bb20613975df9f634c54fb90e75f5e17743a81ce591bc3a0a","sha256:ecf9a6a22ee625790d8d4cd19524fca2c2a2aaa498bf45c0d8e6ce93eefa8987"],"state_sha256":"913a509c6550b205b8be4b470960d6bfb554bf915276e9c1468af81a509a919a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQuBaRowOn/fKWxsIaKHNr3RRw7lLdYUqokwpGLJG2ZyHV+cevlat7j/YHHO0zrwfb+8Sh6CDOoE3CDZLJeiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:26:22.957704Z","bundle_sha256":"7587086d11ae8248e4203eb2c9e6ebf1e20a6a43670b1708e469bfb16a54a305"}}