{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WMSHKEVHHL6HOX4SHT35ZN4VXC","short_pith_number":"pith:WMSHKEVH","canonical_record":{"source":{"id":"1108.1972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-08-09T16:32:20Z","cross_cats_sorted":["stat.AP","stat.TH"],"title_canon_sha256":"51e8803581a87a923f9a424ac4acc02b2b1919e632606138a7633b435e4dcedb","abstract_canon_sha256":"f3e9e3b7c46320df8af79875ae1985c1eeda93024e7fc9e20cda50e1e67469e1"},"schema_version":"1.0"},"canonical_sha256":"b3247512a73afc775f923cf7dcb795b89c231c225db6e652773ed1b12981056e","source":{"kind":"arxiv","id":"1108.1972","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1972","created_at":"2026-05-18T04:15:50Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1972v1","created_at":"2026-05-18T04:15:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1972","created_at":"2026-05-18T04:15:50Z"},{"alias_kind":"pith_short_12","alias_value":"WMSHKEVHHL6H","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WMSHKEVHHL6HOX4S","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WMSHKEVH","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WMSHKEVHHL6HOX4SHT35ZN4VXC","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-08-09T16:32:20Z","cross_cats_sorted":["stat.AP","stat.TH"],"title_canon_sha256":"51e8803581a87a923f9a424ac4acc02b2b1919e632606138a7633b435e4dcedb","abstract_canon_sha256":"f3e9e3b7c46320df8af79875ae1985c1eeda93024e7fc9e20cda50e1e67469e1"},"schema_version":"1.0"},"canonical_sha256":"b3247512a73afc775f923cf7dcb795b89c231c225db6e652773ed1b12981056e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:50.788708Z","signature_b64":"lN2yTFgxDjBw+at0RDPKDkgNqsX2wSxZ/mvqxbtk0sCMvgLbgBsx7iPms84VJtnrwvfn7czlV3IADBNQKsEYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3247512a73afc775f923cf7dcb795b89c231c225db6e652773ed1b12981056e","last_reissued_at":"2026-05-18T04:15:50.788172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:50.788172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1972","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":"2026-05-18T04:15:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+2gFkA2HbYfwNqljBEDl8I4mVlQe/0k7xqKK/0K3hP+IAOP6Z7NUgH3BXz6OuzWzvyDNUw1Yc3ZxJ++dgYhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:49:02.979861Z"},"content_sha256":"69107e1b2790a499d6c73525db64db5cab9ee26bd265c32e3c28b05850a42683","schema_version":"1.0","event_id":"sha256:69107e1b2790a499d6c73525db64db5cab9ee26bd265c32e3c28b05850a42683"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WMSHKEVHHL6HOX4SHT35ZN4VXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal dependence: some contributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP","stat.TH"],"primary_cat":"math.ST","authors_text":"Helena Ferreira, Marta Ferreira","submitted_at":"2011-08-09T16:32:20Z","abstract_excerpt":"Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to assess the amount of dependence in $d$-variate random vectors based on bidimensional techniques. Ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1972","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":"2026-05-18T04:15:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"idfYtCGGXsSmYOYCH26Ar4fdLHhoo0drt/gLB/F9xGvpZVe59NawlfbLL5gYiuICBqQ9CuMNoCQ6GsWubXefDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:49:02.980220Z"},"content_sha256":"c83292f0af086709b0f7f4ab02989e3addcd3eeaa70d24b34ff99732a6fc6c40","schema_version":"1.0","event_id":"sha256:c83292f0af086709b0f7f4ab02989e3addcd3eeaa70d24b34ff99732a6fc6c40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC/bundle.json","state_url":"https://pith.science/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC/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":"2026-06-05T12:49:02Z","links":{"resolver":"https://pith.science/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC","bundle":"https://pith.science/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC/bundle.json","state":"https://pith.science/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMSHKEVHHL6HOX4SHT35ZN4VXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WMSHKEVHHL6HOX4SHT35ZN4VXC","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":"f3e9e3b7c46320df8af79875ae1985c1eeda93024e7fc9e20cda50e1e67469e1","cross_cats_sorted":["stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-08-09T16:32:20Z","title_canon_sha256":"51e8803581a87a923f9a424ac4acc02b2b1919e632606138a7633b435e4dcedb"},"schema_version":"1.0","source":{"id":"1108.1972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1972","created_at":"2026-05-18T04:15:50Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1972v1","created_at":"2026-05-18T04:15:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1972","created_at":"2026-05-18T04:15:50Z"},{"alias_kind":"pith_short_12","alias_value":"WMSHKEVHHL6H","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WMSHKEVHHL6HOX4S","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WMSHKEVH","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c83292f0af086709b0f7f4ab02989e3addcd3eeaa70d24b34ff99732a6fc6c40","target":"graph","created_at":"2026-05-18T04:15:50Z","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":"Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to assess the amount of dependence in $d$-variate random vectors based on bidimensional techniques. Ver","authors_text":"Helena Ferreira, Marta Ferreira","cross_cats":["stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-08-09T16:32:20Z","title":"Extremal dependence: some contributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1972","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":"sha256:69107e1b2790a499d6c73525db64db5cab9ee26bd265c32e3c28b05850a42683","target":"record","created_at":"2026-05-18T04:15:50Z","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":"f3e9e3b7c46320df8af79875ae1985c1eeda93024e7fc9e20cda50e1e67469e1","cross_cats_sorted":["stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-08-09T16:32:20Z","title_canon_sha256":"51e8803581a87a923f9a424ac4acc02b2b1919e632606138a7633b435e4dcedb"},"schema_version":"1.0","source":{"id":"1108.1972","kind":"arxiv","version":1}},"canonical_sha256":"b3247512a73afc775f923cf7dcb795b89c231c225db6e652773ed1b12981056e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3247512a73afc775f923cf7dcb795b89c231c225db6e652773ed1b12981056e","first_computed_at":"2026-05-18T04:15:50.788172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:50.788172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lN2yTFgxDjBw+at0RDPKDkgNqsX2wSxZ/mvqxbtk0sCMvgLbgBsx7iPms84VJtnrwvfn7czlV3IADBNQKsEYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:50.788708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69107e1b2790a499d6c73525db64db5cab9ee26bd265c32e3c28b05850a42683","sha256:c83292f0af086709b0f7f4ab02989e3addcd3eeaa70d24b34ff99732a6fc6c40"],"state_sha256":"2f3b76676e8e4b1e848a88c875a12ce429998930cdf07377dabb92fe1e3db5de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipjuT/AjEUT0lkdlGiulauYpMK3J6PRaGm9Mc5k4LK98Ejj3ZX6g0SYWBgODGTmeGbxDGqpyD9M3jAdOkJisAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:49:02.982401Z","bundle_sha256":"6b2a4db9f2dfaab2be129cb1989799cc420d74004a907e0eef49282c02dd26ff"}}