{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GH4Q2667VPPM77BWQ4ULUYWWGQ","short_pith_number":"pith:GH4Q2667","canonical_record":{"source":{"id":"1602.01955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-02-05T08:48:09Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"366e09ef635273792d27c17edf0579da7fe68172c2adcfbed5aa6300f67c65a8","abstract_canon_sha256":"2f00ebd759b3753756afd38cfa1dcfb3b21d70de657a72e04b169726b1a22b3e"},"schema_version":"1.0"},"canonical_sha256":"31f90d7bdfabdecffc368728ba62d6343c76bd69363d05e795b67359d77600b5","source":{"kind":"arxiv","id":"1602.01955","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01955","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01955v1","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01955","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"GH4Q2667VPPM","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GH4Q2667VPPM77BW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GH4Q2667","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GH4Q2667VPPM77BWQ4ULUYWWGQ","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-02-05T08:48:09Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"366e09ef635273792d27c17edf0579da7fe68172c2adcfbed5aa6300f67c65a8","abstract_canon_sha256":"2f00ebd759b3753756afd38cfa1dcfb3b21d70de657a72e04b169726b1a22b3e"},"schema_version":"1.0"},"canonical_sha256":"31f90d7bdfabdecffc368728ba62d6343c76bd69363d05e795b67359d77600b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:14.931928Z","signature_b64":"gnQ+JsU8EouZtn+W5WPEnN+bx/aFzJI+ydNctQhmSR6EcGCm2hZTodhPD6x8roux1NWkxJCRIXeQXLQjtA6CAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31f90d7bdfabdecffc368728ba62d6343c76bd69363d05e795b67359d77600b5","last_reissued_at":"2026-05-18T01:21:14.931380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:14.931380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01955","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":"2026-05-18T01:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYUkInLQUQo3t2LMAdpzoCpZeIdLwpNTA+AzUbO+1U9m0U8BhjwgnIHwkITtRsxSydU2LalAMOTVSZAezCN9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:39:09.151036Z"},"content_sha256":"1e18a28610a0a302de392a94ddbac66b57bfb5ccb6fb6d94684c5e1c7ec68219","schema_version":"1.0","event_id":"sha256:1e18a28610a0a302de392a94ddbac66b57bfb5ccb6fb6d94684c5e1c7ec68219"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GH4Q2667VPPM77BWQ4ULUYWWGQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exchangeable exogenous shock models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jan-Frederik Mai, Matthias Scherer, Steffen Schenk","submitted_at":"2016-02-05T08:48:09Z","abstract_excerpt":"We characterize a comprehensive family of $d$-variate exogenous shock models. Analytically, we consider a family of multivariate distribution functions that arises from ordering, idiosyncratically distorting, and finally multiplying the arguments. Necessary and sufficient conditions on the involved distortions to yield a multivariate distribution function are given. Probabilistically, the attainable set of distribution functions corresponds to a large class of exchangeable exogenous shock models. Besides, the vector of exceedance times of an increasing additive stochastic process across indepe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01955","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":"2026-05-18T01:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2iqFSRaQCC5nTj++QFVSZUEWRbgNsrTpR8Fn6Vsn61qAVrWQM2O3bD3CECwlmnYBPYA6PFuKx7Ganthsky+YCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:39:09.151414Z"},"content_sha256":"6ed95e1c60a3c94f769da58699829555973c481a91b000456954c9adaccb6063","schema_version":"1.0","event_id":"sha256:6ed95e1c60a3c94f769da58699829555973c481a91b000456954c9adaccb6063"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ/bundle.json","state_url":"https://pith.science/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ/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":"2026-06-07T21:39:09Z","links":{"resolver":"https://pith.science/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ","bundle":"https://pith.science/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ/bundle.json","state":"https://pith.science/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GH4Q2667VPPM77BWQ4ULUYWWGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GH4Q2667VPPM77BWQ4ULUYWWGQ","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":"2f00ebd759b3753756afd38cfa1dcfb3b21d70de657a72e04b169726b1a22b3e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-02-05T08:48:09Z","title_canon_sha256":"366e09ef635273792d27c17edf0579da7fe68172c2adcfbed5aa6300f67c65a8"},"schema_version":"1.0","source":{"id":"1602.01955","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01955","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01955v1","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01955","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"GH4Q2667VPPM","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GH4Q2667VPPM77BW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GH4Q2667","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:6ed95e1c60a3c94f769da58699829555973c481a91b000456954c9adaccb6063","target":"graph","created_at":"2026-05-18T01:21:14Z","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 characterize a comprehensive family of $d$-variate exogenous shock models. Analytically, we consider a family of multivariate distribution functions that arises from ordering, idiosyncratically distorting, and finally multiplying the arguments. Necessary and sufficient conditions on the involved distortions to yield a multivariate distribution function are given. Probabilistically, the attainable set of distribution functions corresponds to a large class of exchangeable exogenous shock models. Besides, the vector of exceedance times of an increasing additive stochastic process across indepe","authors_text":"Jan-Frederik Mai, Matthias Scherer, Steffen Schenk","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-02-05T08:48:09Z","title":"Exchangeable exogenous shock models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01955","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":"sha256:1e18a28610a0a302de392a94ddbac66b57bfb5ccb6fb6d94684c5e1c7ec68219","target":"record","created_at":"2026-05-18T01:21:14Z","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":"2f00ebd759b3753756afd38cfa1dcfb3b21d70de657a72e04b169726b1a22b3e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-02-05T08:48:09Z","title_canon_sha256":"366e09ef635273792d27c17edf0579da7fe68172c2adcfbed5aa6300f67c65a8"},"schema_version":"1.0","source":{"id":"1602.01955","kind":"arxiv","version":1}},"canonical_sha256":"31f90d7bdfabdecffc368728ba62d6343c76bd69363d05e795b67359d77600b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31f90d7bdfabdecffc368728ba62d6343c76bd69363d05e795b67359d77600b5","first_computed_at":"2026-05-18T01:21:14.931380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:14.931380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gnQ+JsU8EouZtn+W5WPEnN+bx/aFzJI+ydNctQhmSR6EcGCm2hZTodhPD6x8roux1NWkxJCRIXeQXLQjtA6CAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:14.931928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01955","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e18a28610a0a302de392a94ddbac66b57bfb5ccb6fb6d94684c5e1c7ec68219","sha256:6ed95e1c60a3c94f769da58699829555973c481a91b000456954c9adaccb6063"],"state_sha256":"417f7ab73f6fbcdb986942bab7ebe11ff87699a352ad8866767c7f64413f0377"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQGLwISsoJJItrqxzGiI5qxE6mIFy0R9iqM3a7MJNUxCJwh6S9Kladu+1gxXSKmuVU4a+uFlIJx/nam/nAxOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:39:09.153497Z","bundle_sha256":"92a8c12b40f41db1bf5906b59919c17ed5f6d1139e2392ad6f36bdc40b30731a"}}