{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MEBPC6JF2BMB3SZVEN7T53OWAT","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":"874d84121ad403c0e4258bb01903a622bc0d4759e870ee84c43aa056d49b7ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-28T12:46:15Z","title_canon_sha256":"4fadce9ea69adfff69e7d8dfcfd8561707cd70af860d7c756dc0c7b1b930f585"},"schema_version":"1.0","source":{"id":"1107.5696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5696","created_at":"2026-05-18T04:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5696v2","created_at":"2026-05-18T04:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5696","created_at":"2026-05-18T04:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"MEBPC6JF2BMB","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MEBPC6JF2BMB3SZV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MEBPC6JF","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:ab3b249ad1940e355a0253303686a4c08427e0ce9bf670c728a3420e110cc780","target":"graph","created_at":"2026-05-18T04:05:48Z","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 investigate the sojourn time above a high threshold of a continuous stochastic process Y on [0,1]. It turns out that the limit, as the threshold increases, of the expected sojourn time given that it is positive, exists if the copula process corresponding to Y is in the functional domain of attraction of of an extreme value process. This limit coincides with the limit of the fragility index corresponding to finite (n-)dimensional distributions of Y as n and the threshold increase.\n  If the process is in a certain neighborhood of a generalized Pareto process, then we can replace the constant ","authors_text":"Martin Hofmann, Michael Falk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-28T12:46:15Z","title":"Sojourn Times and the Fragility Index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5696","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":"sha256:543fd7b9b210c07db4f385562757ebbe471aefdb93e924c6c50779a5ce90e6be","target":"record","created_at":"2026-05-18T04:05:48Z","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":"874d84121ad403c0e4258bb01903a622bc0d4759e870ee84c43aa056d49b7ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-28T12:46:15Z","title_canon_sha256":"4fadce9ea69adfff69e7d8dfcfd8561707cd70af860d7c756dc0c7b1b930f585"},"schema_version":"1.0","source":{"id":"1107.5696","kind":"arxiv","version":2}},"canonical_sha256":"6102f17925d0581dcb35237f3eedd604fff09b1674dea9fb88c66f7a2e9c77c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6102f17925d0581dcb35237f3eedd604fff09b1674dea9fb88c66f7a2e9c77c6","first_computed_at":"2026-05-18T04:05:48.289598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:48.289598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eUb+eEaO12+AM6iYZ5Nhpqj+UMQbJAN4k3PjrFx6fSELi/KbnUHHAFVgQZ/P5fDcJTVloVHhZkkQTqllxxr4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:48.290085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:543fd7b9b210c07db4f385562757ebbe471aefdb93e924c6c50779a5ce90e6be","sha256:ab3b249ad1940e355a0253303686a4c08427e0ce9bf670c728a3420e110cc780"],"state_sha256":"e9ff2f270f7df0863b828fccf3fc7a3a2eeb350f9bf036c3039e9905726a1015"}