{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4MH7CZ3UK5AUVU7X7DVATGXH2B","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":"c8d7696752d7597ca66bd6479b4dd4b3e74892ba3f5123f6f9862b3a540c2fde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-29T11:27:39Z","title_canon_sha256":"e1d39606e1deb2bd7db4dcb4f5cc554d212fa92291a024dbd04dc5a489ac8d9f"},"schema_version":"1.0","source":{"id":"1307.7546","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7546","created_at":"2026-05-18T01:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7546v2","created_at":"2026-05-18T01:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7546","created_at":"2026-05-18T01:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"4MH7CZ3UK5AU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4MH7CZ3UK5AUVU7X","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4MH7CZ3U","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:7cb140f8d0037781857ea775ab1daa44a4552574ddade98caead5fcfdd6f2d0c","target":"graph","created_at":"2026-05-18T01:46:39Z","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":"The concept of \"stochastic precedence\" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence and analyze its relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stoch","authors_text":"Emilio De Santis, Fabio Fantozzi, Fabio Spizzichino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-29T11:27:39Z","title":"Relations Between Stochastic Orderings and generalized Stochastic Precedence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7546","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:ab2205347dc925568804a05f9599538b20bb085a39b266881332e53eba524cd0","target":"record","created_at":"2026-05-18T01:46:39Z","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":"c8d7696752d7597ca66bd6479b4dd4b3e74892ba3f5123f6f9862b3a540c2fde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-29T11:27:39Z","title_canon_sha256":"e1d39606e1deb2bd7db4dcb4f5cc554d212fa92291a024dbd04dc5a489ac8d9f"},"schema_version":"1.0","source":{"id":"1307.7546","kind":"arxiv","version":2}},"canonical_sha256":"e30ff1677457414ad3f7f8ea099ae7d05dc3f8b50f440b0c422ef5456c8dc5be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e30ff1677457414ad3f7f8ea099ae7d05dc3f8b50f440b0c422ef5456c8dc5be","first_computed_at":"2026-05-18T01:46:39.176730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:39.176730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ac/DkJqqOvYbtFG+/xj6HngCFMIrU3acvYrPYEPMryJgeFXeIs/ZJnnegutHOE3bBzKjIUacsictLrSHSdD3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:39.177219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7546","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab2205347dc925568804a05f9599538b20bb085a39b266881332e53eba524cd0","sha256:7cb140f8d0037781857ea775ab1daa44a4552574ddade98caead5fcfdd6f2d0c"],"state_sha256":"53f989af8dac5cdf227cd0f50cf6c028631e399db9cb6581a7e7e742db71fd93"}