{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5KZESCBQ4SRGSY5UHNVLTTHXFS","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":"7136825decca4d251646b91cdbf87fe895b856dba6045f956b19deeb57e3ad61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-11-18T12:28:16Z","title_canon_sha256":"3a2289b149d13f15c3764a383c4f5dc0a069d6c7e20327a56083f4ee80966e1c"},"schema_version":"1.0","source":{"id":"1411.4824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4824","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4824v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4824","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"5KZESCBQ4SRG","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5KZESCBQ4SRGSY5U","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5KZESCBQ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:90020285c5f645658d5275046bdc839b74ae64211c4e22c37a772691dc104747","target":"graph","created_at":"2026-05-18T02:34:51Z","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":"In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial information is available (Bernard and Vanduffel (2014)).","authors_text":"Carole Bernard, Steven Vanduffel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-11-18T12:28:16Z","title":"Quantile of a Mixture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4824","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:d8deb0349d62ce63dd6bcf9dff5cac48a2086c5374807c61965ea16877039fe7","target":"record","created_at":"2026-05-18T02:34:51Z","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":"7136825decca4d251646b91cdbf87fe895b856dba6045f956b19deeb57e3ad61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-11-18T12:28:16Z","title_canon_sha256":"3a2289b149d13f15c3764a383c4f5dc0a069d6c7e20327a56083f4ee80966e1c"},"schema_version":"1.0","source":{"id":"1411.4824","kind":"arxiv","version":1}},"canonical_sha256":"eab2490830e4a26963b43b6ab9ccf72cb5ed438f1b799147cd0dae236f2f04c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eab2490830e4a26963b43b6ab9ccf72cb5ed438f1b799147cd0dae236f2f04c6","first_computed_at":"2026-05-18T02:34:51.163312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:51.163312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LB20JkzNWHRb2ot8utkReUQ8U8c7hYk29cPV1aZ4SmX3DtsX1lDQrYz/AHuBlc0h7inKcagL/hpb67HWt2RdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:51.163681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8deb0349d62ce63dd6bcf9dff5cac48a2086c5374807c61965ea16877039fe7","sha256:90020285c5f645658d5275046bdc839b74ae64211c4e22c37a772691dc104747"],"state_sha256":"5129a6306188b1b87f432396df0f901612b4ab13d00a1961150b5db0d306884d"}