{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YD6PRUVUECGXS2VI2R35ZDSL5E","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":"dec150b05ea563b201311d50e3c995b5cd4b8a10a52457754e0b3b02e82c8b14","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-12-27T01:17:49Z","title_canon_sha256":"52909944941b9c8179ce933fb67741a6897f71069d73cfa3f1164ac49cf2e987"},"schema_version":"1.0","source":{"id":"1512.08159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08159","created_at":"2026-05-18T01:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08159v1","created_at":"2026-05-18T01:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08159","created_at":"2026-05-18T01:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"YD6PRUVUECGX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YD6PRUVUECGXS2VI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YD6PRUVU","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:552cc3dee06d9c9722842dde3e10c2d8a450e2454ecde53ed89c98363d7ae561","target":"graph","created_at":"2026-05-18T01:14:17Z","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 show that the distribution of the scalar Schur complement in a noncentral Wishart matrix is a mixture of central chi-square distributions with different degrees of freedom. For the case of a rank-1 noncentrality matrix, the weights of the mixture representation arise from a noncentral beta mixture of Poisson distributions.","authors_text":"Akimichi Takemura, Constantin Siriteanu, Donald Richards, Satoshi Kuriki","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-12-27T01:17:49Z","title":"Chi-Square Mixture Representations for the Distribution of the Scalar Schur Complement in a Noncentral Wishart Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08159","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":"sha256:0b57b4b48bf5703254d41430a388e1dbb47591700d5a76f8251944925e364670","target":"record","created_at":"2026-05-18T01:14:17Z","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":"dec150b05ea563b201311d50e3c995b5cd4b8a10a52457754e0b3b02e82c8b14","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-12-27T01:17:49Z","title_canon_sha256":"52909944941b9c8179ce933fb67741a6897f71069d73cfa3f1164ac49cf2e987"},"schema_version":"1.0","source":{"id":"1512.08159","kind":"arxiv","version":1}},"canonical_sha256":"c0fcf8d2b4208d796aa8d477dc8e4be91a6f38f3e899c0955477c7d920980764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0fcf8d2b4208d796aa8d477dc8e4be91a6f38f3e899c0955477c7d920980764","first_computed_at":"2026-05-18T01:14:17.513730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:17.513730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IHwMPTEtWY9dVi4b4qG90f1PsLrCenjhIXpSYc/9G9VKbY6Ad0iZk6+a7M+pcJ+4sCnC2yzxyeSJ9JvA14rDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:17.514262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b57b4b48bf5703254d41430a388e1dbb47591700d5a76f8251944925e364670","sha256:552cc3dee06d9c9722842dde3e10c2d8a450e2454ecde53ed89c98363d7ae561"],"state_sha256":"d106b244a88262122de1c57e3d3308d563d1381f4f50a21e675017626f970885"}