{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TPP6YNT6CUAULOTAMWGZXF34N6","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":"19376103240480847e3f3f83395aefda31006a2704842182c543be1c9615f417","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-01T23:56:25Z","title_canon_sha256":"1498812fd979ab4b3e92cafb19af64bdaefaff44d1e6e5bbf8102e3a49fc3215"},"schema_version":"1.0","source":{"id":"1503.00378","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00378","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00378v3","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00378","created_at":"2026-05-18T01:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"TPP6YNT6CUAU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TPP6YNT6CUAULOTA","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TPP6YNT6","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:6f878dec6bdfce1c70f9534107037ccf9f01bdfab2aca9bbe525090d8e386b03","target":"graph","created_at":"2026-05-18T01:34:35Z","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 apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution.","authors_text":"Akimichi Takemura, Tamio Koyama","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-01T23:56:25Z","title":"Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00378","kind":"arxiv","version":3},"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":"sha256:0a7db63db3e6279290529136a7a44d82937e5ef78b2ed6c487a0f5520d3c117c","target":"record","created_at":"2026-05-18T01:34:35Z","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":"19376103240480847e3f3f83395aefda31006a2704842182c543be1c9615f417","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-01T23:56:25Z","title_canon_sha256":"1498812fd979ab4b3e92cafb19af64bdaefaff44d1e6e5bbf8102e3a49fc3215"},"schema_version":"1.0","source":{"id":"1503.00378","kind":"arxiv","version":3}},"canonical_sha256":"9bdfec367e150145ba60658d9b977c6f80059e6d2b03c8cb255befc1e19b3af9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bdfec367e150145ba60658d9b977c6f80059e6d2b03c8cb255befc1e19b3af9","first_computed_at":"2026-05-18T01:34:35.017525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:35.017525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1h9wqN1nAEzSZyWpdBSKAgmEVbZuQXOsGSu14IBgUmWm5T5k5fiVcz2SicyqS1FEAqpDl5j+oWeXXuYmaa9HCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:35.018062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00378","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a7db63db3e6279290529136a7a44d82937e5ef78b2ed6c487a0f5520d3c117c","sha256:6f878dec6bdfce1c70f9534107037ccf9f01bdfab2aca9bbe525090d8e386b03"],"state_sha256":"eb7a15f26649ecfd417b7ead1f244b60b6cec6d139a5a0e6b6bca67b4d0ba59d"}