{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z33WAP324VTI3NUXLTOV3EHV4W","short_pith_number":"pith:Z33WAP32","canonical_record":{"source":{"id":"1404.0302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-01T16:33:41Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"484d4eaa999be8d0d8ab43a4206b7fbe498768be31c4081cfdac151469cafe00","abstract_canon_sha256":"b09917d0fef8d843a17cb871ecea12c90425a563aff4e2b8d1dab57ee0e96b8c"},"schema_version":"1.0"},"canonical_sha256":"cef7603f7ae5668db6975cdd5d90f5e59eaf663e65d4f5d3ffaa6291867e73fe","source":{"kind":"arxiv","id":"1404.0302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0302","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0302v1","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0302","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z33WAP324VTI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z33WAP324VTI3NUX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z33WAP32","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z33WAP324VTI3NUXLTOV3EHV4W","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-01T16:33:41Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"484d4eaa999be8d0d8ab43a4206b7fbe498768be31c4081cfdac151469cafe00","abstract_canon_sha256":"b09917d0fef8d843a17cb871ecea12c90425a563aff4e2b8d1dab57ee0e96b8c"},"schema_version":"1.0"},"canonical_sha256":"cef7603f7ae5668db6975cdd5d90f5e59eaf663e65d4f5d3ffaa6291867e73fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:04.696535Z","signature_b64":"umq3x3fWy3XU6gtf7TGc3TFBIkaoJ8G7qkIgZLFmjmrMqIhpc1TgadH0zIrcIvLjEqdf4abWdRf/wDssoEBjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cef7603f7ae5668db6975cdd5d90f5e59eaf663e65d4f5d3ffaa6291867e73fe","last_reissued_at":"2026-05-18T02:55:04.696002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:04.696002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0302","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+QRqlXAEHziuvBHGubg/cH/x+ocBZawR8h8udM2q68ie19dZ2ki0C7bwQcjFefwCHlbAhU2IDsbNJ8Qx2gsIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T13:40:18.956333Z"},"content_sha256":"0a47024e56396ae462229a6c716c244c12c12ddb0b49cdfc3644c1cb73fe6fa8","schema_version":"1.0","event_id":"sha256:0a47024e56396ae462229a6c716c244c12c12ddb0b49cdfc3644c1cb73fe6fa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z33WAP324VTI3NUXLTOV3EHV4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The asymptotic and numerical inversion of the Marcum $Q-$function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CA","authors_text":"A. Gil, J. Segura, N. M. Temme","submitted_at":"2014-04-01T16:33:41Z","abstract_excerpt":"The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi-squared cumulative distribution functions. In this paper we describe a new asymptotic method for inverting the generalized Marcum $Q-$function and for the complementary Marcum $P-$function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0302","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNJQiWToo4pZlvjFosfaPSsvI/IbcE77/D0B5F2JjFBNyx5uItMHg65dGi13tcmjrM3dOSA8d/EVk+wcs7cOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T13:40:18.956687Z"},"content_sha256":"42e18dacefe62f84db4f5bd18b9fa5d9a87d7cdd31d3eb3b9513502da61c22b5","schema_version":"1.0","event_id":"sha256:42e18dacefe62f84db4f5bd18b9fa5d9a87d7cdd31d3eb3b9513502da61c22b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z33WAP324VTI3NUXLTOV3EHV4W/bundle.json","state_url":"https://pith.science/pith/Z33WAP324VTI3NUXLTOV3EHV4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z33WAP324VTI3NUXLTOV3EHV4W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T13:40:18Z","links":{"resolver":"https://pith.science/pith/Z33WAP324VTI3NUXLTOV3EHV4W","bundle":"https://pith.science/pith/Z33WAP324VTI3NUXLTOV3EHV4W/bundle.json","state":"https://pith.science/pith/Z33WAP324VTI3NUXLTOV3EHV4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z33WAP324VTI3NUXLTOV3EHV4W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z33WAP324VTI3NUXLTOV3EHV4W","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":"b09917d0fef8d843a17cb871ecea12c90425a563aff4e2b8d1dab57ee0e96b8c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-01T16:33:41Z","title_canon_sha256":"484d4eaa999be8d0d8ab43a4206b7fbe498768be31c4081cfdac151469cafe00"},"schema_version":"1.0","source":{"id":"1404.0302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0302","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0302v1","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0302","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z33WAP324VTI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z33WAP324VTI3NUX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z33WAP32","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:42e18dacefe62f84db4f5bd18b9fa5d9a87d7cdd31d3eb3b9513502da61c22b5","target":"graph","created_at":"2026-05-18T02:55:04Z","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 generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi-squared cumulative distribution functions. In this paper we describe a new asymptotic method for inverting the generalized Marcum $Q-$function and for the complementary Marcum $P-$function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant method","authors_text":"A. Gil, J. Segura, N. M. Temme","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-01T16:33:41Z","title":"The asymptotic and numerical inversion of the Marcum $Q-$function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0302","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":"sha256:0a47024e56396ae462229a6c716c244c12c12ddb0b49cdfc3644c1cb73fe6fa8","target":"record","created_at":"2026-05-18T02:55:04Z","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":"b09917d0fef8d843a17cb871ecea12c90425a563aff4e2b8d1dab57ee0e96b8c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-01T16:33:41Z","title_canon_sha256":"484d4eaa999be8d0d8ab43a4206b7fbe498768be31c4081cfdac151469cafe00"},"schema_version":"1.0","source":{"id":"1404.0302","kind":"arxiv","version":1}},"canonical_sha256":"cef7603f7ae5668db6975cdd5d90f5e59eaf663e65d4f5d3ffaa6291867e73fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cef7603f7ae5668db6975cdd5d90f5e59eaf663e65d4f5d3ffaa6291867e73fe","first_computed_at":"2026-05-18T02:55:04.696002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:04.696002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umq3x3fWy3XU6gtf7TGc3TFBIkaoJ8G7qkIgZLFmjmrMqIhpc1TgadH0zIrcIvLjEqdf4abWdRf/wDssoEBjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:04.696535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a47024e56396ae462229a6c716c244c12c12ddb0b49cdfc3644c1cb73fe6fa8","sha256:42e18dacefe62f84db4f5bd18b9fa5d9a87d7cdd31d3eb3b9513502da61c22b5"],"state_sha256":"c6bc98f600f913fd00614ba67e4a5176c09fff193fde5563a2d8e368aaa5ed13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"727klTYMked5uO/wHnb6EaWwZbp8872c5rTDS01Rp5lrxQamL1paRfYI+B998MJwtguyEMQCOq08XKRIGm9GDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T13:40:18.958617Z","bundle_sha256":"148ddbc00c4dacb32a8bcdd4d64d1794a3af78a8b680cf1561b47385ab9d3da0"}}