{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EFCIBJ5XL5BW72N4IZ3STPTZ2J","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":"f614e655315b6b87e7d913ae5d1ecf12c00db635f16ad1368e15d41da18b204d","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-03-14T05:50:42Z","title_canon_sha256":"6db3287bdfd45af3081ea4b97ab2d91895aa0a1e950fd31ff9a0f25b7b3a4b00"},"schema_version":"1.0","source":{"id":"1003.2760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2760","created_at":"2026-05-18T02:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2760v1","created_at":"2026-05-18T02:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2760","created_at":"2026-05-18T02:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"EFCIBJ5XL5BW","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EFCIBJ5XL5BW72N4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EFCIBJ5X","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:987a7f27d84c1c7041f669ddb19a0842c38cb8d5a5ac20f0f3c983db43ba1370","target":"graph","created_at":"2026-05-18T02:24:37Z","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 paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q-functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum Q-function and its deformations is established with respect to each of the three parameters. Since the Nuttall Q-function has similar probabilistic interpretations as the generalized Marcum Q-function, we deduce the log-concavity of the Nuttall Q-function. By exploiting the log-concavity of these tw","authors_text":"Arpad Baricz, Shidong Zhou, Yin Sun","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-03-14T05:50:42Z","title":"On the monotonicity, log-concavity and tight bounds of the generalized Marcum and Nuttall Q-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2760","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":"sha256:3a53b5630d3582293a7b8b5022685d36088be384e4cecb494a70680f6991cbf4","target":"record","created_at":"2026-05-18T02:24:37Z","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":"f614e655315b6b87e7d913ae5d1ecf12c00db635f16ad1368e15d41da18b204d","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-03-14T05:50:42Z","title_canon_sha256":"6db3287bdfd45af3081ea4b97ab2d91895aa0a1e950fd31ff9a0f25b7b3a4b00"},"schema_version":"1.0","source":{"id":"1003.2760","kind":"arxiv","version":1}},"canonical_sha256":"214480a7b75f436fe9bc467729be79d279bde2eeb8c7f65a20c68028c3fb08a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"214480a7b75f436fe9bc467729be79d279bde2eeb8c7f65a20c68028c3fb08a3","first_computed_at":"2026-05-18T02:24:37.364907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:37.364907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbKfCNc+jscuyD2H8RXP2VJEtrONMvnTyG5Jo4R6wbQ2kbU7dug/ivlsqpTo/04w5hNyZeUrrOWsJvNbf3PTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:37.365645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a53b5630d3582293a7b8b5022685d36088be384e4cecb494a70680f6991cbf4","sha256:987a7f27d84c1c7041f669ddb19a0842c38cb8d5a5ac20f0f3c983db43ba1370"],"state_sha256":"098f084e9e575d6a68f1e2fbb34592532d08e525734e6918b71d36cfe3079c92"}