{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CE2BQV6INS6OXBVO7ZFCQMK7G3","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":"626c124fcdb61df8348a66cae42d41b1caf0e1491a4e7d89218c41c749b78c4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-25T06:33:02Z","title_canon_sha256":"8b7c8178073578de7d2fd75cade4cae4af03631775980a7a3e9a8857615a6bef"},"schema_version":"1.0","source":{"id":"2410.19330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19330","created_at":"2026-07-05T09:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19330v1","created_at":"2026-07-05T09:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19330","created_at":"2026-07-05T09:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"CE2BQV6INS6O","created_at":"2026-07-05T09:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"CE2BQV6INS6OXBVO","created_at":"2026-07-05T09:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"CE2BQV6I","created_at":"2026-07-05T09:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:a4ea0d2c3c7a4fdfca77d9539fe2b65f5883e5af590589ed43222878e586f90e","target":"graph","created_at":"2026-07-05T09:25:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.19330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of positive random variables having moments of Gamma type, whose density can be expressed by the three-parametric Mittag-Leffler functions. We give some necessary conditions and some sufficient conditions for their existence. As a corollary, we give some conditions for non-negativity of the three-parametric Mittag-Leffler functions. As an application, we study the infinite divisibility of the powers of half $\\a$-Cauchy variable. In addition, we find that a random variable $\\X$ having moment of Gamma type if and only if $\\log \\X$ is quasi infinitely divisible. From this perspec","authors_text":"Min Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-25T06:33:02Z","title":"Moments of Gamma type and three-parametric Mittag-Leffler function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19330","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":"sha256:6ee7c2b69077676f79f90b8bed3b5da524ab965da941939d99e94f11ebe5a696","target":"record","created_at":"2026-07-05T09:25:55Z","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":"626c124fcdb61df8348a66cae42d41b1caf0e1491a4e7d89218c41c749b78c4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-25T06:33:02Z","title_canon_sha256":"8b7c8178073578de7d2fd75cade4cae4af03631775980a7a3e9a8857615a6bef"},"schema_version":"1.0","source":{"id":"2410.19330","kind":"arxiv","version":1}},"canonical_sha256":"11341857c86cbceb86aefe4a28315f36f7723ae7dc005b90c333eb6d8b1401c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11341857c86cbceb86aefe4a28315f36f7723ae7dc005b90c333eb6d8b1401c9","first_computed_at":"2026-07-05T09:25:55.109206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:55.109206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VWZWhddqKbXsveJLj3xkJyyDAzfcaBAGwkUPG09qO1zDZV629I6P80S+jccMlv+j+WeRdClguuvfT7kwj1wPCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:55.109765Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ee7c2b69077676f79f90b8bed3b5da524ab965da941939d99e94f11ebe5a696","sha256:a4ea0d2c3c7a4fdfca77d9539fe2b65f5883e5af590589ed43222878e586f90e"],"state_sha256":"0cf05dc85ace70dfa0ec53387a0231ca80b4023be8cb30df2d06b582fefeef91"}