{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6DVP3UFOVQSFAPZKJKJUNCL7ZB","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":"a7c0270ef9dd72a3bf057fbdb4f3a74e46c6e00fadf91ccbc079cd5238b94923","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2010-01-13T20:30:37Z","title_canon_sha256":"a2b14a3454ba0975ecd678b2fd5499c267007d485903fd23de96506754347ee4"},"schema_version":"1.0","source":{"id":"1001.2295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2295","created_at":"2026-05-18T02:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2295v1","created_at":"2026-05-18T02:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2295","created_at":"2026-05-18T02:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"6DVP3UFOVQSF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6DVP3UFOVQSFAPZK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6DVP3UFO","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:6022c4a996bc0aa5ce2b8f0cdae1ffe410bb6123ea9ab49e9ba11ee0d752bc8a","target":"graph","created_at":"2026-05-18T02:09:52Z","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":"Geometric generalized Mittag-Leffler distributions having the Laplace transform $\\frac{1}{1+\\beta\\log(1+t^\\alpha)},0<\\alpha\\le 2,\\beta>0$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms ","authors_text":"H.J. Haubold, K.K. Jose, P. Uma, V. Seetha Lekshmi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2010-01-13T20:30:37Z","title":"Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2295","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":"sha256:3bb19d3efc5f1847710adbc62021261d0b180eb9f14c462a9ac9af4124ec67b8","target":"record","created_at":"2026-05-18T02:09:52Z","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":"a7c0270ef9dd72a3bf057fbdb4f3a74e46c6e00fadf91ccbc079cd5238b94923","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2010-01-13T20:30:37Z","title_canon_sha256":"a2b14a3454ba0975ecd678b2fd5499c267007d485903fd23de96506754347ee4"},"schema_version":"1.0","source":{"id":"1001.2295","kind":"arxiv","version":1}},"canonical_sha256":"f0eafdd0aeac24503f2a4a9346897fc85265cb5348e55bacb20e30fd2de84ea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0eafdd0aeac24503f2a4a9346897fc85265cb5348e55bacb20e30fd2de84ea1","first_computed_at":"2026-05-18T02:09:52.587730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:52.587730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NjlbR539tjP32BDl91/pRarB5kGHibe6jyKCZe47+6ltC4YYh6Zn1Gyc/gvnWmFjIGym7iP3S5bAnmMm+bdlCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:52.588423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bb19d3efc5f1847710adbc62021261d0b180eb9f14c462a9ac9af4124ec67b8","sha256:6022c4a996bc0aa5ce2b8f0cdae1ffe410bb6123ea9ab49e9ba11ee0d752bc8a"],"state_sha256":"97605f1a1af5f311f4a574b707d66c73af9546c9388f0a39a18500b3ce65cc90"}