{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PJGVFAOJZ7H4AWM5WMMLBMDRVJ","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":"33de66acb268314ace1b03055fb36e1307d2c3cd6a9b7e490a67cf99f9fc0a8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T05:12:17Z","title_canon_sha256":"2bf2ac5f70fb3224f7e876cf89d806fd9f3c7447524695e982b64c5cbf3c24fa"},"schema_version":"1.0","source":{"id":"1506.02778","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02778","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02778v5","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02778","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"PJGVFAOJZ7H4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PJGVFAOJZ7H4AWM5","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PJGVFAOJ","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:b726526a732baa0b00d024c54287ada563a0929b8372abec83a6458aba21781b","target":"graph","created_at":"2026-05-18T01:11:55Z","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"},"paper":{"abstract_excerpt":"We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the representation of the Linnik distribution as a normal scale mixture with the Mittag-Leffler mixing distribution. As a corollary, we obtain the known representation of the Linnik distribution as a scale mixture of Laplace distributions. Another corollary of the main representation is the theorem establishing that the distributions of random sums of independent identi","authors_text":"Alexander Zeifman, Victor Korolev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T05:12:17Z","title":"A note on mixture representations for the Linnik and Mittag-Leffler distributions and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02778","kind":"arxiv","version":5},"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":"sha256:7766d1ee32043fbbf148baee471d718fd2dae04972e951685480cebbc69ce9cd","target":"record","created_at":"2026-05-18T01:11:55Z","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":"33de66acb268314ace1b03055fb36e1307d2c3cd6a9b7e490a67cf99f9fc0a8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T05:12:17Z","title_canon_sha256":"2bf2ac5f70fb3224f7e876cf89d806fd9f3c7447524695e982b64c5cbf3c24fa"},"schema_version":"1.0","source":{"id":"1506.02778","kind":"arxiv","version":5}},"canonical_sha256":"7a4d5281c9cfcfc0599db318b0b071aa55544bcfce4183109a0d1fc2da9e3224","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4d5281c9cfcfc0599db318b0b071aa55544bcfce4183109a0d1fc2da9e3224","first_computed_at":"2026-05-18T01:11:55.141488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.141488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ObJAf2ftQIU96dlWkO1TVQT4+zvLbrCUCD5O2Ebym3i41vg3u7zZG7dnHSsi/qpNa8Uyp41On6WBLV3ssg9NAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.141858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02778","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7766d1ee32043fbbf148baee471d718fd2dae04972e951685480cebbc69ce9cd","sha256:b726526a732baa0b00d024c54287ada563a0929b8372abec83a6458aba21781b"],"state_sha256":"b2b844bb2a58e9775fbdd74b74ac2f18af87663e4b5f58fdc4c07e5092875f42"}