{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TF6UTHVWRRZ2BHTIKZ7TFPXZVO","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":"6ea75c933c66a1c01b0a55fed6d67021a0215df697f86f70f4a006198cc1b75e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-19T12:44:44Z","title_canon_sha256":"d9da6ae336671098b48f1c8189daed8ff6e87e03608847758ebab16e9fa76c74"},"schema_version":"1.0","source":{"id":"1804.07119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07119","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07119v2","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07119","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"TF6UTHVWRRZ2","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TF6UTHVWRRZ2BHTI","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TF6UTHVW","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:f5cf398e269b20d144004e8649853fdb059fee670d16abe4e6666ccfea2ea124","target":"graph","created_at":"2026-05-18T00:04:07Z","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 article the relation between the tail behaviours of a free regular infinitely divisible (positively supported) probability measure and its L\\'evy measure is studied. An important example of such a measure is the compound free Poisson distribution, which often occurs as a limiting spectral distribution of certain sequences of random matrices. We also describe a connection between an analogous classical result of Embrechts et al. [1979] and our result using the Bercovici-Pata bijection.","authors_text":"Arijit Chakrabarty, Rajat Subhra Hazra, Sukrit Chakraborty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-19T12:44:44Z","title":"Regular variation and free regular infinitely divisible laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07119","kind":"arxiv","version":2},"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":"sha256:35c9afc84de0241091f0582914eaff053bda69440f551ef34f6f72cd6d621e02","target":"record","created_at":"2026-05-18T00:04:07Z","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":"6ea75c933c66a1c01b0a55fed6d67021a0215df697f86f70f4a006198cc1b75e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-19T12:44:44Z","title_canon_sha256":"d9da6ae336671098b48f1c8189daed8ff6e87e03608847758ebab16e9fa76c74"},"schema_version":"1.0","source":{"id":"1804.07119","kind":"arxiv","version":2}},"canonical_sha256":"997d499eb68c73a09e68567f32bef9ab999b471395280bc922359253ca20e9ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"997d499eb68c73a09e68567f32bef9ab999b471395280bc922359253ca20e9ed","first_computed_at":"2026-05-18T00:04:07.753932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:07.753932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4EiW46byL4/N2pSQDACKlIZ7P9D+se9rI4GT3W+n35aVJHpHe/j614A5j+XpF/pIrmEWsaCR3vsH1dwTD0ZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:07.754511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35c9afc84de0241091f0582914eaff053bda69440f551ef34f6f72cd6d621e02","sha256:f5cf398e269b20d144004e8649853fdb059fee670d16abe4e6666ccfea2ea124"],"state_sha256":"b25ebc9d6ed5392958e95cc4bd3440a7b9b424643cd7610118186977b7634fdc"}