{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XQEJXALCZ7D3NSIFXJ24K6KIKC","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":"b3a39fd5066ee37b7ad3c2b03210c99b9fbaf40ad9b9845074193a38ec252799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T10:10:51Z","title_canon_sha256":"1f9a9a4f4680953bbf86a6a8682b58710c6f4056cdc6af38f53507f8f9087f06"},"schema_version":"1.0","source":{"id":"1406.4669","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4669","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4669v3","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4669","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"XQEJXALCZ7D3","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XQEJXALCZ7D3NSIF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XQEJXALC","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:0655acb1921b89762abdafb3f28b1dc8710dcef2fe125b7020e6b9f023c9c33d","target":"graph","created_at":"2026-05-18T02:05:24Z","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":"The study of distributed order calculus usually concerns about fractional derivatives of the form $\\int_0^1 \\partial^\\alpha u \\, m(d\\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\\'evy mixing is proposed. Non-decreasing L\\'evy processes associated to L\\'evy triplets of the form $\\l a(y), b(y), \\nu(ds, y) \\r$ are considered and the parameter $y$ is randomized by means of a probability measure. The related subordinators are studied from different point of views. Some distributional properties are obtained and the interplay with inverse local ","authors_text":"Bruno Toaldo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T10:10:51Z","title":"L\\'evy mixing related to distributed order calculus, subordinators and slow diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4669","kind":"arxiv","version":3},"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:ef89787bd2a85dd78acffb24859874bbc43fd5b38097bad9fd75cad121897345","target":"record","created_at":"2026-05-18T02:05:24Z","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":"b3a39fd5066ee37b7ad3c2b03210c99b9fbaf40ad9b9845074193a38ec252799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T10:10:51Z","title_canon_sha256":"1f9a9a4f4680953bbf86a6a8682b58710c6f4056cdc6af38f53507f8f9087f06"},"schema_version":"1.0","source":{"id":"1406.4669","kind":"arxiv","version":3}},"canonical_sha256":"bc089b8162cfc7b6c905ba75c5794850a0d795cc8d16739f5b45595cd413b99a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc089b8162cfc7b6c905ba75c5794850a0d795cc8d16739f5b45595cd413b99a","first_computed_at":"2026-05-18T02:05:24.398290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:24.398290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ADkCFG5bf+On+bmVYEeWUkA50Rp2s6CYX8krJ6OliAKajPXFk0W9aWfoLYZlg6RzGBar/VzxQlwTxwpsi0HTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:24.399039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4669","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef89787bd2a85dd78acffb24859874bbc43fd5b38097bad9fd75cad121897345","sha256:0655acb1921b89762abdafb3f28b1dc8710dcef2fe125b7020e6b9f023c9c33d"],"state_sha256":"7d13298cd3315a9a00b684b1a65758a1ee1e62070be730fcca0e119504501f18"}