{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XQEJXALCZ7D3NSIFXJ24K6KIKC","short_pith_number":"pith:XQEJXALC","schema_version":"1.0","canonical_sha256":"bc089b8162cfc7b6c905ba75c5794850a0d795cc8d16739f5b45595cd413b99a","source":{"kind":"arxiv","id":"1406.4669","version":3},"attestation_state":"computed","paper":{"title":"L\\'evy mixing related to distributed order calculus, subordinators and slow diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo","submitted_at":"2014-06-18T10:10:51Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.4669","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T10:10:51Z","cross_cats_sorted":[],"title_canon_sha256":"1f9a9a4f4680953bbf86a6a8682b58710c6f4056cdc6af38f53507f8f9087f06","abstract_canon_sha256":"b3a39fd5066ee37b7ad3c2b03210c99b9fbaf40ad9b9845074193a38ec252799"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:24.399039Z","signature_b64":"ADkCFG5bf+On+bmVYEeWUkA50Rp2s6CYX8krJ6OliAKajPXFk0W9aWfoLYZlg6RzGBar/VzxQlwTxwpsi0HTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc089b8162cfc7b6c905ba75c5794850a0d795cc8d16739f5b45595cd413b99a","last_reissued_at":"2026-05-18T02:05:24.398290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:24.398290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L\\'evy mixing related to distributed order calculus, subordinators and slow diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo","submitted_at":"2014-06-18T10:10:51Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4669","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.4669","created_at":"2026-05-18T02:05:24.398435+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.4669v3","created_at":"2026-05-18T02:05:24.398435+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4669","created_at":"2026-05-18T02:05:24.398435+00:00"},{"alias_kind":"pith_short_12","alias_value":"XQEJXALCZ7D3","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XQEJXALCZ7D3NSIF","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XQEJXALC","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC","json":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC.json","graph_json":"https://pith.science/api/pith-number/XQEJXALCZ7D3NSIFXJ24K6KIKC/graph.json","events_json":"https://pith.science/api/pith-number/XQEJXALCZ7D3NSIFXJ24K6KIKC/events.json","paper":"https://pith.science/paper/XQEJXALC"},"agent_actions":{"view_html":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC","download_json":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC.json","view_paper":"https://pith.science/paper/XQEJXALC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.4669&json=true","fetch_graph":"https://pith.science/api/pith-number/XQEJXALCZ7D3NSIFXJ24K6KIKC/graph.json","fetch_events":"https://pith.science/api/pith-number/XQEJXALCZ7D3NSIFXJ24K6KIKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC/action/storage_attestation","attest_author":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC/action/author_attestation","sign_citation":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC/action/citation_signature","submit_replication":"https://pith.science/pith/XQEJXALCZ7D3NSIFXJ24K6KIKC/action/replication_record"}},"created_at":"2026-05-18T02:05:24.398435+00:00","updated_at":"2026-05-18T02:05:24.398435+00:00"}