{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CP3U7A52IQEMNFY2HMIDMVM37Q","short_pith_number":"pith:CP3U7A52","schema_version":"1.0","canonical_sha256":"13f74f83ba4408c6971a3b1036559bfc310ead80365baa3ef0cf152cc1db2096","source":{"kind":"arxiv","id":"1807.07060","version":1},"attestation_state":"computed","paper":{"title":"Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo, Mladen Savov","submitted_at":"2018-07-18T17:55:09Z","abstract_excerpt":"In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order $\\alpha(x)$-fractional diffusion equation is a particular case of our analysis and it turns out that it is associated with a suitable (non-independent) time-change of the Brownian motion. The resulting process is semi-Markovian and its paths have intervals of constancy, as it happens for the delayed Brownian motion, suitable to model trapping effects induced by "},"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":"1807.07060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-18T17:55:09Z","cross_cats_sorted":[],"title_canon_sha256":"e51462cde739ffc67a4119ce8d591bb89056bb9214c9a148a8a082ae325e4f4d","abstract_canon_sha256":"1b46a04c8d76053cc2d0c55f687a4b8b7d02efc853ddb2b0c0d2e0340008ca96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:24.891065Z","signature_b64":"5HBpxTSiXUb0UYjStuHy9Nydd1hgDXKX7K/UpjGaUgceE3N4MavBw1apbED9HBuPglz7+vvjhjC28kxTLGUZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13f74f83ba4408c6971a3b1036559bfc310ead80365baa3ef0cf152cc1db2096","last_reissued_at":"2026-05-18T00:10:24.890492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:24.890492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo, Mladen Savov","submitted_at":"2018-07-18T17:55:09Z","abstract_excerpt":"In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order $\\alpha(x)$-fractional diffusion equation is a particular case of our analysis and it turns out that it is associated with a suitable (non-independent) time-change of the Brownian motion. The resulting process is semi-Markovian and its paths have intervals of constancy, as it happens for the delayed Brownian motion, suitable to model trapping effects induced by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07060","kind":"arxiv","version":1},"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":"1807.07060","created_at":"2026-05-18T00:10:24.890587+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.07060v1","created_at":"2026-05-18T00:10:24.890587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07060","created_at":"2026-05-18T00:10:24.890587+00:00"},{"alias_kind":"pith_short_12","alias_value":"CP3U7A52IQEM","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CP3U7A52IQEMNFY2","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CP3U7A52","created_at":"2026-05-18T12:32:16.446611+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/CP3U7A52IQEMNFY2HMIDMVM37Q","json":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q.json","graph_json":"https://pith.science/api/pith-number/CP3U7A52IQEMNFY2HMIDMVM37Q/graph.json","events_json":"https://pith.science/api/pith-number/CP3U7A52IQEMNFY2HMIDMVM37Q/events.json","paper":"https://pith.science/paper/CP3U7A52"},"agent_actions":{"view_html":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q","download_json":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q.json","view_paper":"https://pith.science/paper/CP3U7A52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.07060&json=true","fetch_graph":"https://pith.science/api/pith-number/CP3U7A52IQEMNFY2HMIDMVM37Q/graph.json","fetch_events":"https://pith.science/api/pith-number/CP3U7A52IQEMNFY2HMIDMVM37Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q/action/storage_attestation","attest_author":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q/action/author_attestation","sign_citation":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q/action/citation_signature","submit_replication":"https://pith.science/pith/CP3U7A52IQEMNFY2HMIDMVM37Q/action/replication_record"}},"created_at":"2026-05-18T00:10:24.890587+00:00","updated_at":"2026-05-18T00:10:24.890587+00:00"}