{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I7TJQGPTGI2PL4OOKNLO7EP7SS","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":"9b161f417e0c26cc22456c91e14b5b641a129b6cb96998e561be66da4b27a441","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T12:35:08Z","title_canon_sha256":"c53e081e80d666d204ea67e830b2085e9bd67fd69b4a64f27b73059618bb358e"},"schema_version":"1.0","source":{"id":"1705.02846","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02846","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02846v1","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02846","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"pith_short_12","alias_value":"I7TJQGPTGI2P","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I7TJQGPTGI2PL4OO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I7TJQGPT","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:62a07de451309a99c6aa789ceaa66ff1980d1c8999de02e5e4aba6c08225f436","target":"graph","created_at":"2026-05-18T00:33:18Z","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 paper we study continuous time random walks (CTRWs) such that the holding time in each state has a distribution depending on the state itself. For such processes, we provide integro-differential (backward and forward) equations of Volterra type, exhibiting a position dependent convolution kernel. Particular attention is devoted to the case where the holding times have a power-law decaying density, whose exponent depends on the state itself, which leads to variable order fractional equations. A suitable limit yields a variable order fractional heat equation, which models anomalous diffu","authors_text":"Bruno Toaldo, Costantino Ricciuti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T12:35:08Z","title":"Semi-Markov models and motion in heterogeneous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02846","kind":"arxiv","version":1},"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:d102d9eab1e2376ca7415d18a2a47bbeed546dc10eebfa2e22244d28a80100cd","target":"record","created_at":"2026-05-18T00:33:18Z","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":"9b161f417e0c26cc22456c91e14b5b641a129b6cb96998e561be66da4b27a441","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T12:35:08Z","title_canon_sha256":"c53e081e80d666d204ea67e830b2085e9bd67fd69b4a64f27b73059618bb358e"},"schema_version":"1.0","source":{"id":"1705.02846","kind":"arxiv","version":1}},"canonical_sha256":"47e69819f33234f5f1ce5356ef91ff94b7cd4932d53f79b4636f2f633fea40ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e69819f33234f5f1ce5356ef91ff94b7cd4932d53f79b4636f2f633fea40ec","first_computed_at":"2026-05-18T00:33:18.376939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:18.376939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eVKArkKcPu/DxvSwBkN7wqZqHPf3ZsRZq3DxuZ9ObNqsezuJ+jTCVqTFVPcQolX7sfwGVwxKGYS1ipmwzxJ6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:18.377432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02846","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d102d9eab1e2376ca7415d18a2a47bbeed546dc10eebfa2e22244d28a80100cd","sha256:62a07de451309a99c6aa789ceaa66ff1980d1c8999de02e5e4aba6c08225f436"],"state_sha256":"b9ce14fe43b5adaac1fbf043bad424a4fc8b6237a5b37287dc661800b6d8b133"}