{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:I7TJQGPTGI2PL4OOKNLO7EP7SS","short_pith_number":"pith:I7TJQGPT","canonical_record":{"source":{"id":"1705.02846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T12:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"c53e081e80d666d204ea67e830b2085e9bd67fd69b4a64f27b73059618bb358e","abstract_canon_sha256":"9b161f417e0c26cc22456c91e14b5b641a129b6cb96998e561be66da4b27a441"},"schema_version":"1.0"},"canonical_sha256":"47e69819f33234f5f1ce5356ef91ff94b7cd4932d53f79b4636f2f633fea40ec","source":{"kind":"arxiv","id":"1705.02846","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:I7TJQGPTGI2PL4OOKNLO7EP7SS","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-08T12:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"c53e081e80d666d204ea67e830b2085e9bd67fd69b4a64f27b73059618bb358e","abstract_canon_sha256":"9b161f417e0c26cc22456c91e14b5b641a129b6cb96998e561be66da4b27a441"},"schema_version":"1.0"},"canonical_sha256":"47e69819f33234f5f1ce5356ef91ff94b7cd4932d53f79b4636f2f633fea40ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:18.377432Z","signature_b64":"eVKArkKcPu/DxvSwBkN7wqZqHPf3ZsRZq3DxuZ9ObNqsezuJ+jTCVqTFVPcQolX7sfwGVwxKGYS1ipmwzxJ6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47e69819f33234f5f1ce5356ef91ff94b7cd4932d53f79b4636f2f633fea40ec","last_reissued_at":"2026-05-18T00:33:18.376939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:18.376939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02846","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TllfBpAr3wlEmO5T9D4HySfuPcesI7ESKjr+kzd5egiE9owTq+a2IBxeoiKHSDwf5dtl6TbMgXSSlOHAfSv/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:43.046087Z"},"content_sha256":"d102d9eab1e2376ca7415d18a2a47bbeed546dc10eebfa2e22244d28a80100cd","schema_version":"1.0","event_id":"sha256:d102d9eab1e2376ca7415d18a2a47bbeed546dc10eebfa2e22244d28a80100cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:I7TJQGPTGI2PL4OOKNLO7EP7SS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-Markov models and motion in heterogeneous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Toaldo, Costantino Ricciuti","submitted_at":"2017-05-08T12:35:08Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02846","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"azHW12b5gdkjyk0wnPeUDtneDxMTcSSnHvOXz3FpU6hgE0wHZjyres59FwTNCmCR+llS0j1QXEP+3u56IhRNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:43.046453Z"},"content_sha256":"62a07de451309a99c6aa789ceaa66ff1980d1c8999de02e5e4aba6c08225f436","schema_version":"1.0","event_id":"sha256:62a07de451309a99c6aa789ceaa66ff1980d1c8999de02e5e4aba6c08225f436"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS/bundle.json","state_url":"https://pith.science/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T08:33:43Z","links":{"resolver":"https://pith.science/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS","bundle":"https://pith.science/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS/bundle.json","state":"https://pith.science/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7TJQGPTGI2PL4OOKNLO7EP7SS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1P1MB7r7rCtzmktmOGDB/inU7pDFV4jsKlmy0yYrI3CpvLQ39oWDH+MJHikkV29v66n+td/dC8qi+QIMnOvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:33:43.048544Z","bundle_sha256":"b712223c80247cf17bb6ea8d2b873405480127b13ef3eebc3f0cb74e82e3ec37"}}