{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WQ3O3SAKE7RZSLWSSMHEPAYSJQ","short_pith_number":"pith:WQ3O3SAK","canonical_record":{"source":{"id":"1307.1696","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-05T19:40:25Z","cross_cats_sorted":[],"title_canon_sha256":"f45b313556f2eba46c09918b0024c7722b639c1756901246ed0f451c8f1dd235","abstract_canon_sha256":"36daa8fa5440fbe328038f3eef45e33aae5897eba17482af432b3d570fdb460a"},"schema_version":"1.0"},"canonical_sha256":"b436edc80a27e3992ed2930e4783124c0a860f379613f0e7c31bd2bdd4707181","source":{"kind":"arxiv","id":"1307.1696","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1696","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1696v4","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1696","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"WQ3O3SAKE7RZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WQ3O3SAKE7RZSLWS","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WQ3O3SAK","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WQ3O3SAKE7RZSLWSSMHEPAYSJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1696","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-05T19:40:25Z","cross_cats_sorted":[],"title_canon_sha256":"f45b313556f2eba46c09918b0024c7722b639c1756901246ed0f451c8f1dd235","abstract_canon_sha256":"36daa8fa5440fbe328038f3eef45e33aae5897eba17482af432b3d570fdb460a"},"schema_version":"1.0"},"canonical_sha256":"b436edc80a27e3992ed2930e4783124c0a860f379613f0e7c31bd2bdd4707181","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:55.698860Z","signature_b64":"3M0ag7zKp4PN7yAepUf8cNCBdYpSXmsYWDlhU+BdRGGUDp1pCtha7h6SRfZRPCE8chctkfjlvTRtYZoJh+VrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b436edc80a27e3992ed2930e4783124c0a860f379613f0e7c31bd2bdd4707181","last_reissued_at":"2026-05-18T00:30:55.698144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:55.698144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1696","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f40mu26d3BQAF+wMgD3McdEhh9StQf6Gm+bsh306gxtsnDUwogCn6u4UQCu+CWrm3E0caQcUxgWBf/0HHwYKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:41:16.356524Z"},"content_sha256":"f847014daf4bb70f008f4a3b2b4f21aca45ad0b69699a11134e612c10aabd9ea","schema_version":"1.0","event_id":"sha256:f847014daf4bb70f008f4a3b2b4f21aca45ad0b69699a11134e612c10aabd9ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WQ3O3SAKE7RZSLWSSMHEPAYSJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Diffusion-Telegraph Equations and their Associated Stochastic Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Federico Polito, Mirko D'Ovidio","submitted_at":"2013-07-05T19:40:25Z","abstract_excerpt":"We present the stochastic solution to a generalized fractional partial differential equation involving a regularized operator related to the so-called Prabhakar operator and admitting, amongst others, as specific cases the fractional diffusion equation and the fractional telegraph equation. The stochastic solution is expressed as a L\\'evy process time-changed with the inverse process to a linear combination of (possibly subordinated) independent stable subordinators of different indices. Furthermore a related SDE is derived and discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1696","kind":"arxiv","version":4},"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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPacwywGDy2QoOrLxcMSZz8wUdSM69zmqkjebk+R4DvB2W523dFcFE12cIGlOH0boOOkaPM4tsmpejNMZKJ8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:41:16.357215Z"},"content_sha256":"d6dcb78124aa0421c1391bb9ac8bec591a29aa19a5cd071f65f8f10ac4cae317","schema_version":"1.0","event_id":"sha256:d6dcb78124aa0421c1391bb9ac8bec591a29aa19a5cd071f65f8f10ac4cae317"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ/bundle.json","state_url":"https://pith.science/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ/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":"2026-06-09T05:41:16Z","links":{"resolver":"https://pith.science/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ","bundle":"https://pith.science/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ/bundle.json","state":"https://pith.science/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQ3O3SAKE7RZSLWSSMHEPAYSJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WQ3O3SAKE7RZSLWSSMHEPAYSJQ","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":"36daa8fa5440fbe328038f3eef45e33aae5897eba17482af432b3d570fdb460a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-05T19:40:25Z","title_canon_sha256":"f45b313556f2eba46c09918b0024c7722b639c1756901246ed0f451c8f1dd235"},"schema_version":"1.0","source":{"id":"1307.1696","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1696","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1696v4","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1696","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"WQ3O3SAKE7RZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WQ3O3SAKE7RZSLWS","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WQ3O3SAK","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:d6dcb78124aa0421c1391bb9ac8bec591a29aa19a5cd071f65f8f10ac4cae317","target":"graph","created_at":"2026-05-18T00:30:55Z","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":"We present the stochastic solution to a generalized fractional partial differential equation involving a regularized operator related to the so-called Prabhakar operator and admitting, amongst others, as specific cases the fractional diffusion equation and the fractional telegraph equation. The stochastic solution is expressed as a L\\'evy process time-changed with the inverse process to a linear combination of (possibly subordinated) independent stable subordinators of different indices. Furthermore a related SDE is derived and discussed.","authors_text":"Federico Polito, Mirko D'Ovidio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-05T19:40:25Z","title":"Fractional Diffusion-Telegraph Equations and their Associated Stochastic Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1696","kind":"arxiv","version":4},"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:f847014daf4bb70f008f4a3b2b4f21aca45ad0b69699a11134e612c10aabd9ea","target":"record","created_at":"2026-05-18T00:30:55Z","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":"36daa8fa5440fbe328038f3eef45e33aae5897eba17482af432b3d570fdb460a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-05T19:40:25Z","title_canon_sha256":"f45b313556f2eba46c09918b0024c7722b639c1756901246ed0f451c8f1dd235"},"schema_version":"1.0","source":{"id":"1307.1696","kind":"arxiv","version":4}},"canonical_sha256":"b436edc80a27e3992ed2930e4783124c0a860f379613f0e7c31bd2bdd4707181","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b436edc80a27e3992ed2930e4783124c0a860f379613f0e7c31bd2bdd4707181","first_computed_at":"2026-05-18T00:30:55.698144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:55.698144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3M0ag7zKp4PN7yAepUf8cNCBdYpSXmsYWDlhU+BdRGGUDp1pCtha7h6SRfZRPCE8chctkfjlvTRtYZoJh+VrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:55.698860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1696","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f847014daf4bb70f008f4a3b2b4f21aca45ad0b69699a11134e612c10aabd9ea","sha256:d6dcb78124aa0421c1391bb9ac8bec591a29aa19a5cd071f65f8f10ac4cae317"],"state_sha256":"19af338c8c6bc58df99b09ebd6cd7d3b42e50d220c5ece2403074148c4874caf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oO4RyZ2vXCfbSRvPm+A+TQaGNbrIi/15KsuDTfC7mVezoA+u1gmzEUQp38Ko6h7YJQNYKDPbLACb02Qe+HkcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:41:16.361441Z","bundle_sha256":"1db22a22273c67dc95b4cdbcbcce11ce5b4e428c3957d58f78f04ad8c7046684"}}