{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QF7KI7PG5C5I6MQ3ZPGYBOLCZR","short_pith_number":"pith:QF7KI7PG","canonical_record":{"source":{"id":"1102.4729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-23T13:00:03Z","cross_cats_sorted":[],"title_canon_sha256":"6ddac8feae1e18b6fed3e0d4e9da75a15007175af2b1c76f273de08c87c0f323","abstract_canon_sha256":"86343fbb6e1e282ee90be26fec3c04498772e24d2333d9a3371acc31196e9851"},"schema_version":"1.0"},"canonical_sha256":"817ea47de6e8ba8f321bcbcd80b962cc6771f8f9565d64fa00ca6fc21c914ad3","source":{"kind":"arxiv","id":"1102.4729","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4729","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4729v1","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4729","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"QF7KI7PG5C5I","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QF7KI7PG5C5I6MQ3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QF7KI7PG","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QF7KI7PG5C5I6MQ3ZPGYBOLCZR","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-23T13:00:03Z","cross_cats_sorted":[],"title_canon_sha256":"6ddac8feae1e18b6fed3e0d4e9da75a15007175af2b1c76f273de08c87c0f323","abstract_canon_sha256":"86343fbb6e1e282ee90be26fec3c04498772e24d2333d9a3371acc31196e9851"},"schema_version":"1.0"},"canonical_sha256":"817ea47de6e8ba8f321bcbcd80b962cc6771f8f9565d64fa00ca6fc21c914ad3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:07.482811Z","signature_b64":"5pho6mxLJnkflDymsNOIu93GVG0woXOHCpCAjfHD77esLqPc65ncRpro75tSQ/CR5rqvoCbSThT4Rr2tcltVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"817ea47de6e8ba8f321bcbcd80b962cc6771f8f9565d64fa00ca6fc21c914ad3","last_reissued_at":"2026-05-18T04:28:07.482127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:07.482127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4729","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":"2026-05-18T04:28:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKL/f91sURr6v0m1URqZLMfFHXiy3agXEg6WDM5q9Vagj0lFx4f9JBkITwzjtup52rEu5ATjoV7ImouQJ9YBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:05:55.776296Z"},"content_sha256":"0c875b29798fb825d85c8cb32c2f3cd645f2b3f5a5658ff22e2b3bfe61073fbc","schema_version":"1.0","event_id":"sha256:0c875b29798fb825d85c8cb32c2f3cd645f2b3f5a5658ff22e2b3bfe61073fbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QF7KI7PG5C5I6MQ3ZPGYBOLCZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional diffusion equations and processes with randomly varying time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Luisa Beghin","submitted_at":"2011-02-23T13:00:03Z","abstract_excerpt":"In this paper the solutions $u_{\\nu}=u_{\\nu}(x,t)$ to fractional diffusion equations of order $0<\\nu \\leq 2$ are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations of order $\\nu =\\frac{1}{2^n}$, $n\\geq 1,$ we show that the solutions $u_{{1/2^n}}$ correspond to the distribution of the $n$-times iterated Brownian motion. For these processes the distributions of the maximum and of the sojourn time are explicitly given. The case of fractional equations of order $\\nu =\\frac{2}{3^n}$, $n\\geq 1,$ is also investigated and rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4729","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":"2026-05-18T04:28:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URFUAcU9lwqeAk8tU/WB2T3rjxxtG+RAtaRci64oid5tugeA1IhHY+myI1mcoyjUCktOkSrPmwayeXTGj0+NAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:05:55.776946Z"},"content_sha256":"0d4ff0e72f492c4bb02742c7c88f58a776baa283f8ef4912278cdaf8c211afb3","schema_version":"1.0","event_id":"sha256:0d4ff0e72f492c4bb02742c7c88f58a776baa283f8ef4912278cdaf8c211afb3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR/bundle.json","state_url":"https://pith.science/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR/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":"2026-06-05T05:05:55Z","links":{"resolver":"https://pith.science/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR","bundle":"https://pith.science/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR/bundle.json","state":"https://pith.science/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QF7KI7PG5C5I6MQ3ZPGYBOLCZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QF7KI7PG5C5I6MQ3ZPGYBOLCZR","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":"86343fbb6e1e282ee90be26fec3c04498772e24d2333d9a3371acc31196e9851","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-23T13:00:03Z","title_canon_sha256":"6ddac8feae1e18b6fed3e0d4e9da75a15007175af2b1c76f273de08c87c0f323"},"schema_version":"1.0","source":{"id":"1102.4729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4729","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4729v1","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4729","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"QF7KI7PG5C5I","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QF7KI7PG5C5I6MQ3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QF7KI7PG","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:0d4ff0e72f492c4bb02742c7c88f58a776baa283f8ef4912278cdaf8c211afb3","target":"graph","created_at":"2026-05-18T04:28:07Z","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 the solutions $u_{\\nu}=u_{\\nu}(x,t)$ to fractional diffusion equations of order $0<\\nu \\leq 2$ are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations of order $\\nu =\\frac{1}{2^n}$, $n\\geq 1,$ we show that the solutions $u_{{1/2^n}}$ correspond to the distribution of the $n$-times iterated Brownian motion. For these processes the distributions of the maximum and of the sojourn time are explicitly given. The case of fractional equations of order $\\nu =\\frac{2}{3^n}$, $n\\geq 1,$ is also investigated and rel","authors_text":"Enzo Orsingher, Luisa Beghin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-23T13:00:03Z","title":"Fractional diffusion equations and processes with randomly varying time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4729","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":"sha256:0c875b29798fb825d85c8cb32c2f3cd645f2b3f5a5658ff22e2b3bfe61073fbc","target":"record","created_at":"2026-05-18T04:28:07Z","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":"86343fbb6e1e282ee90be26fec3c04498772e24d2333d9a3371acc31196e9851","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-23T13:00:03Z","title_canon_sha256":"6ddac8feae1e18b6fed3e0d4e9da75a15007175af2b1c76f273de08c87c0f323"},"schema_version":"1.0","source":{"id":"1102.4729","kind":"arxiv","version":1}},"canonical_sha256":"817ea47de6e8ba8f321bcbcd80b962cc6771f8f9565d64fa00ca6fc21c914ad3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"817ea47de6e8ba8f321bcbcd80b962cc6771f8f9565d64fa00ca6fc21c914ad3","first_computed_at":"2026-05-18T04:28:07.482127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:07.482127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5pho6mxLJnkflDymsNOIu93GVG0woXOHCpCAjfHD77esLqPc65ncRpro75tSQ/CR5rqvoCbSThT4Rr2tcltVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:07.482811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c875b29798fb825d85c8cb32c2f3cd645f2b3f5a5658ff22e2b3bfe61073fbc","sha256:0d4ff0e72f492c4bb02742c7c88f58a776baa283f8ef4912278cdaf8c211afb3"],"state_sha256":"b2aee109809b44596908d08dceaa4cdaffa038edd8f5c3bb9e36ce2f1b28071a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFqtyKbLwSTjsUwrBqEz5oUymAvkqmVC5rktaqwpgTGL4gG7X/LNRIf09+jQcBkJsHv1dbS0rhIYzkSO9m3vDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:05:55.780270Z","bundle_sha256":"842c4ef47e86843874d8c9fb046c0be0fc53e243874077751d69632a736deb71"}}