{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TINRFIGWE5OQV5QMNCKTCROC5A","short_pith_number":"pith:TINRFIGW","canonical_record":{"source":{"id":"1601.01476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T10:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"ea0a0b85f4a7a0292d45d8c346c7294835a521c83c2706d06906eaf0e7c934de","abstract_canon_sha256":"89c54b790e8b59d10852679a4a24a4fbe24d99a43592440437f49a56f7c2eaf5"},"schema_version":"1.0"},"canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","source":{"kind":"arxiv","id":"1601.01476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01476","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01476v1","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01476","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"TINRFIGWE5OQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TINRFIGWE5OQV5QM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TINRFIGW","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TINRFIGWE5OQV5QMNCKTCROC5A","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T10:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"ea0a0b85f4a7a0292d45d8c346c7294835a521c83c2706d06906eaf0e7c934de","abstract_canon_sha256":"89c54b790e8b59d10852679a4a24a4fbe24d99a43592440437f49a56f7c2eaf5"},"schema_version":"1.0"},"canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:13.541723Z","signature_b64":"hQm3DxdDEaFt11vSqC85LTUaWvxcu+nyGcHNmdnCEQjeoTa8t9n6RcAwPE8MUwcsqBRxnCx0jManOQ2A1m+jDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","last_reissued_at":"2026-05-18T01:23:13.541106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:13.541106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01476","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":"2026-05-18T01:23:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmImrguDVJTFyAKtxQac+uWWee7u8/0n94uBjJiWWm/MDsmQdnDcqagUj4SB6qUy0D+vjv28k1T9stN71bjFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T21:22:59.750182Z"},"content_sha256":"3601004a857d9b31d2fcde1e1b3bd51ef206bf30f203865e15f4e45a9abd67da","schema_version":"1.0","event_id":"sha256:3601004a857d9b31d2fcde1e1b3bd51ef206bf30f203865e15f4e45a9abd67da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TINRFIGWE5OQV5QMNCKTCROC5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional diffusion-type equations with exponential and logarithmic differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luisa Beghin","submitted_at":"2016-01-07T10:44:01Z","abstract_excerpt":"We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential differential operator expressed in terms of the Riesz-Feller derivative. We prove that this produces a random additional term in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involvi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01476","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":"2026-05-18T01:23:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6Njw2vMQ2XeBTtv6elgorgoDRUngjjN4vbstFvS+6BUsmfi4R40W/sj2E69qzAQmbdwNHPVK2HJmGNjIHefDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T21:22:59.750537Z"},"content_sha256":"250d12016d81d72a9b9df51154d8c3f1456bce6d23c3f2fa48c987d29caffce0","schema_version":"1.0","event_id":"sha256:250d12016d81d72a9b9df51154d8c3f1456bce6d23c3f2fa48c987d29caffce0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/bundle.json","state_url":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TINRFIGWE5OQV5QMNCKTCROC5A/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":"2026-06-27T21:22:59Z","links":{"resolver":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A","bundle":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/bundle.json","state":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TINRFIGWE5OQV5QMNCKTCROC5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TINRFIGWE5OQV5QMNCKTCROC5A","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":"89c54b790e8b59d10852679a4a24a4fbe24d99a43592440437f49a56f7c2eaf5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T10:44:01Z","title_canon_sha256":"ea0a0b85f4a7a0292d45d8c346c7294835a521c83c2706d06906eaf0e7c934de"},"schema_version":"1.0","source":{"id":"1601.01476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01476","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01476v1","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01476","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"TINRFIGWE5OQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TINRFIGWE5OQV5QM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TINRFIGW","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:250d12016d81d72a9b9df51154d8c3f1456bce6d23c3f2fa48c987d29caffce0","target":"graph","created_at":"2026-05-18T01:23:13Z","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 deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential differential operator expressed in terms of the Riesz-Feller derivative. We prove that this produces a random additional term in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involvi","authors_text":"Luisa Beghin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T10:44:01Z","title":"Fractional diffusion-type equations with exponential and logarithmic differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01476","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":"sha256:3601004a857d9b31d2fcde1e1b3bd51ef206bf30f203865e15f4e45a9abd67da","target":"record","created_at":"2026-05-18T01:23:13Z","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":"89c54b790e8b59d10852679a4a24a4fbe24d99a43592440437f49a56f7c2eaf5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T10:44:01Z","title_canon_sha256":"ea0a0b85f4a7a0292d45d8c346c7294835a521c83c2706d06906eaf0e7c934de"},"schema_version":"1.0","source":{"id":"1601.01476","kind":"arxiv","version":1}},"canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","first_computed_at":"2026-05-18T01:23:13.541106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:13.541106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hQm3DxdDEaFt11vSqC85LTUaWvxcu+nyGcHNmdnCEQjeoTa8t9n6RcAwPE8MUwcsqBRxnCx0jManOQ2A1m+jDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:13.541723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3601004a857d9b31d2fcde1e1b3bd51ef206bf30f203865e15f4e45a9abd67da","sha256:250d12016d81d72a9b9df51154d8c3f1456bce6d23c3f2fa48c987d29caffce0"],"state_sha256":"c49847bcd6bca2610c19efc0403e60e081ff37c9d1a5d476d563e5f61d9cff94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LEeAlWXi/D53uCGEPqQOtrUMkZ0BI5EKuUpgXi0Eq1KB145BYUcShDp8Zrjnmr1rVil/8x4GcB6ZVXd5fZE2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T21:22:59.752502Z","bundle_sha256":"84560614954d1eea4206c9e21532f81fa872ff9ef2e2b5c54a03b67310a07d88"}}