{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ILO7GLQTLCJ4VISLKDYNO6PTGT","short_pith_number":"pith:ILO7GLQT","canonical_record":{"source":{"id":"1109.0622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-03T13:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"ece273f5a9437ffab28888a94dd98ef1cc41c8bc76e213bc29e12b805fdbd7e5","abstract_canon_sha256":"e816744bbae03cc2901bea9452d3cf1009b7a8590b841a16d5246f288b22fa6b"},"schema_version":"1.0"},"canonical_sha256":"42ddf32e135893caa24b50f0d779f334e473464b3442cd14dfe3482b50ade6d0","source":{"kind":"arxiv","id":"1109.0622","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0622","created_at":"2026-05-18T02:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0622v2","created_at":"2026-05-18T02:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0622","created_at":"2026-05-18T02:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"ILO7GLQTLCJ4","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"ILO7GLQTLCJ4VISL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"ILO7GLQT","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ILO7GLQTLCJ4VISLKDYNO6PTGT","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-03T13:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"ece273f5a9437ffab28888a94dd98ef1cc41c8bc76e213bc29e12b805fdbd7e5","abstract_canon_sha256":"e816744bbae03cc2901bea9452d3cf1009b7a8590b841a16d5246f288b22fa6b"},"schema_version":"1.0"},"canonical_sha256":"42ddf32e135893caa24b50f0d779f334e473464b3442cd14dfe3482b50ade6d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:40.416438Z","signature_b64":"uAlwgPDtagj7yiRJrrEU/u/3GsdoNWwNEqst0MvQpMwMbzXV4p6gO76nl2iqgCHE0o7ZFru7ntLtfYFmm8U0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42ddf32e135893caa24b50f0d779f334e473464b3442cd14dfe3482b50ade6d0","last_reissued_at":"2026-05-18T02:00:40.415699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:40.415699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0622","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gm4v6R80DooL0VKF517uJHODEIT9qxacDhNmBskjE05ViFBYqxaxy80f03l2XRhiyGxVCiVPBEDnxMzaNTgqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:35:38.177647Z"},"content_sha256":"7757c03cbfe3d483593b54423f835be4570fb9f7c3e740d9b97dcd91a819b67e","schema_version":"1.0","event_id":"sha256:7757c03cbfe3d483593b54423f835be4570fb9f7c3e740d9b97dcd91a819b67e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ILO7GLQTLCJ4VISLKDYNO6PTGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator solutions for fractional Fokker-Planck equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"D. Babusci, G. Dattoli, G. H. E. Duchamp, K. A. Penson, K. Gorska","submitted_at":"2011-09-03T13:50:04Z","abstract_excerpt":"We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0622","kind":"arxiv","version":2},"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":"2026-05-18T02:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7iU9RQfjNmK2A/IrJszCkUBmyIwoRXQNQA5H0Nh5+TxczaJsHpNt+sfYxlO4zZXVM8czVGhKWB2gbVQBRv/XCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:35:38.178305Z"},"content_sha256":"c70d82ef190c965e5113f8cb842a18be61ab840956a45bddfdbde90be2925aad","schema_version":"1.0","event_id":"sha256:c70d82ef190c965e5113f8cb842a18be61ab840956a45bddfdbde90be2925aad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT/bundle.json","state_url":"https://pith.science/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT/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":"2026-05-25T07:35:38Z","links":{"resolver":"https://pith.science/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT","bundle":"https://pith.science/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT/bundle.json","state":"https://pith.science/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ILO7GLQTLCJ4VISLKDYNO6PTGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ILO7GLQTLCJ4VISLKDYNO6PTGT","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":"e816744bbae03cc2901bea9452d3cf1009b7a8590b841a16d5246f288b22fa6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-03T13:50:04Z","title_canon_sha256":"ece273f5a9437ffab28888a94dd98ef1cc41c8bc76e213bc29e12b805fdbd7e5"},"schema_version":"1.0","source":{"id":"1109.0622","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0622","created_at":"2026-05-18T02:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0622v2","created_at":"2026-05-18T02:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0622","created_at":"2026-05-18T02:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"ILO7GLQTLCJ4","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"ILO7GLQTLCJ4VISL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"ILO7GLQT","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:c70d82ef190c965e5113f8cb842a18be61ab840956a45bddfdbde90be2925aad","target":"graph","created_at":"2026-05-18T02:00:40Z","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 obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.","authors_text":"D. Babusci, G. Dattoli, G. H. E. Duchamp, K. A. Penson, K. Gorska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-03T13:50:04Z","title":"Operator solutions for fractional Fokker-Planck equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0622","kind":"arxiv","version":2},"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":"sha256:7757c03cbfe3d483593b54423f835be4570fb9f7c3e740d9b97dcd91a819b67e","target":"record","created_at":"2026-05-18T02:00:40Z","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":"e816744bbae03cc2901bea9452d3cf1009b7a8590b841a16d5246f288b22fa6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-09-03T13:50:04Z","title_canon_sha256":"ece273f5a9437ffab28888a94dd98ef1cc41c8bc76e213bc29e12b805fdbd7e5"},"schema_version":"1.0","source":{"id":"1109.0622","kind":"arxiv","version":2}},"canonical_sha256":"42ddf32e135893caa24b50f0d779f334e473464b3442cd14dfe3482b50ade6d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42ddf32e135893caa24b50f0d779f334e473464b3442cd14dfe3482b50ade6d0","first_computed_at":"2026-05-18T02:00:40.415699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:40.415699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uAlwgPDtagj7yiRJrrEU/u/3GsdoNWwNEqst0MvQpMwMbzXV4p6gO76nl2iqgCHE0o7ZFru7ntLtfYFmm8U0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:40.416438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0622","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7757c03cbfe3d483593b54423f835be4570fb9f7c3e740d9b97dcd91a819b67e","sha256:c70d82ef190c965e5113f8cb842a18be61ab840956a45bddfdbde90be2925aad"],"state_sha256":"0face23c408a47b838833402ac1744c2710e89ed905c826a53ff2d6f096298b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yitNgEggTUQGxZp9IWG2FtC3bWHdVUSz9QmBidMOlGf7HFjPtp/nwavE+nWSaizJIf0B+cX6xghgmsOvqR7ZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T07:35:38.181722Z","bundle_sha256":"6bace204c03124eccec5bb30704ed88f5b20510919075e8dc5efce4182f63e3d"}}