{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HG42JMJRXA23QDP55K5NBJ3AQW","short_pith_number":"pith:HG42JMJR","canonical_record":{"source":{"id":"1902.01598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-05T09:15:41Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"d7ae7fcea6966386119887276d1ba9149071b4ae7112afea077cd5ec96fc2593","abstract_canon_sha256":"943f323319c1391bf91f13cc58eb0f15bfdf02fcb03d95b6de76a8096920ba5c"},"schema_version":"1.0"},"canonical_sha256":"39b9a4b131b835b80dfdeabad0a76085bc6d088e9b90c2f0591dc7e5c4bc7305","source":{"kind":"arxiv","id":"1902.01598","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01598","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01598v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01598","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"HG42JMJRXA23","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HG42JMJRXA23QDP5","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HG42JMJR","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HG42JMJRXA23QDP55K5NBJ3AQW","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-05T09:15:41Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"d7ae7fcea6966386119887276d1ba9149071b4ae7112afea077cd5ec96fc2593","abstract_canon_sha256":"943f323319c1391bf91f13cc58eb0f15bfdf02fcb03d95b6de76a8096920ba5c"},"schema_version":"1.0"},"canonical_sha256":"39b9a4b131b835b80dfdeabad0a76085bc6d088e9b90c2f0591dc7e5c4bc7305","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:47.203616Z","signature_b64":"yuKI5rCx+lE//zEjJEziAvk3lj3yNJ1QK9O4s/vHr+h022kwcitNYj5gWKu0ThllaHEQRlgsLkCv2K2rJQrdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39b9a4b131b835b80dfdeabad0a76085bc6d088e9b90c2f0591dc7e5c4bc7305","last_reissued_at":"2026-05-17T23:54:47.202968Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:47.202968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01598","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":"2026-05-17T23:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBuEmtcr3hhbNm1ZjxrTsTk1BlK/dHRFQXYvxuVzU4rKccQN0tz7tPNyUu0JDdsPGMNQyy4wqOTocIa7DmHGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:07:47.382670Z"},"content_sha256":"2c3888f4b7985c087ddae7ee85560e78d7479f6ebe71d318472af35a0cf64981","schema_version":"1.0","event_id":"sha256:2c3888f4b7985c087ddae7ee85560e78d7479f6ebe71d318472af35a0cf64981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HG42JMJRXA23QDP55K5NBJ3AQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable L\\'{e}vy diffusion and related model fitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"Hong Wang, Paramita Chakraborty, Xu Guo","submitted_at":"2019-02-05T09:15:41Z","abstract_excerpt":"A fractional advection-dispersion equation (fADE) has been advocated for heavy-tailed flows where the usual Brownian diffusion models fail. A stochastic differential equation (SDE) driven by a stable L\\'{e}vy process gives a forward equation that matches the space-fractional advection-dispersion equation and thus gives the stochastic framework of particle tracking for heavy-tailed flows. For constant advection and dispersion coefficient functions, the solution to such SDE itself is a stable process and can be derived easily by least square parameter fitting from the observed flow concentration"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01598","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":"2026-05-17T23:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ViGhcMqGtpibT59/0SfxgFtieU362Fx2gNVyW8yUlM2JtLFZW24labDAiV3ZqiNWpSxbr2FNaS3HubC74j1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:07:47.383326Z"},"content_sha256":"edc26d67be6c6b21d1642589fb28311af0bea1511e00155159c4a93f2015af11","schema_version":"1.0","event_id":"sha256:edc26d67be6c6b21d1642589fb28311af0bea1511e00155159c4a93f2015af11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HG42JMJRXA23QDP55K5NBJ3AQW/bundle.json","state_url":"https://pith.science/pith/HG42JMJRXA23QDP55K5NBJ3AQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HG42JMJRXA23QDP55K5NBJ3AQW/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":"2026-06-08T02:07:47Z","links":{"resolver":"https://pith.science/pith/HG42JMJRXA23QDP55K5NBJ3AQW","bundle":"https://pith.science/pith/HG42JMJRXA23QDP55K5NBJ3AQW/bundle.json","state":"https://pith.science/pith/HG42JMJRXA23QDP55K5NBJ3AQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HG42JMJRXA23QDP55K5NBJ3AQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HG42JMJRXA23QDP55K5NBJ3AQW","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":"943f323319c1391bf91f13cc58eb0f15bfdf02fcb03d95b6de76a8096920ba5c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-05T09:15:41Z","title_canon_sha256":"d7ae7fcea6966386119887276d1ba9149071b4ae7112afea077cd5ec96fc2593"},"schema_version":"1.0","source":{"id":"1902.01598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01598","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01598v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01598","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"HG42JMJRXA23","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HG42JMJRXA23QDP5","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HG42JMJR","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:edc26d67be6c6b21d1642589fb28311af0bea1511e00155159c4a93f2015af11","target":"graph","created_at":"2026-05-17T23:54:47Z","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":"A fractional advection-dispersion equation (fADE) has been advocated for heavy-tailed flows where the usual Brownian diffusion models fail. A stochastic differential equation (SDE) driven by a stable L\\'{e}vy process gives a forward equation that matches the space-fractional advection-dispersion equation and thus gives the stochastic framework of particle tracking for heavy-tailed flows. For constant advection and dispersion coefficient functions, the solution to such SDE itself is a stable process and can be derived easily by least square parameter fitting from the observed flow concentration","authors_text":"Hong Wang, Paramita Chakraborty, Xu Guo","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-05T09:15:41Z","title":"Stable L\\'{e}vy diffusion and related model fitting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01598","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":"sha256:2c3888f4b7985c087ddae7ee85560e78d7479f6ebe71d318472af35a0cf64981","target":"record","created_at":"2026-05-17T23:54:47Z","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":"943f323319c1391bf91f13cc58eb0f15bfdf02fcb03d95b6de76a8096920ba5c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-05T09:15:41Z","title_canon_sha256":"d7ae7fcea6966386119887276d1ba9149071b4ae7112afea077cd5ec96fc2593"},"schema_version":"1.0","source":{"id":"1902.01598","kind":"arxiv","version":1}},"canonical_sha256":"39b9a4b131b835b80dfdeabad0a76085bc6d088e9b90c2f0591dc7e5c4bc7305","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39b9a4b131b835b80dfdeabad0a76085bc6d088e9b90c2f0591dc7e5c4bc7305","first_computed_at":"2026-05-17T23:54:47.202968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:47.202968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yuKI5rCx+lE//zEjJEziAvk3lj3yNJ1QK9O4s/vHr+h022kwcitNYj5gWKu0ThllaHEQRlgsLkCv2K2rJQrdAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:47.203616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c3888f4b7985c087ddae7ee85560e78d7479f6ebe71d318472af35a0cf64981","sha256:edc26d67be6c6b21d1642589fb28311af0bea1511e00155159c4a93f2015af11"],"state_sha256":"4acf737b188fd420f9fc52ef4a6c8366d11c626fe4093829321d301a0f940f8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hh0FfmWXeKfREXdiIWp1sCneKh+Pv00Y9o9yD9RixrgLGavP1zhVPnQeD1WttKfR3whMciV7T2eF11MgPXhdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T02:07:47.387104Z","bundle_sha256":"b23a276918e36433fbe776042dc3f47348dd80be8814db7052e0b37a2c494e69"}}