{"as_of":"2026-08-16T12:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:36cfb9fbae5180b4c3c7ffff1b753bf75aa808e073c0cc2fd1f8f36825abbd57","coverage":[{"denominator":61,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":61,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T15:28:16.052147Z","state":"measured"},{"denominator":61,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":61,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.01770/citation-record","integrity":"/paper/1908.01770/integrity","json":"/paper/1908.01770/citation-record.json","paper":"/paper/1908.01770"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.799193Z","title":"Weitz, and Michael P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.799193Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:5aa56264abbbb4d7cd37080baeb106066871e2049bfc86c6872b55160ed74d58","observation_id":"764c7a8e-7d85-4e82-811d-dc8b797f4ba7","resolution":{"observed_at":"2026-08-14T15:28:15.799193Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.857108Z","title":null,"venue":null,"work_id":"9438a517-88f4-4ec3-abcc-38bde128ba51","year":1972},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.804396Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:bf310590ccda1d5c43e67b8038e452f73adff0f93d64bc287a124ca56be8c409","observation_id":"51209b46-8f89-4f2c-9cc3-a2b5425ff427","resolution":{"observed_at":"2026-08-14T15:28:16.862288Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.841929Z","title":"Probability density function of non- reactive solute concentration in heterogeneous porous formations.Journal of contaminant hydrology, 94(1-2):109–125, 2007","venue":null,"work_id":"e5892d95-5bd9-4100-896e-34a61c46ab2c","year":2007},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.808218Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:14f036dcc32b569939e35aee00882bc26b3a3dd0b01c3cce05965d6cbdd30563","observation_id":"b570f4ce-e63c-451f-8643-592eb27af695","resolution":{"observed_at":"2026-08-14T15:28:16.846898Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.813524Z","title":"Tar- takovsky, Diogo Bolster, and Philippe Davy","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.813524Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:3820091023763156ed0b72d538e476af1ff7fc77449195c82737589317b1a3fe","observation_id":"0760faf2-9be7-4da2-aa40-1c5e272299f8","resolution":{"observed_at":"2026-08-14T15:28:15.813524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.818143Z","title":"Pre- diction of the low-velocity distribution from the pore structure in sim- ple porous media","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.818143Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:e9aacdd33a72c56edd0afea98af8452e5d998eeaef49bc681d06de8a319aad1e","observation_id":"283543ab-7844-4938-a9cf-3c8c655fb2e5","resolution":{"observed_at":"2026-08-14T15:28:15.818143Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/2013wr015024","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.340837Z","title":null,"venue":null,"work_id":"ecd0fba4-c750-43d7-aa39-edcd96fa3fe0","year":2014},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.823002Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:9c967073cb0200a739221758f1bb862d087f5c20a7fdac889e6a9d77585b6b8a","observation_id":"72350fb5-8b6b-4a6c-af51-c762e9d2347c","resolution":{"observed_at":"2026-08-14T15:28:16.344557Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.827471Z","title":"de Josselin de Jong","venue":null,"work_id":"78d0660e-54a2-46fb-84e1-337b8a48dfac","year":1958},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.827667Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:ade6efc5af424f88c7d21d87be1d27c12be3f0f0c123e3818246de6567fe4672","observation_id":"1812af93-022b-4359-9762-478ff88fc24e","resolution":{"observed_at":"2026-08-14T15:28:16.832447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/jfm.2018.588","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.328406Z","title":"Dentz, F","venue":null,"work_id":"24ffc368-2517-4b40-9f69-229949d319a4","year":2018},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.831926Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:a4aadeb1a438507bcb5e22d30eca1072985bcb78770aa773c1a8b8beb026848e","observation_id":"409b84c8-a6d1-4b6b-b40a-903a5f65ce08","resolution":{"observed_at":"2026-08-14T15:28:16.332889Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.835874Z","title":"Concentration statistics for transport in heterogeneous me- dia due to stochastic fluctuations of the center of mass velocity.Advances in Water Resources, 36:11–22, February 2012","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.835874Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:c9a720ea5e070358735954fe8ef124fd2d6fb006fbd8e934e60166d30b3900c8","observation_id":"c982c1ee-9395-41d9-9e80-0edecefa11eb","resolution":{"observed_at":"2026-08-14T15:28:15.835874Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.813037Z","title":"Probability density functions for passive scalars dispersed in random velocity fields.Geophysical Research Letters, 37(24), 2010","venue":null,"work_id":"bd1843da-4be1-47e4-b8b6-2e30fc003883","year":2010},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.840124Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:afa4f92cbae337d4f1d09ba51571698bec698d073800692a479ddbd45dc5eef8","observation_id":"aaf7975e-8137-4931-8dbc-2e6afd26ee84","resolution":{"observed_at":"2026-08-14T15:28:16.817619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.799596Z","title":"Continuous time random walks for the evolution of la- grangian velocities","venue":null,"work_id":"4df947a9-40dd-4471-9b18-672c813604cc","year":2016},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.844351Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:75d53663f7bdea6c9dbc9c17f431132a48b28e210018492959b4b3a5320e64dc","observation_id":"4d8ec7d5-7485-4770-9370-2570a70a7811","resolution":{"observed_at":"2026-08-14T15:28:16.804089Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.783920Z","title":"Mechanisms of dis- persion in a porous medium","venue":null,"work_id":"e181ff49-fddd-4337-a151-52c091e30613","year":2018},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.848601Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:9bc3a89ae4037ce6e9cae8315139c4adc782d2d62edfd5849a70de7559f1aa6b","observation_id":"1a0d34af-a999-4a2a-ac76-e8628c4bb2da","resolution":{"observed_at":"2026-08-14T15:28:16.789339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physreve.99.013303","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.309113Z","title":"System- atic derivation of hybrid coarse-grained models","venue":null,"work_id":"3ccccb06-749a-477d-8093-028cf724570a","year":2019},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.854182Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:67e787e1302f72cd64fd4724a636b27512a857155e0a58f0d2a9ca2d9a01c6fb","observation_id":"406db89a-286f-43ec-85a9-7932bc01aec5","resolution":{"observed_at":"2026-08-14T15:28:16.313203Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.858021Z","title":"Chebfun guide, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.858021Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:6b2b8cdae9f79dbcf86eb1e77ad85a900e494af40f9a1e41444f2bd53a62b72f","observation_id":"045cadfe-b68a-40a7-8955-a1cb68c61272","resolution":{"observed_at":"2026-08-14T15:28:15.858021Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1361-6544/aaced5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.296069Z","title":"Quan- tification of coarse-graining error in Langevin and overdamped Langevin dynamics","venue":null,"work_id":"8735b818-8139-459a-b603-67f9992be8ab","year":2018},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.862384Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:5414ad0f912a9bb6de106ca6cc73bdfee52a1a7c1949aa3f8389c37a8b28ff2b","observation_id":"f021e9c2-aa6d-4665-b610-76ce4bd01b4e","resolution":{"observed_at":"2026-08-14T15:28:16.300232Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.759552Z","title":"Einstein","venue":null,"work_id":"7363376e-d265-4cf6-8b0a-dc27cc41b548","year":1905},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.866305Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:e35b7cbdf3d6caed46f82ead78bb6d9e602d8a5f9dd8f0f1f4ed819d6834e1fa","observation_id":"44557b4e-8e32-42f9-9b1d-bbfb61d5e265","resolution":{"observed_at":"2026-08-14T15:28:16.764279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.746889Z","title":null,"venue":null,"work_id":"be63a9b0-68ca-40af-b5b1-fddac7e66aee","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.869860Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:dac88918febdc1e379c671ce6f7e93ad597f1dc21b18b25257d54b5aad34ca81","observation_id":"d339d3d1-8ded-43a9-b36d-4cc9acb1ff40","resolution":{"observed_at":"2026-08-14T15:28:16.750858Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.720703Z","title":"Stochastic Methods: A Handbook for the Natural and Social Sciences, 2009","venue":null,"work_id":"2201749e-08b0-4496-85e6-4783086b0c52","year":2009},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.877729Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:98113a96d449e2f11e7d818fe751ff4b2cb432b2f36ce15e7c7c1f2af99ace6b","observation_id":"54d17ca8-693e-4621-b9dd-f0955dc95506","resolution":{"observed_at":"2026-08-14T15:28:16.724930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/0951-7715/17/","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.284390Z","title":"Extracting macro- scopic dynamics: model problems and algorithms","venue":null,"work_id":"7733f7e2-aa74-493d-8752-8076b1ebd1ef","year":2004},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.881445Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:f7c4746a346856fe5de7f1b61c538077826603aa87e082c8197d43f1be5aa8d0","observation_id":"9843d74a-bfbb-47ab-9abf-dca569d4cf39","resolution":{"observed_at":"2026-08-14T15:28:16.288747Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.707144Z","title":"Grabert.Projection Operator Techniquesin Nonequilibrium Statistical Mechanics","venue":null,"work_id":"bfedb356-3581-4ab2-a953-034ea2fb65ba","year":2006},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.885070Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:225bcce92d9e9d6a2a864b8d60fafa0d49cedb8d5c4c037b7afe65bedee52fe1","observation_id":"0027f980-012b-48d0-b8ff-cb53a07364fc","resolution":{"observed_at":"2026-08-14T15:28:16.711419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.693810Z","title":"Progress in probability density function methods for turbulent reacting flows.Progress in Energy and Combustion Science, 36(2):168–259, 2010","venue":null,"work_id":"913309bf-f415-4e6c-a88c-371e68c1971b","year":2010},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.888615Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:942fe0af135f53193de74c5692d2af1160c196b9f083819e01f64cbd8149e5ef","observation_id":"93b04294-ce5f-4132-9479-91dee2a57aef","resolution":{"observed_at":"2026-08-14T15:28:16.698337Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.2390701","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.271254Z","title":"Markovian approximation in a coarse-grained description of atomic systems.J","venue":null,"work_id":"4dbe17e0-1fbc-4504-9f42-3ca5d33d6747","year":2006},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.892155Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:53957fad16f1641ee28b53690746660068feed0ed971ed2bb4f4d3af67514e88","observation_id":"fddbb165-65ca-45e9-857b-9fabc29d6813","resolution":{"observed_at":"2026-08-14T15:28:16.275888Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.679015Z","title":"Intermittent La- grangian velocities and accelerations in three-dimensional porous medium flow.Phys","venue":null,"work_id":"a9199f33-da5d-4365-977d-5d674aedf575","year":2015},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.896355Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:a936925a96310bc4f16f5b9deb119682b8414159b2df2b5a58855918b0f8e4de","observation_id":"feb953f4-6b56-4dfa-ab50-7ae767332330","resolution":{"observed_at":"2026-08-14T15:28:16.684508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.08175","last_updated":"2018-10-18T17:32:06Z","snapshot_observed_at":"2026-08-14T18:12:32.878041Z","submitted_at":"2018-10-18T17:32:06Z","title":"Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism","version":1},"cited_work":{"arxiv_id":"1810.08175","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.08175","snapshot_observed_at":"2026-08-14T15:28:16.385203Z","title":"Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism","venue":"math.DS","work_id":"d731d177-1be0-4a45-a59b-ebd63a1b8117","year":2018},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.899912Z"},"links":{"cited_paper":"/paper/1810.08175","citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:5c1998cd4ecac0e3f0f68da95c5e747ab362fc1da2ec166b2f95275bde515ad2","observation_id":"e0f9282b-2444-4980-8e9e-2f6f8483d18e","resolution":{"observed_at":"2026-08-14T15:28:16.390094Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-23370-9","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.257265Z","title":"FlowingMatter,Soft and Biological Matter, chapter Upscaling Flow and Transport Processes","venue":null,"work_id":"4655e264-aa95-43ca-8a25-e058a198aeea","year":2019},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.904134Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:45a0d7f28fd3cd19f20a9ac94ee2bcd3c5a8b1b5258337ae7022a9eb505584fb","observation_id":"7acd1dd0-d55b-4d3b-8acc-d3943e170786","resolution":{"observed_at":"2026-08-14T15:28:16.262192Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.663716Z","title":null,"venue":null,"work_id":"aa15e6ff-9a89-469d-9193-a663af6d5c5d","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.908297Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:6dec8908277ed620c33d3124d3841286cd04ca305d027830c89fda1852deecb0","observation_id":"37373364-5f1d-42a5-b1e1-957e1cef4afa","resolution":{"observed_at":"2026-08-14T15:28:16.669112Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.917564Z","title":"Stochastic Processes in Physics and Chemistry","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.917564Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:d52b26c5d9bf4d85406d126aef8bdab356680a1959be998f5e5fdacc1f2ef957","observation_id":"6fca9c5e-d0db-4975-bab3-197269b6f9bf","resolution":{"observed_at":"2026-08-14T15:28:15.917564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/2014gl061475","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.223921Z","title":"Kang, Pietro de Anna, Joao P","venue":null,"work_id":"7a3e2bfe-db8e-414e-b270-9b11659f01bd","year":2014},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.921920Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:9239ae3892c120eb2370af1545000d009f1084f0db85864b2f274a7acd397ae1","observation_id":"8e5a22b7-b5a2-47f2-8a28-a53c74ecdc1e","resolution":{"observed_at":"2026-08-14T15:28:16.228151Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.648952Z","title":"Langevin","venue":null,"work_id":"f9632b65-9eeb-4204-981b-b0c3c6dbfbef","year":1908},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.925929Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:cb63990f8f0dc8934e3569962da67f790bb893ee8f19a3e10ea1273c516a2f74","observation_id":"39b0aeb6-4e17-4a5f-ad1c-87f2cc225317","resolution":{"observed_at":"2026-08-14T15:28:16.653313Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.635271Z","title":"Effective dynamics using conditional expectations","venue":null,"work_id":"62cd5657-3440-461f-ad75-3c2074c9508a","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.929703Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:c6f72c2e10407216ea4ee00b052a353cbae5b5be3eb1b960e9386392f02d208c","observation_id":"3ec8bdb4-4b44-4b00-b1c7-0f0bc326928b","resolution":{"observed_at":"2026-08-14T15:28:16.640077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.620697Z","title":null,"venue":null,"work_id":"8de71816-7813-4d74-869d-01da7855616b","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.937663Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:edbec188ad108cc070daf94a2707aa0ca5a13f093ef8840184b2419547b93b2e","observation_id":"834f9564-3124-4909-b5ac-c5430a153b34","resolution":{"observed_at":"2026-08-14T15:28:16.625083Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.606897Z","title":"Kitanidis","venue":null,"work_id":"a66b666c-a169-43d9-84a0-cc6a1c5ad9a5","year":2012},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.945634Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:15c83135968e8c50ff89790d0e5d3432ad0c2faa101982b648777d1a3ede1bcb","observation_id":"d91e18d9-4e54-4df0-8c54-eea24e5f54b7","resolution":{"observed_at":"2026-08-14T15:28:16.611660Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.593009Z","title":"The mathematical nature of the problem of relating la- grangian and eulerian statistical functions in turbulence.Mécanique de la Turbulence, 108:17–26, 1962","venue":null,"work_id":"82b79438-b6a3-4954-8e67-df13eaa12ed8","year":1962},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.950093Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:b76524cb720c7edb02dea8048969893ed6e42510b7438ab07ce21c43e8153598","observation_id":"ec2dce15-fe99-4fb3-9c8e-20e36ec7a7e0","resolution":{"observed_at":"2026-08-14T15:28:16.597559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.1762249","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.191507Z","title":null,"venue":null,"work_id":"cc84e3b0-a1a6-40d6-a963-022858f2bb21","year":1967},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.953958Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:abcee6aba011efa7772f03d1c99b07078a9b60b53dce720c74e341b067f48b42","observation_id":"4c1c9d80-91c1-40df-9b4d-2bf6f8b1db05","resolution":{"observed_at":"2026-08-14T15:28:16.195552Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00477-003-0163-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.203737Z","title":"URLhttps://doi.org/10.1007/ s00477-003-0163-3","venue":null,"work_id":"a71591d4-f5e0-4c8d-aa26-160077ec2979","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.941816Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:d09f261cabc03acc5113b5f2ec89c0f31a38505b17996e052653aa8dc6cd98e9","observation_id":"2c5402f6-fba3-4863-8585-6bd5ab3d8300","resolution":{"observed_at":"2026-08-14T15:28:16.207765Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.579837Z","title":"Meyer, Patrick Jenny, and Hamdi a","venue":null,"work_id":"52915696-b414-4bc6-a8a7-aca980fa2676","year":2010},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.967402Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:9a25cde2d556e06736dcf9442dc342a2054fe3319925b66651d9ddefa701efc2","observation_id":"a49ea618-b63c-4dd5-a74e-2a25c3073366","resolution":{"observed_at":"2026-08-14T15:28:16.584153Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/2017gl074326","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.159358Z","title":null,"venue":null,"work_id":"47d87967-2f9e-4f86-9062-f8a6ca598f33","year":2017},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.971386Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:0a7bf336595d09c9c721efed667b48eac1030c06c706ef37df0583118ed4c3f0","observation_id":"4f39f649-b10c-4af0-91d8-05f32a2991aa","resolution":{"observed_at":"2026-08-14T15:28:16.163356Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physreve.93.013110","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.179298Z","title":"Power- exponential velocity distributions in disordered porous media","venue":null,"work_id":"9de932fd-132f-4653-9ef0-653297591ee6","year":2016},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.957802Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:81d363a3ec31d9a8c470aae915e237ba349a081b6fc14dc2bd65d1cce9c3c072","observation_id":"cc5d82f1-71dc-4dcf-ab76-6d62f00bc412","resolution":{"observed_at":"2026-08-14T15:28:16.183716Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/2016wr018969","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.133653Z","title":null,"venue":null,"work_id":"0bb5654c-a926-4464-b8f9-3bb7d26da0bb","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.979019Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:f019ff950aa5799b7d9fb7ce028de71b47f5244a5094ea710ee7838586a94c45","observation_id":"b405e8b6-59b3-4649-8414-e38287799076","resolution":{"observed_at":"2026-08-14T15:28:16.137758Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.565819Z","title":"Probability density functions of hydraulic head and velocity in three- dimensional heterogeneous porous media.Water Resources Research, 44 (8), 2008","venue":null,"work_id":"9040b00a-4d73-4c90-95a5-00bcda9930fc","year":2008},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.983894Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:492a5767188eac3de30b68faab6b82b796529c141440303c97db81f9b194cd11","observation_id":"1f3c2208-e8d2-41a2-8d64-a6fd9920d4cd","resolution":{"observed_at":"2026-08-14T15:28:16.570469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.552502Z","title":null,"venue":null,"work_id":"4ec93e66-6211-4bdc-872d-53bd7073557a","year":1994},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.987508Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:0c227922e9803796137971cd2c16245ddbfedbb1d11d249cfd2b804031a18b19","observation_id":"37a0cc8b-51ac-41d7-ab59-b4ef78abe617","resolution":{"observed_at":"2026-08-14T15:28:16.556689Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.1328076","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.146474Z","title":null,"venue":null,"work_id":"f5b78ee6-4d81-4c08-90d5-c6750fb90bd2","year":2001},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.975274Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:61d8be2f5491bfab8e4f3b6f0a26104da8b9f1dc9398c4cfbaf815c8ae8e7a43","observation_id":"133e3b8f-4e6f-43d1-a822-4a077a0fb9cf","resolution":{"observed_at":"2026-08-14T15:28:16.150732Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.523917Z","title":"Pdf methods for turbulent reactive flows.Progress in energy and combustion science, 11(2):119–192, 1985","venue":null,"work_id":"37b53d98-b8d8-4987-8a99-26fe831c7a09","year":1985},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.995073Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:2d71304d0ef845d05659fc959000df727bde88b97900b6fbc22ae279eeb55446","observation_id":"3b06b895-6663-4ca8-a540-dce291f26b3a","resolution":{"observed_at":"2026-08-14T15:28:16.528474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.510024Z","title":"Random measures and their applica- tion to motion in an incompressible fluid.Journal of Applied Probability, 13(3):498–506, 1976","venue":null,"work_id":"8c2821d1-4f36-446a-8a3f-072c9f1c3806","year":1976},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.998798Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:ad20a7690662c565f64d6d1977cecfdcda673c6457d18f8572d482846eca0c17","observation_id":"1f666347-3460-4e3d-af77-969265eb1110","resolution":{"observed_at":"2026-08-14T15:28:16.514734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11242-019-01273-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.120421Z","title":"Upscaling of anomalous pore-scale dispersion.Transport in Porous Media, 128(2):837– 855, April 2019","venue":null,"work_id":"efab9ee3-d480-4bf8-bb21-bce65d28a63f","year":2019},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.003647Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:cff835b5f9a24c190155ac8bec78646457aa1dd39f927271a56e55617558b6b3","observation_id":"0ab87407-0ccf-4afa-a2b5-0dd1c193cbb6","resolution":{"observed_at":"2026-08-14T15:28:16.125564Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.537678Z","title":"Pope and S.B","venue":null,"work_id":"4fe2f18f-8495-4a82-8ae8-f1e2098a0717","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.991391Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:e2ab795c0f060364bdb519b7b5e9dfccef3789da5123480561c60d7f9a27b2de","observation_id":"cee128b0-5920-4b95-8f24-0d644be805e1","resolution":{"observed_at":"2026-08-14T15:28:16.542198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.482530Z","title":"Conditional probability density functions of concentrations for mixing- controlled reactive transport in heterogeneous aquifers","venue":null,"work_id":"248e80b0-5eba-4f5f-98a6-e7d06d648d29","year":2009},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.011513Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:8623346226bb2b541bc05f9b2890624e906f9197c138dcb22b020bea38ce8567","observation_id":"02c3af16-dd64-46ab-914f-a7a7586d65a3","resolution":{"observed_at":"2026-08-14T15:28:16.487175Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.469950Z","title":"Probabilitydensityfunctionsforsolute transport in random field","venue":null,"work_id":"d4770f93-5fbc-4304-9a1e-e64be8e6d538","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.015687Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:e1e08496dcf6daa2e9d6bf1a852a093837326ef83269b182c7234f07a48e0c94","observation_id":"ebd80af1-2c91-4bcc-b98f-445f0123ccbd","resolution":{"observed_at":"2026-08-14T15:28:16.473893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.024070Z","title":"Siena, A","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.024070Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:7b7df473e3b57860c95187b5aac5f723c3ac3487e4c66f4d89992b62e4d8532e","observation_id":"fef763e6-841d-4cad-af3f-3e9a13c7bfe0","resolution":{"observed_at":"2026-08-14T15:28:16.024070Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.496588Z","title":"A theory of dispersion in a porous medium.Journal of Fluid Mechanics, 6(03):321–349, 1959","venue":null,"work_id":"40716cca-513e-444a-8711-bf822b700c7c","year":1959},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.007483Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:e2b9368972f0fb3f7ada4216f0a38d1b3759f17d6addd3b42b7c4cb01c88625d","observation_id":"82f53721-3fc9-4842-b44a-106bf6cce1d3","resolution":{"observed_at":"2026-08-14T15:28:16.501250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.441194Z","title":"Towards a filtered density function approach for reactive transport in groundwater","venue":null,"work_id":"08d008e9-6410-4839-a918-e2768ba4430c","year":2016},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.032294Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:2b63f953b2ba736d8e4cc2a44cab374dc4093f66ce843eaf48def552c4ec29ed","observation_id":"6639c5a9-553c-4375-9096-c3ca5677ead5","resolution":{"observed_at":"2026-08-14T15:28:16.446562Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.427150Z","title":"PDF equations for advective-reactive transport in heterogeneous porous media with uncertain properties","venue":null,"work_id":"d03094d9-4fe3-465f-8083-7c92be3952d8","year":2011},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.036148Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:c0274810a5d43b154cab8d88256a7049908cfc8266513657a68647a4fc467a91","observation_id":"d0576104-9820-41b1-9bd6-b50bf65928a2","resolution":{"observed_at":"2026-08-14T15:28:16.431726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1021129325701","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.108257Z","title":"URLhttps://doi.org/10.1023/a: 1021129325701","venue":null,"work_id":"3d510041-b00e-4218-9608-3d39da740bd5","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.019880Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:ae45e6a4a7bab73bbdbd9d782f191f7e0acef26bb18bc3008393c046290d9617","observation_id":"724e1823-de1a-4499-a2e0-bec65bbbd4a0","resolution":{"observed_at":"2026-08-14T15:28:16.112344Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1029/2008wr007383","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.081553Z","title":"Tartakovsky, Marco Dentz, and Peter C","venue":null,"work_id":"a33428ee-1733-4a52-9952-e18125c63480","year":2009},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.043525Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:37f83074b7d2063c8fde480d58bc763c59223d8d66f84e8f15a827f3123be051","observation_id":"f417cd2b-8a09-4234-abce-be7126622146","resolution":{"observed_at":"2026-08-14T15:28:16.087287Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.455992Z","title":"Suciu, F.a","venue":null,"work_id":"9a375e23-7e39-47ce-b6ff-5a8b77275e8a","year":2015},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.028278Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:98fee202ffcf9fe9c036fdbf53d6bf24d9ed22fbe21ff0af2c13a67cab86645c","observation_id":"3da1ef67-aae0-464a-9e34-4702b86b591f","resolution":{"observed_at":"2026-08-14T15:28:16.460643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.399090Z","title":"von Smoluchowski","venue":null,"work_id":"3b471d98-7f64-4566-b268-76775e352999","year":1906},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.052147Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:baa187323896a0a99a8a769d10e4e321e3d38be7d4a8e399274af17a8cc27f55","observation_id":"618e93c1-cdd7-4271-a8b2-bcc0701648c7","resolution":{"observed_at":"2026-08-14T15:28:16.403194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.advwatres.2012.04.007","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.095875Z","title":"Tartakovsky","venue":null,"work_id":"b55a56b9-4567-45a9-bb96-1523067ea755","year":2013},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.039875Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:abcae810bd1b3aa20a83e726a22b236d1ebaccdedf73d86c42b823142a7f95d2","observation_id":"8976e366-13d5-4eba-a4e4-d43a9c740915","resolution":{"observed_at":"2026-08-14T15:28:16.099823Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.412539Z","title":"Venturi, D","venue":null,"work_id":"add62e8d-9417-47c1-b91a-76097bae0ad1","year":2013},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:16.047848Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:73c234a9fe59cce465886a04ff774b93c34e58bb6809ce679f752bec5c44b04d","observation_id":"0f261aa4-d4da-454e-9728-2428b4183080","resolution":{"observed_at":"2026-08-14T15:28:16.416628Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.733306Z","title":"URL https://books.google.it/books? id=aIW6ECRlDDoC","venue":null,"work_id":"485b9be0-4b51-43f6-930a-037f38bb210d","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.873603Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:3291c8eb73b0e623b7b531d4ffbea0297352ceba79913f48d4e1a1b1ec9c99ae","observation_id":"422bfb60-46a2-4fe7-9113-c489e1d5edfd","resolution":{"observed_at":"2026-08-14T15:28:16.737806Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:15.933544Z","title":"doi: 10.1088/0951-7715/23/9/006","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.933544Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:02bcec287dbdd975589abeb6f51164edf5ecb49670f5e0bb161ef5468b8459d0","observation_id":"a0923d4d-447a-49e1-95ec-6aa91d1e5411","resolution":{"observed_at":"2026-08-14T15:28:15.933544Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physreve.93.013122","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:28:16.244650Z","title":"URLhttps://doi.org/10.1103/ physreve.93.013122","venue":null,"work_id":"ce19514d-22b4-4ebc-8399-4f0a16fceda4","year":null},"citing_paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media","version":2},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-14T15:28:15.912693Z"},"links":{"citing_paper":"/paper/1908.01770"},"observation_digest":"sha256:c518dad97bc5190d6653deb523740469917351345197602f38f2aa7af4beca00","observation_id":"a702aa15-1efc-415c-a815-a265bba48a8e","resolution":{"observed_at":"2026-08-14T15:28:16.248663Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.01770","last_updated":"2020-05-29T16:44:22Z","latest_version":2,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-15T22:47:19.052707Z","submitted_at":"2019-08-04T23:12:46Z","title":"Probability density function (PDF) models for particle transport in porous media"},"reference_resolution":{"displayed":61,"state_counts":{"malformed_identifier":5,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":19,"verified_fuzzy":28},"total_outbound_references":61},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 0 inbound Pith citation observations for arXiv:1908.01770."}