{"as_of":"2026-08-23T16:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:493503322bb5822f29f7447ed90896c295a0ebdd10564ba08348402eea1d3a7f","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":14,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T12:15:20.758082Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-08T16:55:08.403158Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"1910.03193","last_updated":"2020-04-15T00:51:54Z","snapshot_observed_at":"2026-08-20T20:32:49.543971Z","submitted_at":"2019-10-08T03:21:14Z","title":"DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-15T03:17:25.281108Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/1910.03193"},"observation_digest":"sha256:adcb9751fac44cebc904112281e85ed3aff885a7b480b2cfdf6517b34cf14cd6","observation_id":"e9421cde-6f1e-45ac-aa31-75a21c8a13a5","resolution":{"observed_at":"2026-05-15T03:17:25.374340Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2001.04385","last_updated":"2021-11-02T12:06:44Z","snapshot_observed_at":"2026-08-16T18:06:54.871127Z","submitted_at":"2020-01-13T16:40:35Z","title":"Universal Differential Equations for Scientific Machine Learning","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-18T00:24:43.260892Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2001.04385"},"observation_digest":"sha256:83a9c5a6d97381492d776392e6a5bd8b308f12636ed87033e46403d9491d09f3","observation_id":"534229ca-0367-4424-9598-3f3be24bf974","resolution":{"observed_at":"2026-05-18T00:24:43.345114Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2212.08989","last_updated":"2023-06-20T01:01:34Z","snapshot_observed_at":"2026-08-15T01:57:41.390401Z","submitted_at":"2022-12-18T02:03:00Z","title":"Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics","version":3},"reference_index":273,"source":"pdf_text","source_observed_at":"2026-05-24T10:22:00.419523Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2212.08989"},"observation_digest":"sha256:9d974ed309c5c463db57f200d24213aaa03c5f951bd67fe87e0cd908db6eac64","observation_id":"02cb394a-6ef7-4c7e-941d-66f73b0928c6","resolution":{"observed_at":"2026-05-24T10:24:20.273209Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2408.01914","last_updated":"2026-05-02T12:14:51Z","snapshot_observed_at":"2026-07-06T18:56:31.851481Z","submitted_at":"2024-07-13T22:48:17Z","title":"Partial-differential-algebraic equations of nonlinear dynamics by Physics-Informed Neural-Network: (I) Operator splitting and framework assessment","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-23T22:57:22.329543Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2408.01914"},"observation_digest":"sha256:426f4f830b1ca5ce7da09a40f001fcda16613c48b27fb643e2ada14e4a0ee328","observation_id":"87f91273-f837-45ea-a5f0-0e2498943f86","resolution":{"observed_at":"2026-05-23T22:58:34.401658Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-08-12T00:08:09.232971Z","title":null,"venue":null,"work_id":null,"year":1907},"citing_paper":{"arxiv_id":"2412.01954","last_updated":"2024-12-02T20:30:53Z","snapshot_observed_at":"2026-08-13T13:21:33.102599Z","submitted_at":"2024-12-02T20:30:53Z","title":"Geometry-aware PINNs for Turbulent Flow Prediction","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-12T00:08:09.232971Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2412.01954"},"observation_digest":"sha256:b186e9b59747fcb9879ad38ccfde560a94ec0267dfd1a94ad72423d7777e83fd","observation_id":"0e7fee0b-779f-4e1b-a395-86aa6f30dbf2","resolution":{"observed_at":"2026-08-12T00:08:09.232971Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-08-11T12:07:19.200561Z","title":"arXiv preprint arXiv:1907.04502 (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2501.04013","last_updated":"2024-12-19T10:22:22Z","snapshot_observed_at":"2026-08-13T12:14:04.208613Z","submitted_at":"2024-12-19T10:22:22Z","title":"Convergence of Physics-Informed Neural Networks for Fully Nonlinear PDE's","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T12:07:19.200561Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2501.04013"},"observation_digest":"sha256:b27291ba5987032316662db27c246a81f83e4879e9eaa42571d7eb5d027bedef","observation_id":"2c482d4f-ae67-4760-8b10-72f26c8c91b3","resolution":{"observed_at":"2026-08-11T12:07:19.200561Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-08-16T12:15:20.758082Z","title":"Karniadakis","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2504.13412","last_updated":"2025-04-18T02:18:08Z","snapshot_observed_at":"2026-08-21T03:03:39.526863Z","submitted_at":"2025-04-18T02:18:08Z","title":"How Learnable Grids Recover Fine Detail in Low Dimensions: A Neural Tangent Kernel Analysis of Multigrid Parametric Encodings","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-16T12:15:20.758082Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2504.13412"},"observation_digest":"sha256:81b0f4f592b7b6e18765189b2cf46f7cdc7f917e509ccf86719b40e9677ff1cc","observation_id":"32ee540e-76f4-4da0-a13e-126bcbd686a4","resolution":{"observed_at":"2026-08-16T12:15:20.758082Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-08-07T15:42:50.458811Z","title":"arXiv preprint arXiv:1907.04502 (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.14252","last_updated":"2025-08-22T07:13:06Z","snapshot_observed_at":"2026-08-12T10:53:09.723235Z","submitted_at":"2025-05-20T12:05:17Z","title":"Hybrid Adaptive Modeling in Process Monitoring: Leveraging Sequence Encoders and Physics-Informed Neural Networks","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:42:50.458811Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2505.14252"},"observation_digest":"sha256:52e094a4b2fdc58e975cfadffebb3e0a9d1d03cce46d65462686f71b14371095","observation_id":"8fbb337a-ff2b-4a14-912a-56c4620da4a5","resolution":{"observed_at":"2026-08-07T15:42:50.458811Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-08-06T04:35:57.299669Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.03326","last_updated":"2025-08-05T11:07:33Z","snapshot_observed_at":"2026-08-16T22:50:37.588940Z","submitted_at":"2025-08-05T11:07:33Z","title":"Estimation of Hemodynamic Parameters via Physics Informed Neural Networks including Hematocrit Dependent Rheology","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T04:35:57.299669Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2508.03326"},"observation_digest":"sha256:6d98df365b7c685ab6e78c54e880f64d147e4298e623939da2557f7236708026","observation_id":"85323955-890a-4ba8-bdbd-aa249540f355","resolution":{"observed_at":"2026-08-06T04:35:57.299669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2604.02976","last_updated":"2026-04-03T11:26:15Z","snapshot_observed_at":"2026-08-19T19:35:01.064972Z","submitted_at":"2026-04-03T11:26:15Z","title":"Extending deep learning U-Net architecture for predicting unsteady fluid flows in textured microchannels","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-13T18:35:19.456505Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2604.02976"},"observation_digest":"sha256:a8089e2ea49f98adcbcd94db38e0ebae2b6bc616831aa83d66fd3a78c5155c44","observation_id":"a84da6cc-ccab-4684-a24d-d329cf2d5500","resolution":{"observed_at":"2026-05-13T18:38:07.633143Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2604.22862","last_updated":"2026-05-13T09:35:26Z","snapshot_observed_at":"2026-08-13T13:02:04.896300Z","submitted_at":"2026-04-23T02:55:17Z","title":"Physics-Informed Neural Networks for Solving Two-Flavor Neutrino Oscillations in Vacuum and Matter Environments for Atmospheric and Reactor Neutrinos","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-09T22:07:50.346937Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2604.22862"},"observation_digest":"sha256:0a4c5ff2c41e219323c443a0d404021df34be193ce58503d3f9604b13754dbbf","observation_id":"a5aef369-85af-4baa-97c2-7a1663d0420e","resolution":{"observed_at":"2026-05-11T14:16:20.093122Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2604.22862","last_updated":"2026-05-13T09:35:26Z","snapshot_observed_at":"2026-08-13T13:02:04.896300Z","submitted_at":"2026-04-23T02:55:17Z","title":"Physics-Informed Neural Networks for Solving Two-Flavor Neutrino Oscillations in Vacuum and Matter Environments for Atmospheric and Reactor Neutrinos","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-14T22:17:35.300012Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2604.22862"},"observation_digest":"sha256:e3c8fe456fe3782ae874dae2128d2dee5c6953da517ff2c3b6157fd7b71925db","observation_id":"18dda1c8-87bd-4373-9366-8ba869286fd9","resolution":{"observed_at":"2026-05-14T22:18:04.128463Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2606.22075","last_updated":"2026-06-20T14:50:40Z","snapshot_observed_at":"2026-08-14T07:53:33.016389Z","submitted_at":"2026-06-20T14:50:40Z","title":"Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systems","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-26T12:28:40.928088Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2606.22075"},"observation_digest":"sha256:b64588e0bba1c8933ad4355689a103eb2dc43c1befef4bf919697c3f6c50b0ae","observation_id":"6076bf3e-0b69-427d-8f71-070f8eed8dd0","resolution":{"observed_at":"2026-07-04T07:59:39.702374Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations","version":2},"cited_work":{"arxiv_id":"1907.04502","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.04502","snapshot_observed_at":"2026-07-08T16:55:08.403158Z","title":"Deepxde: A deep learning library for solving diﬀerential equations","venue":"cs.LG","work_id":"4491f5a9-ea8a-4a11-9a23-7c6625566536","year":2019},"citing_paper":{"arxiv_id":"2607.06091","last_updated":"2026-07-07T10:07:41Z","snapshot_observed_at":"2026-08-20T12:38:44.073192Z","submitted_at":"2026-07-07T10:07:41Z","title":"Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-08T16:51:40.082489Z"},"links":{"cited_paper":"/paper/1907.04502","citing_paper":"/paper/2607.06091"},"observation_digest":"sha256:bd11853a56354069c776b39f3134ad0572c3346a65e471501f2b1b1fa13e2286","observation_id":"dca11367-663e-41ae-b512-9e6ca3ac5130","resolution":{"observed_at":"2026-07-08T16:55:08.404689Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1907.04502/citation-record","integrity":"/paper/1907.04502/integrity","json":"/paper/1907.04502/citation-record.json","paper":"/paper/1907.04502"},"outbound":[],"paper":{"arxiv_id":"1907.04502","last_updated":"2020-02-14T23:05:44Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-18T13:58:49.563453Z","submitted_at":"2019-07-10T04:06:21Z","title":"DeepXDE: A deep learning library for solving differential equations"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 14 inbound Pith citation observations for arXiv:1907.04502."}