{"as_of":"2026-08-12T17:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c1d5231edce73ed7d330af55e2f61eec656934f312898512753788b548b564a0","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:26:35.371134Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-15T02:34:15.922046Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-15T02:39:41.714435Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"cited_work":{"arxiv_id":"2507.00278","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.00278","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:2507.00278 (2025)","venue":null,"work_id":"13f70fd9-1f83-49b1-b8ac-eac82ccf8152","year":2025},"citing_paper":{"arxiv_id":"2605.07828","last_updated":"2026-05-11T14:21:12Z","snapshot_observed_at":"2026-08-10T20:55:35.854944Z","submitted_at":"2026-05-08T14:56:46Z","title":"NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-11T02:11:00.389145Z"},"links":{"cited_paper":"/paper/2507.00278","citing_paper":"/paper/2605.07828"},"observation_digest":"sha256:016b5501520987233b054b49530e7f68ef77d11ffa08b44f50c8851b2678e1ed","observation_id":"37ed778d-6c3d-4d65-9551-577fc14dcbff","resolution":{"observed_at":"2026-05-11T03:50:57.800252Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"cited_work":{"arxiv_id":"2507.00278","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.00278","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:2507.00278 (2025)","venue":null,"work_id":"13f70fd9-1f83-49b1-b8ac-eac82ccf8152","year":2025},"citing_paper":{"arxiv_id":"2605.07828","last_updated":"2026-05-11T14:21:12Z","snapshot_observed_at":"2026-08-10T20:55:35.854944Z","submitted_at":"2026-05-08T14:56:46Z","title":"NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-12T04:00:14.645983Z"},"links":{"cited_paper":"/paper/2507.00278","citing_paper":"/paper/2605.07828"},"observation_digest":"sha256:33348a9c2865d3654cb1f11415130c0593c63ed31f4d3f400ef4372ccfba25cd","observation_id":"a50cc221-c8ca-4abe-8d55-c75f816ba35c","resolution":{"observed_at":"2026-05-12T06:46:37.177045Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"cited_work":{"arxiv_id":"2507.00278","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.00278","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:2507.00278 (2025)","venue":null,"work_id":"13f70fd9-1f83-49b1-b8ac-eac82ccf8152","year":2025},"citing_paper":{"arxiv_id":"2605.14332","last_updated":"2026-05-14T03:55:39Z","snapshot_observed_at":"2026-07-06T23:25:44.508166Z","submitted_at":"2026-05-14T03:55:39Z","title":"PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-15T02:34:15.922046Z"},"links":{"cited_paper":"/paper/2507.00278","citing_paper":"/paper/2605.14332"},"observation_digest":"sha256:1a5ca60905fb1e2927efd69e98070c380e51cee0a77cc18f9dd52942feb50b70","observation_id":"2c557c96-8a20-42a9-ab79-5e31c8dcd250","resolution":{"observed_at":"2026-05-15T02:39:41.716095Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.00278/citation-record","integrity":"/paper/2507.00278/integrity","json":"/paper/2507.00278/citation-record.json","paper":"/paper/2507.00278"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:39.906168Z","title":"Amestoy, A","venue":null,"work_id":"15a2b930-c0ab-4b00-a64e-b45f15150d25","year":2019},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.331900Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:5d8d6cf97c93c4ef6b65eeafbbfea78a266c8a63d8fbd680e18ca217749b8b1b","observation_id":"91745541-90f1-4ca4-baa5-0b6d749ffc61","resolution":{"observed_at":"2026-08-06T21:26:39.966733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.796545Z","title":"Amestoy, I","venue":null,"work_id":"30fb5bcf-574b-463e-a363-96f34dad3240","year":2001},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.374293Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:1180e5df314c3729ca3602855a92d5b8cd758a502d61b306ae606521ee1a86f6","observation_id":"79b994eb-a7ba-4011-9a86-2e4be83ef35b","resolution":{"observed_at":"2026-08-06T21:26:39.853020Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.660216Z","title":"Implicit-explicit runge-kutta methods for time-dependent partial differential equations","venue":null,"work_id":"b6db70e5-decf-46ea-b0bc-96cd1ee5ced7","year":1997},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.448210Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:c15f9fc49b4a4883fecd2ef82aa85e345fafa3a342c45a242af8c1f60ddb7499","observation_id":"801c19e8-5212-465e-88f7-3d97d7e2c3e7","resolution":{"observed_at":"2026-08-06T21:26:39.706680Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.509508Z","title":"Bashforth and J.C","venue":null,"work_id":"dd5f3069-c33f-47d0-9348-8f8a8559aa6e","year":null},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.497587Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:b1dd9d5b5d8663728935b04b7cb26f7dc4689dc1fb08adda0c2aa84a5b4e31ae","observation_id":"acfc1a98-cbe1-4b4f-b166-de4c2b196431","resolution":{"observed_at":"2026-08-06T21:26:39.553871Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.430838Z","title":"Finite element procedures","venue":null,"work_id":"906e5da1-dbba-46ec-aaa1-035effd665ee","year":2006},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.530262Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:dd0824bfca9d5b68b8d23cadef6735f71b5f5529a5d8ab8b64461ce223e5264a","observation_id":"59ea3fc1-da47-4829-a7ea-bd3dddf78475","resolution":{"observed_at":"2026-08-06T21:26:39.477923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.344737Z","title":"Parallel multilevel preconditioners","venue":null,"work_id":"b0befa1f-21fe-4b9e-b796-bdd044204832","year":1990},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.594930Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:aaab46142b1173d1fcc725982d331cc40adf67776795e8c9d14391b157ae2fbb","observation_id":"af537396-72fd-4431-9728-d68a6339af95","resolution":{"observed_at":"2026-08-06T21:26:39.385960Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.183876Z","title":"Pareto optimality in multiobjective problems","venue":null,"work_id":"a5585882-b1d1-40eb-b370-4f150bdfaac2","year":1977},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.649762Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:a4a0d5dcedfc06b436b18f47858ae743fed7e87021baf26a256c7194e0339e43","observation_id":"b0b8666a-2953-47c6-9e93-846d089b4292","resolution":{"observed_at":"2026-08-06T21:26:39.262476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2501.12215","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:35.958504Z","title":"Automatic selection of the best neural architecture for time series forecasting via multi-objective optimization and pareto optimality conditions","venue":null,"work_id":"32d95cc9-5a3d-4724-a8cb-758ce8dffa61","year":2025},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.703697Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:220f7a898f9549aae411dc12d6d6ff6f8b060255c64f32cd45b2c2e61efe87d9","observation_id":"ac073e45-0bd3-4574-91aa-25ce243af4bd","resolution":{"observed_at":"2026-08-06T21:26:36.061028Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:39.087408Z","title":"Physics-informed neural networks (pinns) for fluid mechanics: A review","venue":null,"work_id":"4b08c18a-25cb-42f5-9301-fbdd9efb5675","year":2021},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.781055Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:26142df6565ce888212ab3a8db2d74b2444a113e28a8054ec5826c59a54aa98d","observation_id":"f5396eff-2746-4fc0-bcda-9d40dc05d0df","resolution":{"observed_at":"2026-08-06T21:26:39.132008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:38.957090Z","title":"Crank and P","venue":null,"work_id":"1a2fd148-1178-4778-a38d-caf42045b205","year":1996},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.839810Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:ef92b4fa61363aa09de84568f16b0d87f4fe4efb866ef7e1ea7967d7a40fbec2","observation_id":"bf5705f5-9c61-451e-a863-c7c4024a3648","resolution":{"observed_at":"2026-08-06T21:26:39.021967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:38.846550Z","title":"U-DeepONet : U-Net enhanced deep operator network for geologic carbon sequestration","venue":null,"work_id":"47b70f51-597a-4672-b9a4-8660cd13d802","year":2024},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.905056Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:495732feccda94b1e5c29257230e7e82217423f9c49aa57cc685465e735cce20","observation_id":"583f0b98-a26b-455c-850c-95a1f5a37234","resolution":{"observed_at":"2026-08-06T21:26:38.900776Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:38.715362Z","title":"Ross Ethier and D","venue":null,"work_id":"dba7c603-3cd9-4b8d-ba13-1c98c0a2ae23","year":1994},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.946373Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:b7c51900d63d88918751a707b3fc4697e4db0370ae210b318e657372b262fe33","observation_id":"f68aaf68-62f8-4117-a89b-4965d68d795e","resolution":{"observed_at":"2026-08-06T21:26:38.772342Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:38.581452Z","title":null,"venue":null,"work_id":"edcc8354-2e1d-4f5c-b01c-183637131715","year":1937},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:33.994232Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:6f0548245a993b4ba91834bdad10b6f272792d5a5f47ef7dfed6bcf29c88c262","observation_id":"769abaa2-ff62-43ad-94f2-1f88ca38fbab","resolution":{"observed_at":"2026-08-06T21:26:38.663273Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:38.464677Z","title":"Iterative methods for solving linear systems","venue":null,"work_id":"1202160c-8f94-409d-8dcf-1bc8262ca287","year":1997},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.069352Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:807ed232e9025a893f649816f76c7d990417b850b19551d2eb373369eb65094f","observation_id":"10dd3c3f-2f60-4ba1-8fc4-41261fc37a9d","resolution":{"observed_at":"2026-08-06T21:26:38.519359Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:34.112579Z","title":"Solving nonlinear equations with Newton's method","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.112579Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:5ed003c30f3d980598d7f18e23bdf96615e7a2f6488380ce068b7fd6000b1704","observation_id":"5f76cc9c-446a-4121-8bff-821e6be7e2c5","resolution":{"observed_at":"2026-08-06T21:26:34.112579Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:38.335173Z","title":"DeepONet based preconditioning strategies for solving parametric linear systems of equations","venue":null,"work_id":"ae92dd7c-f99e-41e7-a686-30b46a9827fe","year":2025},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.193087Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:d19e9619c800764a73e1b0445299c4e921cadc2659c357a9bbc9bbc31c217e05","observation_id":"6c4e75ae-8b35-45ea-b35e-47b5173d9f69","resolution":{"observed_at":"2026-08-06T21:26:38.375635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:38.191211Z","title":"Physics-informed machine learning: Nature reviews physics","venue":null,"work_id":"4e5abc6f-e6ff-4498-a2c8-aa485820b36d","year":2021},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.249240Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:02cd938bf01e981dd7a2df342e11cfdbc1df8623841d32e001b92dae3501b003","observation_id":"3d633774-2ff1-45b4-8ced-5f5e124fc1f1","resolution":{"observed_at":"2026-08-06T21:26:38.285266Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-09T18:35:34.344652Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T21:26:34.338031Z","title":"Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.338031Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:fe2643f50b8792826a13d7b542fd57a97c70cd1958051cfc8fc8f974a1a0a428","observation_id":"1b4e4631-634c-431a-842d-0a1d3ee9410c","resolution":{"observed_at":"2026-08-06T21:26:34.338031Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:38.018408Z","title":"Spectral/hp element methods for computational fluid dynamics","venue":null,"work_id":"b2a8d60f-18b0-4e69-b9c0-c433e64ef28d","year":2005},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.406105Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:f87c012980dd8aee5e61e588d5cdc8d5d0d9e849e6c93affd81db94875ea5994","observation_id":"0fbd08a1-8ca4-49c8-81c9-741129a7dfc7","resolution":{"observed_at":"2026-08-06T21:26:38.102455Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:34.475428Z","title":"Decoupled weight decay regularization","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.475428Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:43aac4ab24d53bcc6ff86edab62c7f870c6e8086a2bf9794e82c692299bbe0ce","observation_id":"7a138a94-ee5f-44ed-88ed-ae0157a6370e","resolution":{"observed_at":"2026-08-06T21:26:34.475428Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:37.789466Z","title":"Learning nonlinear operators via deeponet based on the universal approximation theorem of operators","venue":null,"work_id":"bf0f4979-17c3-48b8-9f5b-0e4dc76f5328","year":2021},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.520299Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:0ccb1c07160f2dcc552e115a3c73e749102e854b9da0ff58113b83a7cdb9a3a4","observation_id":"d8cd046b-b21e-4a2a-8a5a-98f4a2ca2f69","resolution":{"observed_at":"2026-08-06T21:26:37.900666Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2010.08895","last_updated":"2021-05-17T03:12:33Z","snapshot_observed_at":"2026-07-06T10:05:26.653366Z","submitted_at":"2020-10-18T00:34:21Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.08895","snapshot_observed_at":"2026-08-06T21:26:34.564150Z","title":"Fourier neural operator for parametric partial differential equations","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.564150Z"},"links":{"cited_paper":"/paper/2010.08895","citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:a47aaf722dd7f2ecbcb86bfa79ef89d5619d8bb34622d538d4641a90357505b8","observation_id":"101160ed-a1e1-4730-8ee6-209621b7275c","resolution":{"observed_at":"2026-08-06T21:26:34.564150Z","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":"2026-08-06T21:26:34.654207Z","title":"Automatic discovery of optimal meta-solvers via multi-objective optimization","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.654207Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:1a0d4ccb31a9c479db00f00673219aeabd081454109eb9673785efb8b6864eef","observation_id":"7534125d-0080-4d8e-a7f1-a31572bcad77","resolution":{"observed_at":"2026-08-06T21:26:34.654207Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.12308","last_updated":"2024-05-20T18:12:36Z","snapshot_observed_at":"2026-08-10T07:11:53.899467Z","submitted_at":"2024-05-20T18:12:36Z","title":"Continual Deep Reinforcement Learning for Decentralized Satellite Routing","version":1},"cited_work":{"arxiv_id":"2405.12308","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.12308","snapshot_observed_at":"2026-08-06T21:26:35.463940Z","title":"Continual Deep Reinforcement Learning for Decentralized Satellite Routing","venue":"cs.LG","work_id":"b4ac2639-63f2-4dbc-85f0-9d469ec76848","year":2024},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.690586Z"},"links":{"cited_paper":"/paper/2405.12308","citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:8e6347974277a868658143ecd2bf10d96beafeaffeed6ac5d353fb4ce660f8e6","observation_id":"21bf1e92-3973-4b14-9bdd-7de7c305cb47","resolution":{"observed_at":"2026-08-06T21:26:35.561148Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:37.606766Z","title":"Bayesian physics informed neural networks for real-world nonlinear dynamical systems","venue":null,"work_id":"893ac306-c198-48ee-a41a-a645d694f0e3","year":2022},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.746382Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:75085311e186f206d121d0c54e8bb7b85ff4f102cdde6d9e2ba5042ab16ce4e9","observation_id":"609446c5-16c8-4292-b889-8915a8b27d6a","resolution":{"observed_at":"2026-08-06T21:26:37.643103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:34.814943Z","title":"Nonlinear multiobjective optimization , volume 12","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.814943Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:8dc6475bc1641a42192467e367472460dd68c27af4abea4ad7861e97911143d0","observation_id":"cc1b4e9f-f73a-4da2-8ec9-a1f1faf312f3","resolution":{"observed_at":"2026-08-06T21:26:34.814943Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:37.398271Z","title":"On the spectral bias of neural networks","venue":null,"work_id":"491f5dba-f38d-40e4-a8a1-a329240693f4","year":null},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.844544Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:a03e67ae63c82bc461929bd41acdf3536f1f8c96691a422e8e892e5cdb244448","observation_id":"ed8c8a6e-0e03-481a-90f7-afd1e85f1769","resolution":{"observed_at":"2026-08-06T21:26:37.486804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:34.928376Z","title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.928376Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:bba0f75dd6de11c27db0fa31c9ceff46cee62d0df074fe672828e44dc5b56992","observation_id":"a5fce69e-cf6e-4add-b918-f142d493b12a","resolution":{"observed_at":"2026-08-06T21:26:34.928376Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:37.203902Z","title":"A flexible inner-outer preconditioned gmres algorithm","venue":null,"work_id":"46bc32fa-fe22-4d69-bc53-4aa7f6673977","year":1993},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.990626Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:84f3a5b05a82ad0f0b3313195552f898ac88eaf0aa5d7165b3ef08af1b572528","observation_id":"74db8b8c-1a72-4331-97d6-3492e93c943a","resolution":{"observed_at":"2026-08-06T21:26:37.284641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:37.011308Z","title":"Iterative methods for sparse linear systems","venue":null,"work_id":"8d5eeec0-35f3-4497-8284-973289224245","year":2003},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:35.073937Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:a6464e98e555e3e059284efa3f775afb0282993e826e7dc3160b4f4fb57f8b1e","observation_id":"4f281c9b-bd75-4e8b-b52b-9a3154b00ffd","resolution":{"observed_at":"2026-08-06T21:26:37.060288Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:36.811908Z","title":"Finite difference schemes and partial differential equations","venue":null,"work_id":"24e5464c-fe60-4983-97a6-a711b7167328","year":2004},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:35.130955Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:62db942934d36ea3829f2f34a717d679a4fc2287a774a05d79f91af1f2c0b9eb","observation_id":"83701925-514f-4828-a343-38aaaa0b8f3b","resolution":{"observed_at":"2026-08-06T21:26:36.920942Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:36.681393Z","title":"Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems","venue":null,"work_id":"0863a395-f5b7-49d8-b689-6d30f5ecf51a","year":1992},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:35.160262Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:7a8c67b6fd4232e7af9e2c8a36160684243b243ea30fe67e1924c441ca9f4cd0","observation_id":"a8844bba-8961-4b0e-9488-ec2c1da4f4b4","resolution":{"observed_at":"2026-08-06T21:26:36.762527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:36.508102Z","title":"Iterative Krylov methods for large linear systems","venue":null,"work_id":"2f7a98be-d74b-45f2-8502-d760299261ad","year":2003},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:35.237918Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:ff640d645d09283fc25f3114d2cb5bd26d5b61bc034744652397330f2c3b195b","observation_id":"57e138df-c9fe-4030-ad8a-40be548bc0d6","resolution":{"observed_at":"2026-08-06T21:26:36.583502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:36.332372Z","title":"Wesseling","venue":null,"work_id":"85b10d79-2747-49a8-b21a-773b2f1265db","year":2004},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:35.307944Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:ba9eded313fb742e8254443bacb527d7de47b240501674edf31031b09f2251e9","observation_id":"4b1b7a99-1b90-4be5-ab4d-797fe50e710d","resolution":{"observed_at":"2026-08-06T21:26:36.422489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T21:26:36.178432Z","title":"Blending neural operators and relaxation methods in pde numerical solvers","venue":null,"work_id":"1f240491-35e6-4065-bb52-a6f5cabeaeb0","year":2024},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:35.371134Z"},"links":{"citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:f3d3d08dbb12658ada895bdbba398996c6f399f6a4d258eb2d9bc30839249fb2","observation_id":"645b4070-bd1f-4657-a958-dc56242dc626","resolution":{"observed_at":"2026-08-06T21:26:36.264196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-10T04:18:55.407594Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":8,"verified_exact":1,"verified_fuzzy":25},"total_outbound_references":35},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 3 inbound Pith citation observations for arXiv:2507.00278."}