{"as_of":"2026-08-09T14:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:911914af937cb1cf155b24c65560439d2487f79e3fe56889310d758270f1c57d","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:54:50.504588Z","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":"2026-05-10T23:30:51.514192Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","snapshot_observed_at":"2026-07-06T17:54:00.048961Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.01145","snapshot_observed_at":"2026-08-07T10:54:50.504588Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.03979","last_updated":"2025-06-05T04:27:46Z","snapshot_observed_at":"2026-08-08T12:18:48.758557Z","submitted_at":"2025-06-04T14:09:25Z","title":"Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach","version":2},"reference_index":243,"source":"pdf_text","source_observed_at":"2026-08-07T10:54:50.504588Z"},"links":{"cited_paper":"/paper/2404.01145","citing_paper":"/paper/2506.03979"},"observation_digest":"sha256:d42247327293d591a35579f8d081490bcd13061bd970f62c5611d4655909875c","observation_id":"ebcbc036-9c70-4a35-b228-a7f051498bb5","resolution":{"observed_at":"2026-08-07T10:54:50.504588Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","snapshot_observed_at":"2026-07-06T17:54:00.048961Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.01145","snapshot_observed_at":"2026-08-03T04:43:49.083922Z","title":"Zhang, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.04644","last_updated":"2026-07-23T19:05:20Z","snapshot_observed_at":"2026-08-08T16:55:56.417883Z","submitted_at":"2026-02-04T15:11:49Z","title":"An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T04:43:49.083922Z"},"links":{"cited_paper":"/paper/2404.01145","citing_paper":"/paper/2602.04644"},"observation_digest":"sha256:f2e6e75ce3bfd6718cf173c400ef6f1fbc36ecb0adf3dba8c3c4de16387a7939","observation_id":"36641210-6095-41ca-ac4f-ab5c33d80cf1","resolution":{"observed_at":"2026-08-03T04:43:49.083922Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","snapshot_observed_at":"2026-07-06T17:54:00.048961Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","version":1},"cited_work":{"arxiv_id":"2404.01145","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2404.01145","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Sequential-in-time training of nonlinear parametrizations for solv- ing time-dependent partial differential equations","venue":null,"work_id":"22574453-50ee-4db5-a339-d12130430a09","year":2024},"citing_paper":{"arxiv_id":"2604.04920","last_updated":"2026-04-06T17:57:53Z","snapshot_observed_at":"2026-08-02T12:14:15.357911Z","submitted_at":"2026-04-06T17:57:53Z","title":"PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T19:04:32.170198Z"},"links":{"cited_paper":"/paper/2404.01145","citing_paper":"/paper/2604.04920"},"observation_digest":"sha256:38f2c98c803c13749c591f226269b55e85ac418327d0ea7b2d25fb763a28125f","observation_id":"09d67713-af6a-4f2a-abc6-7bb548cc5cb3","resolution":{"observed_at":"2026-05-10T23:30:51.517258Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","snapshot_observed_at":"2026-07-06T17:54:00.048961Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.01145","snapshot_observed_at":"2026-08-02T00:19:07.808710Z","title":"Preprint, arXiv:2404.01145 [math.NA] (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15086","last_updated":"2026-07-16T14:57:44Z","snapshot_observed_at":"2026-08-02T00:19:02.551465Z","submitted_at":"2026-07-16T14:57:44Z","title":"Residual-Based Time Discretization on Nonlinear Approximation Manifolds: Analysis and Gaussian Applications","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T00:19:07.808710Z"},"links":{"cited_paper":"/paper/2404.01145","citing_paper":"/paper/2607.15086"},"observation_digest":"sha256:cb1be81f396bffa43a9fa01d7c63553b16a3925c5e963949d54758ef960d273d","observation_id":"fde3d496-4d2d-4c6b-bb59-406fb3ae45f0","resolution":{"observed_at":"2026-08-02T00:19:07.808710Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2404.01145/citation-record","integrity":"/paper/2404.01145/integrity","json":"/paper/2404.01145/citation-record.json","paper":"/paper/2404.01145"},"outbound":[],"paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-07-06T17:54:00.048961Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial 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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2404.01145."}