{"as_of":"2026-08-09T10:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f089103f9d895f137b3aad0e528ce746337421534edfe87ed5e2e5628b3fde0a","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":"2026-08-05T16:00:55.839526Z","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":"2026-05-23T02:02:23.089302Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2409.20264","last_updated":"2024-09-30T13:04:35Z","snapshot_observed_at":"2026-07-06T19:24:30.632401Z","submitted_at":"2024-09-30T13:04:35Z","title":"First Order System Least Squares Neural Networks","version":1},"cited_work":{"arxiv_id":"2409.20264","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2409.20264","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"First order system least squares neural networks","venue":null,"work_id":"6190cc6b-6567-41b2-bda8-e7296fff6c6f","year":2024},"citing_paper":{"arxiv_id":"2502.20336","last_updated":"2026-07-10T09:38:59Z","snapshot_observed_at":"2026-08-07T17:42:06.968894Z","submitted_at":"2025-02-27T18:05:23Z","title":"A posteriori certification of PDE approximations with particular application to neural networks","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-23T01:58:01.191668Z"},"links":{"cited_paper":"/paper/2409.20264","citing_paper":"/paper/2502.20336"},"observation_digest":"sha256:3ffc1195f5537907fa8ce044a635201c0ae3131aeb97e39c5e34ba71da43ed76","observation_id":"28f9adbf-d213-40a3-9901-c834bbebc8b3","resolution":{"observed_at":"2026-05-23T02:02:23.091449Z","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":"2409.20264","last_updated":"2024-09-30T13:04:35Z","snapshot_observed_at":"2026-07-06T19:24:30.632401Z","submitted_at":"2024-09-30T13:04:35Z","title":"First Order System Least Squares Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.20264","snapshot_observed_at":"2026-08-05T16:00:55.839526Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.19412","last_updated":"2025-08-26T20:28:59Z","snapshot_observed_at":"2026-08-05T16:00:54.465818Z","submitted_at":"2025-08-26T20:28:59Z","title":"A deep first-order system least squares method for the obstacle problem","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T16:00:55.839526Z"},"links":{"cited_paper":"/paper/2409.20264","citing_paper":"/paper/2508.19412"},"observation_digest":"sha256:a83dfe68920969b2d053e0b9a0857a922967d140410e68988ee5f2f1b9d9ee37","observation_id":"6458cc46-749f-4cb6-94dc-adb1de683124","resolution":{"observed_at":"2026-08-05T16:00:55.839526Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.20264","last_updated":"2024-09-30T13:04:35Z","snapshot_observed_at":"2026-07-06T19:24:30.632401Z","submitted_at":"2024-09-30T13:04:35Z","title":"First Order System Least Squares Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.20264","snapshot_observed_at":"2026-08-02T02:03:20.464755Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14498","last_updated":"2026-07-16T02:24:20Z","snapshot_observed_at":"2026-08-07T03:46:45.822540Z","submitted_at":"2026-07-16T02:24:20Z","title":"Neural Very Weak Formulations enabling Hardware-Oriented deep PDE solvers","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T02:03:20.464755Z"},"links":{"cited_paper":"/paper/2409.20264","citing_paper":"/paper/2607.14498"},"observation_digest":"sha256:176d66c175a83768ee53e2ea74b34cade728cdba8db20124f9eeb831019c4eb4","observation_id":"515664e7-9637-433d-854e-254eb7a2e1ee","resolution":{"observed_at":"2026-08-02T02:03:20.464755Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.20264","last_updated":"2024-09-30T13:04:35Z","snapshot_observed_at":"2026-07-06T19:24:30.632401Z","submitted_at":"2024-09-30T13:04:35Z","title":"First Order System Least Squares Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.20264","snapshot_observed_at":"2026-08-01T22:37:46.809625Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15702","last_updated":"2026-07-22T04:37:50Z","snapshot_observed_at":"2026-08-01T22:37:44.587308Z","submitted_at":"2026-07-17T07:26:29Z","title":"Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-01T22:37:46.809625Z"},"links":{"cited_paper":"/paper/2409.20264","citing_paper":"/paper/2607.15702"},"observation_digest":"sha256:180a9ffa3d087fb01f62295ae362dc7c5af74b6993eca77a5e7c898252d878d1","observation_id":"58cb26ba-286e-41be-bb78-468cac8ad695","resolution":{"observed_at":"2026-08-01T22:37:46.809625Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2409.20264/citation-record","integrity":"/paper/2409.20264/integrity","json":"/paper/2409.20264/citation-record.json","paper":"/paper/2409.20264"},"outbound":[],"paper":{"arxiv_id":"2409.20264","last_updated":"2024-09-30T13:04:35Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-07-06T19:24:30.632401Z","submitted_at":"2024-09-30T13:04:35Z","title":"First Order System Least Squares Neural Networks"},"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:2409.20264."}