{"as_of":"2026-08-15T19:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e4cc52ffb08ef106f546270f8c33b737cf5c0fb14ddfcad10bf73b4e6112bd4d","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":"2026-08-15T06:32:42.880941+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":"2026-08-12T13:56:34.762297Z","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":"2026-07-04T13:29:51.898150Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2404.07805","last_updated":"2024-04-11T14:50:11Z","snapshot_observed_at":"2026-08-13T00:32:36.681766Z","submitted_at":"2024-04-11T14:50:11Z","title":"Tensor Neural Network Interpolation and Its Applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.07805","snapshot_observed_at":"2026-08-12T13:56:34.762297Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.15828","last_updated":"2024-11-24T13:09:52Z","snapshot_observed_at":"2026-08-15T00:58:39.040580Z","submitted_at":"2024-11-24T13:09:52Z","title":"FieldTNN-based machine learning method for Maxwell eigenvalue problems","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-12T13:56:34.762297Z"},"links":{"cited_paper":"/paper/2404.07805","citing_paper":"/paper/2411.15828"},"observation_digest":"sha256:b50795561d6b5a35be95d6ff20fe95acbc63e1ffcc099db9c4da20d5b1eab989","observation_id":"2c60dbd6-acd6-4613-97a8-91c45e21009a","resolution":{"observed_at":"2026-08-12T13:56:34.762297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.07805","last_updated":"2024-04-11T14:50:11Z","snapshot_observed_at":"2026-08-13T00:32:36.681766Z","submitted_at":"2024-04-11T14:50:11Z","title":"Tensor Neural Network Interpolation and Its Applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.07805","snapshot_observed_at":"2026-08-09T14:04:34.203668Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01938","last_updated":"2025-02-04T02:15:39Z","snapshot_observed_at":"2026-08-15T18:58:04.989404Z","submitted_at":"2025-02-04T02:15:39Z","title":"A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-09T14:04:34.203668Z"},"links":{"cited_paper":"/paper/2404.07805","citing_paper":"/paper/2502.01938"},"observation_digest":"sha256:755aacc43d76b574c75dfc2c73d6434040b4cf1b1c3af97c9cf0fc082f5ac126","observation_id":"2402d3d1-4772-4cf7-a940-5f2c0705cef3","resolution":{"observed_at":"2026-08-09T14:04:34.203668Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.07805","last_updated":"2024-04-11T14:50:11Z","snapshot_observed_at":"2026-08-13T00:32:36.681766Z","submitted_at":"2024-04-11T14:50:11Z","title":"Tensor Neural Network Interpolation and Its Applications","version":1},"cited_work":{"arxiv_id":"2404.07805","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2404.07805","snapshot_observed_at":"2026-07-04T13:29:51.898150Z","title":"Tensor neural network interpola- tion and its applications.arXiv preprint arXiv:2404.07805, 2024","venue":null,"work_id":"bbfd9d2e-85cf-4485-8ed1-84749173793b","year":2024},"citing_paper":{"arxiv_id":"2606.08685","last_updated":"2026-06-07T15:37:55Z","snapshot_observed_at":"2026-07-06T23:48:07.065806Z","submitted_at":"2026-06-07T15:37:55Z","title":"ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T17:53:23.117920Z"},"links":{"cited_paper":"/paper/2404.07805","citing_paper":"/paper/2606.08685"},"observation_digest":"sha256:9b2ba99892d97f967aaef756856b6dd7c57884069628649270e448faac7d3ed8","observation_id":"f5cf1376-081b-4ae6-8053-493797868947","resolution":{"observed_at":"2026-07-02T23:47:27.949478Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.07805","last_updated":"2024-04-11T14:50:11Z","snapshot_observed_at":"2026-08-13T00:32:36.681766Z","submitted_at":"2024-04-11T14:50:11Z","title":"Tensor Neural Network Interpolation and Its Applications","version":1},"cited_work":{"arxiv_id":"2404.07805","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2404.07805","snapshot_observed_at":"2026-07-04T13:29:51.898150Z","title":"Tensor neural network interpola- tion and its applications.arXiv preprint arXiv:2404.07805, 2024","venue":null,"work_id":"bbfd9d2e-85cf-4485-8ed1-84749173793b","year":2024},"citing_paper":{"arxiv_id":"2606.27140","last_updated":"2026-06-25T15:13:55Z","snapshot_observed_at":"2026-08-03T11:04:22.477248Z","submitted_at":"2026-06-25T15:13:55Z","title":"fTNN: a tensor neural network for fractional PDEs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-26T05:09:15.152114Z"},"links":{"cited_paper":"/paper/2404.07805","citing_paper":"/paper/2606.27140"},"observation_digest":"sha256:8e15ae315a77f324ed9c25e0a4b32e10e0c4cbcab12efa54096bad8f6efbd1f1","observation_id":"52abc9fc-ffaa-4063-acc7-1e1ca1b62e44","resolution":{"observed_at":"2026-07-04T13:29:51.899598Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2404.07805/citation-record","integrity":"/paper/2404.07805/integrity","json":"/paper/2404.07805/citation-record.json","paper":"/paper/2404.07805"},"outbound":[],"paper":{"arxiv_id":"2404.07805","last_updated":"2024-04-11T14:50:11Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-13T00:32:36.681766Z","submitted_at":"2024-04-11T14:50:11Z","title":"Tensor Neural Network Interpolation and Its Applications"},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2404.07805."}