{"as_of":"2026-08-08T20:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9979e5012fab4e985bfeaa1cf64443829db2f02044919ee303bd759c98e30feb","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":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T04:45:58.137354Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":3,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-07T04:45:58.137354Z","title":"Greedy construction of quadratic mani- folds for nonlinear dimensionality reduction and nonlinear model reduction.arXiv preprint arXiv:2403.06732, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.09830","last_updated":"2026-05-25T16:26:40Z","snapshot_observed_at":"2026-08-07T04:37:00.519917Z","submitted_at":"2025-06-11T15:10:02Z","title":"Machine Learning-based quadratic closures for non-intrusive Reduced Order Models","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T04:45:58.137354Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2506.09830"},"observation_digest":"sha256:8ecda48377b4137a4f3d5f08a4d5f24d6d55db852f98640f800d44cf24420930","observation_id":"09c5c690-0b63-438c-a566-cc1473132894","resolution":{"observed_at":"2026-08-07T04:45:58.137354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-05T13:55:43.438706Z","title":"Schwerdtner and B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.00224","last_updated":"2025-08-29T20:25:18Z","snapshot_observed_at":"2026-08-08T03:09:43.906819Z","submitted_at":"2025-08-29T20:25:18Z","title":"Kernel manifolds: nonlinear-augmentation dimensionality reduction using reproducing kernel Hilbert spaces","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-05T13:55:43.438706Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2509.00224"},"observation_digest":"sha256:c231295dcabcded598d4665ac81f546e86a865b1c437482a28c0f2807324c6fe","observation_id":"cef0fd08-494c-42dd-912b-bc39a7356514","resolution":{"observed_at":"2026-08-05T13:55:43.438706Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":"2403.06732","doi":"10.48550/arxiv.2403.06732","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Schwerdtner and B","venue":"arXiv (Cornell University)","work_id":"444b893c-fb5b-4905-b4d5-6a007d3e7896","year":2024},"citing_paper":{"arxiv_id":"2605.26025","last_updated":"2026-05-25T16:49:20Z","snapshot_observed_at":"2026-08-02T07:59:46.299550Z","submitted_at":"2026-05-25T16:49:20Z","title":"A Dynamic Subspace Approach for Low-rank Approximation of Large-scale Nonlinear Systems","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-29T20:22:02.528185Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2605.26025"},"observation_digest":"sha256:20fd91601b4b48c5d018d5b28f80b1e2adb9e05201f24f9780168bf67173825f","observation_id":"6dae9994-6092-4fab-9b39-e3d0616c17e4","resolution":{"observed_at":"2026-06-29T20:23:57.250955Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":"2403.06732","doi":"10.48550/arxiv.2403.06732","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Schwerdtner and B","venue":"arXiv (Cornell University)","work_id":"444b893c-fb5b-4905-b4d5-6a007d3e7896","year":2024},"citing_paper":{"arxiv_id":"2605.26039","last_updated":"2026-05-26T16:18:08Z","snapshot_observed_at":"2026-07-06T23:35:55.988443Z","submitted_at":"2026-05-25T17:06:07Z","title":"Fast Quadratic Manifold Learning For Nonlinear Dimensionality Reduction in Large-scale Systems using Riemannian Optimization","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-29T20:19:16.552474Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2605.26039"},"observation_digest":"sha256:6bb9ec9cd8de07e17921f85e83844ec17ec80fd367e9199b387fcf19c57568e4","observation_id":"dcae13ff-4689-4906-8843-5d36f1117c61","resolution":{"observed_at":"2026-06-29T20:23:57.591972Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":"2403.06732","doi":"10.48550/arxiv.2403.06732","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Schwerdtner and B","venue":"arXiv (Cornell University)","work_id":"444b893c-fb5b-4905-b4d5-6a007d3e7896","year":2024},"citing_paper":{"arxiv_id":"2605.27756","last_updated":"2026-06-30T02:36:36Z","snapshot_observed_at":"2026-07-06T23:37:27.309837Z","submitted_at":"2026-05-26T23:10:05Z","title":"Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-06-29T15:01:24.546920Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2605.27756"},"observation_digest":"sha256:e40d9598f81881c808b1cd161b7f4fd8083e44aae2285ec2e6ea59a2df55b965","observation_id":"f52f2187-b177-4653-819b-10a03271c083","resolution":{"observed_at":"2026-06-29T15:03:31.001421Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":"2403.06732","doi":"10.48550/arxiv.2403.06732","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Schwerdtner and B","venue":"arXiv (Cornell University)","work_id":"444b893c-fb5b-4905-b4d5-6a007d3e7896","year":2024},"citing_paper":{"arxiv_id":"2605.27756","last_updated":"2026-06-30T02:36:36Z","snapshot_observed_at":"2026-07-06T23:37:27.309837Z","submitted_at":"2026-05-26T23:10:05Z","title":"Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks","version":2},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-07-01T07:10:46.294715Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2605.27756"},"observation_digest":"sha256:a152bbb19b6f5c89ad11dd3d9eb26b59eec3a7df32cb560105be50d208f26a32","observation_id":"fb3ebb4a-e03c-4aca-b9d2-c017434ed43d","resolution":{"observed_at":"2026-07-01T07:15:29.092017Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2403.06732/citation-record","integrity":"/paper/2403.06732/integrity","json":"/paper/2403.06732/citation-record.json","paper":"/paper/2403.06732"},"outbound":[],"paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-07T21:27:22.092569Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2403.06732."}