{"as_of":"2026-08-09T23:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:50f98cfd523ee585bae3ba8f38ed3318a40a29a770807b1d4f601fe454749e64","coverage":[{"denominator":19,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":19,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T15:59:13.843182Z","state":"measured"},{"denominator":19,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":19,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2512.14980/citation-record","integrity":"/paper/2512.14980/integrity","json":"/paper/2512.14980/citation-record.json","paper":"/paper/2512.14980"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:59:12.057925Z","title":"Karnakov, P., Litvinov, S., and Koumoutsakos, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.057925Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:ce1503e146a87a71f79a1a43fdb424ec60915d34d31632568a0b88293bd8f4fa","observation_id":"9a9d8c68-8369-4105-85c6-0ce4e464087a","resolution":{"observed_at":"2026-08-03T15:59:12.057925Z","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":"2026-08-03T15:59:13.513113Z","title":"Following these results, we use the truncated log-normal distribution for all our experiments","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.513113Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:003933472b43a2d9b57e4df933d3070a74e597f5e8f066dfb1578daaf9f4c282","observation_id":"87ff3e33-cb02-4259-b05b-fa53f1c26575","resolution":{"observed_at":"2026-08-03T15:59:13.513113Z","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":"2026-08-03T15:59:13.728280Z","title":"Helmholtz Equation For the Helmholtz Equation we used the UNet implementation by Karras et al","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.728280Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:996daa949ad70dd7fcfe6a3e7fed90b734890d2c2017bd2a45109f75b6b5a688","observation_id":"ad3c67ae-f912-4667-884b-dbc4efbf7c8b","resolution":{"observed_at":"2026-08-03T15:59:13.728280Z","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":"2026-08-03T15:59:13.843182Z","title":"Table 7.Runtimes of vanilla and our method on training and sampling on an NVIDIA H200 GPU","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.843182Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:b105f61cefcdedcdbda40ec98cf8008641b06cc487ec521d119b86aca70b2b76","observation_id":"1a4e9c98-2615-478e-8d9a-70dd3906fa3d","resolution":{"observed_at":"2026-08-03T15:59:13.843182Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T15:59:12.714199Z","title":"Bastek et al","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.714199Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:d1f8ddbad6c782bb00a11421b3cfee444a5c4c86875c5fe1ba057daa6c8943f8","observation_id":"37cba9ad-8990-4a1d-8526-f7b56ee6ae69","resolution":{"observed_at":"2026-08-03T15:59:12.714199Z","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":"2026-08-03T15:59:12.806395Z","title":"Injecting Measurement Structure for Training Inverse Problem SolversMathematically, the closest work is the likelihood-informed Doob’s h-transform by Denker et al","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.806395Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:2985ddb1d24980677ce3c89ef255f7bbd639489cc9af675ea4c6878d57f65faf","observation_id":"dfcba813-b539-467e-8258-189f11359fd3","resolution":{"observed_at":"2026-08-03T15:59:12.806395Z","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":"2026-08-03T15:59:12.920200Z","title":"dual path","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.920200Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:a682386684289b40c5f5f6a9d147524fe163637dc3b9d9b55b93469e16b48c99","observation_id":"7e6fca85-5f2a-4208-8495-420852884fe3","resolution":{"observed_at":"2026-08-03T15:59:12.920200Z","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":"2026-08-03T15:59:13.002734Z","title":"We take p(xT ) to be approximately N(0, σ2 maxI), i.e","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.002734Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:f8cbd9d4701bfc0a60e3e247ee3109fc4f6706307bd07453cee023f7b89fd286","observation_id":"ec69d0f1-194d-477b-b4b6-2b6240aa6b41","resolution":{"observed_at":"2026-08-03T15:59:13.002734Z","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":"2026-08-03T15:59:13.096284Z","title":"fine-grained","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.096284Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:99c846b583506ee4914f3ceb415d0eb7e3cb8008a5c569802a2e4f76b0531394","observation_id":"feff8a53-a897-4073-8b29-0e725fd228d7","resolution":{"observed_at":"2026-08-03T15:59:13.096284Z","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":"2026-08-03T15:59:13.189562Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.189562Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:8f1fb2b374cf421c8f65e072dc9a84f9b6800c1bb1813fb31ce22f983fdc029a","observation_id":"348f6dab-3811-488c-81b9-748d8cb093e4","resolution":{"observed_at":"2026-08-03T15:59:13.189562Z","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":"2026-08-03T15:59:13.379943Z","title":"intermediate","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.379943Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:991aa609f3abc87abf0c6f5bb3c72f0b6c7cb8bf1e9a423432d26caa848005da","observation_id":"0dd5cf48-96f1-4a25-ae4d-87d0b411b06c","resolution":{"observed_at":"2026-08-03T15:59:13.379943Z","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":"2026-08-03T15:59:13.611346Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":128,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:13.611346Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:37adcd2ea263bb50c528439c521f7ddd5c0eacdaf8ca9b19a0c58b1d117ab1f1","observation_id":"76aa541e-e3d1-4d7d-961f-7425a30e3d52","resolution":{"observed_at":"2026-08-03T15:59:13.611346Z","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":"2026-08-03T15:59:12.449667Z","title":"Song, J., Vahdat, A., Mardani, M., and Kautz, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.449667Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:9b6e0097e179fe70a449bde91d03a160ceacb8a8f0d424f889425af0d07c187c","observation_id":"459207ba-6f1c-4e69-95a5-5a67d5404bd2","resolution":{"observed_at":"2026-08-03T15:59:12.449667Z","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":"2026-08-03T15:59:12.548403Z","title":"C., Azizzadenesheli, K., and Anandkumar, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.548403Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:34de42fadf9ae77467391f75ee9fd73c4ee3703c6950284e7ad879bbf921a939","observation_id":"7ef05652-1d33-4046-8129-45a4b3c6eb5b","resolution":{"observed_at":"2026-08-03T15:59:12.548403Z","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":"2026-08-03T15:59:12.251137Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.251137Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:7fbb196dd8f6b762a069a90c8f845f9c05eb623fb9d2c767ebab7abb4d575318","observation_id":"d66fe5b1-b178-428e-be74-d47915b5d802","resolution":{"observed_at":"2026-08-03T15:59:12.251137Z","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":"2026-08-03T15:59:12.163407Z","title":"Analyzing and Improving the Training Dy- namics of Diffusion Models.2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.163407Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:7d1264cb61c69799f7c8077ba0ced998ee060e743ec3c086aa090ba24134f305","observation_id":"55f3dece-150f-435d-8542-0f188853c133","resolution":{"observed_at":"2026-08-03T15:59:12.163407Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.08477","last_updated":"2025-02-13T01:09:58Z","snapshot_observed_at":"2026-08-08T17:26:41.651741Z","submitted_at":"2024-09-13T02:07:20Z","title":"Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.08477","snapshot_observed_at":"2026-08-03T15:59:12.336001Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.336001Z"},"links":{"cited_paper":"/paper/2409.08477","citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:7cdbc1af33c5504642c258dd43634a0e9bcd46986cf406238886a3c9c4429dd6","observation_id":"fe636cc9-cce7-49d5-aa5b-fb1b87c08574","resolution":{"observed_at":"2026-08-03T15:59:12.336001Z","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":"2026-08-03T15:59:12.635696Z","title":"Proofs Proposition 3.1.Let D∗ reg(xt, t)be the denoiser that minimizes the regularized objective Lreg","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:12.635696Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:bad26f47cb41d394a96157bc9787154180dc1f6cd033e5e19ff39f972cf5bf16","observation_id":"d367822e-017e-4daa-99a9-b77a0eb94ab9","resolution":{"observed_at":"2026-08-03T15:59:12.635696Z","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":"2026-08-03T15:59:11.989619Z","title":"Bastek, J.-H., Sun, W., and Kochmann, D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations","version":4},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-03T15:59:11.989619Z"},"links":{"citing_paper":"/paper/2512.14980"},"observation_digest":"sha256:6e74f140de729eb9500b36595b30fa7be62d088709babd1688e85745eb63b4d2","observation_id":"14e91450-802b-4a7e-879d-a6306a35cb3d","resolution":{"observed_at":"2026-08-03T15:59:11.989619Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.14980","last_updated":"2026-05-28T21:07:40Z","latest_version":4,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T20:20:45.972436Z","submitted_at":"2025-12-17T00:35:45Z","title":"Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations"},"reference_resolution":{"displayed":19,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":19},"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 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2512.14980."}