{"as_of":"2026-08-01T20:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3d0a0743e6efc7a1ba9a83c374d7d2e6f0ecac7ddaa147a635969c14cb3481ad","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-07T16:25:52.183768Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-01T06:32:01.292127+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T01:33:49.132446Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-01T21:26:16.525396Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"cited_work":{"arxiv_id":"2604.25825","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.25825","snapshot_observed_at":"2026-07-01T21:26:16.525396Z","title":"A Quantum Spectral Framework for Solving PDEs","venue":"quant-ph","work_id":"0fbed3ac-198e-4f88-b831-7b9167124ab0","year":2026},"citing_paper":{"arxiv_id":"2606.01270","last_updated":"2026-05-31T14:47:58Z","snapshot_observed_at":"2026-07-06T23:41:53.635605Z","submitted_at":"2026-05-31T14:47:58Z","title":"Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-28T16:53:19.896177Z"},"links":{"cited_paper":"/paper/2604.25825","citing_paper":"/paper/2606.01270"},"observation_digest":"sha256:3cf2a8410c27e812a09cc3be3734a572b300b61e970887361598454ea23ff2fe","observation_id":"28065ab3-5b15-4a45-b15e-13c3484c8633","resolution":{"observed_at":"2026-07-01T21:26:16.526615Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.25825","snapshot_observed_at":"2026-07-13T01:33:49.132446Z","title":"2026.doi:10.48550/arXiv.2604.25825","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09639","last_updated":"2026-07-10T17:36:20Z","snapshot_observed_at":"2026-07-15T23:18:32.285079Z","submitted_at":"2026-07-10T17:36:20Z","title":"A Quantum Path to Partial Differential Equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-13T01:33:49.132446Z"},"links":{"cited_paper":"/paper/2604.25825","citing_paper":"/paper/2607.09639"},"observation_digest":"sha256:29093a53900b7cf7f544fef09f8a8201d9e5330154c9b1edaf71d53179906fbf","observation_id":"9da499ca-e636-4ad9-890e-c4ca192c1d0a","resolution":{"observed_at":"2026-07-13T01:33:49.132446Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2604.25825/citation-record","integrity":"/paper/2604.25825/integrity","json":"/paper/2604.25825/citation-record.json","paper":"/paper/2604.25825"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2603.19130","last_updated":"2026-06-29T10:09:10Z","snapshot_observed_at":"2026-07-13T22:09:45.926569Z","submitted_at":"2026-03-19T16:49:13Z","title":"Quantum block encoding for one-pair semiseparable matrices","version":2},"cited_work":{"arxiv_id":"2603.19130","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2603.19130","snapshot_observed_at":"2026-06-30T03:17:29.115940Z","title":"Antonioli, P","venue":null,"work_id":"9cfaa36c-fefe-4026-a71e-44924c8cf9d3","year":2026},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"cited_paper":"/paper/2603.19130","citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:799044379a1e3368ddc58e773506195026a51b4814a9fb3ca6bf4064c826736f","observation_id":"ee2d1910-4468-4799-9c19-33befa86a16a","resolution":{"observed_at":"2026-06-30T03:17:29.115940Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bagherimehrab and A","venue":null,"work_id":"e844d996-661c-4d3e-8d21-ea8982491ef9","year":2024},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:05a8dda4c49d2cb433a41bd7fdb700ae4cf88a53fd94a06692d443546ee9dcb9","observation_id":"cddb82be-1648-4999-9c38-2c39b0be5265","resolution":{"observed_at":"2026-05-27T02:13:25.713535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bungartz and M","venue":null,"work_id":"44261d4a-4c97-42a6-84b8-d6208941b99c","year":2004},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:4662cb7c2e253c9fe28136043f83d9637dc709c209d8a3fc388822bccd14eb7e","observation_id":"81e74d9f-148b-47a8-ad2b-ec3304081a81","resolution":{"observed_at":"2026-05-27T02:13:25.702807Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Castelazo, Q","venue":null,"work_id":"da8e7dc9-72a4-453b-a3cd-3bb4bf05d5d0","year":2022},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:8305cb1aa29363c8c8fe36c0e1696b1cdb36324052021b0b461086779fc43572","observation_id":"f9507564-8d40-4d4e-92f5-8de624825761","resolution":{"observed_at":"2026-05-27T02:13:25.710203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f6e8789e-ffd8-410d-8ac4-5eaff748d588","year":2021},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:649044d250e8854a7ac93deb05c90db69c89103a9323de33196b4df94af10542","observation_id":"18bfd60d-1a60-48a3-bea9-0691dee8fb41","resolution":{"observed_at":"2026-05-27T02:13:25.694273Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Cramer, M","venue":null,"work_id":"2e60d7ec-f2d0-433c-9e0f-76014cd23276","year":2010},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:f080a1a763201c8a4b5245f5b38e6aceacdb63d67dd4c8ca065c65fe6d3917f4","observation_id":"a21c961f-1318-4ce3-a60a-9459aca56868","resolution":{"observed_at":"2026-05-27T02:13:25.686629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"De Ryck and S","venue":null,"work_id":"912d55b2-dcbd-471a-9546-07a047c028be","year":2024},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:4bec9ec4e9d530530b6d56df08180003e50ba61dd1a3c35dae67fb0c8e89e3f7","observation_id":"1c925199-c7d2-4d91-953a-abfbc38b2a7e","resolution":{"observed_at":"2026-05-27T02:13:25.690523Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.02151","last_updated":"2024-10-03T02:28:17Z","snapshot_observed_at":"2026-07-06T19:26:43.399756Z","submitted_at":"2024-10-03T02:28:17Z","title":"Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations","version":1},"cited_work":{"arxiv_id":"2410.02151","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.02151","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Furuya, T., Taniguchi, K., and Okuda, S","venue":null,"work_id":"e8e1ae12-6db1-4717-a099-16221d95edad","year":2024},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"cited_paper":"/paper/2410.02151","citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:34355d3c97544067faf9bb708803993ec79218d61c7449bc68db3e36b783c0c0","observation_id":"0753e44a-8a64-4d89-9dcd-0bac8ef8015f","resolution":{"observed_at":"2026-05-11T23:41:19.218295Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"32aa9a7d-e14c-4a9b-9928-4fa5a5bc05da","year":2009},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:ba916d9be9c34c5fb4525680cb066c996f548159281334f50b4522193bd0f0f2","observation_id":"a3ccfab0-1584-4b79-9540-09ba610ff4e1","resolution":{"observed_at":"2026-05-27T02:13:25.698261Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"cbc188ac-b535-4be8-b639-578b2c0d23b8","year":2014},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:e2fa9b2198f95c871f2430fb64c87851141597e113d55f43d56c58080c6d07a0","observation_id":"9dc5e66c-6471-489a-b5f0-c671f87e0b83","resolution":{"observed_at":"2026-05-27T02:13:25.706776Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1603.08675","last_updated":"2016-09-22T09:32:16Z","snapshot_observed_at":"2026-07-06T04:50:59.165738Z","submitted_at":"2016-03-29T08:25:22Z","title":"Quantum Recommendation Systems","version":3},"cited_work":{"arxiv_id":"1603.08675","doi":null,"metadata_source":"pith","pith_arxiv_id":"1603.08675","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Quantum Recommendation Systems","venue":"quant-ph","work_id":"1114eb00-79a9-4bb7-ac81-e1c9f3a15594","year":2016},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"cited_paper":"/paper/1603.08675","citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:71337b6c951b8a6e98759cb99f80d7932bec4f789d615608a6a145e4f422a8fb","observation_id":"b129a040-e6d3-428d-9162-e1ae7b0c3ee5","resolution":{"observed_at":"2026-05-11T23:41:19.189200Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2201.08309","last_updated":"2022-01-20T17:22:33Z","snapshot_observed_at":"2026-07-06T12:29:20.225445Z","submitted_at":"2022-01-20T17:22:33Z","title":"Lecture Notes on Quantum Algorithms for Scientific Computation","version":1},"cited_work":{"arxiv_id":"2201.08309","doi":"10.48550/arxiv.2201.08309","metadata_source":"pith","pith_arxiv_id":"2201.08309","snapshot_observed_at":"2026-07-10T22:07:37.367441Z","title":"Lin, Lecture notes on quantum algorithms for scientific computation (2022), arXiv:2201.08309 [quant-ph]","venue":"quant-ph","work_id":"feb69041-4b7d-45d8-900a-c4668d2ed8e6","year":2022},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"cited_paper":"/paper/2201.08309","citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:51979fce60282be990b02ced3fe632151d44edc7933969fd3d58d86f5da8656b","observation_id":"c10a8d62-c6e4-4ed2-8bd8-2a0733a2cbd2","resolution":{"observed_at":"2026-05-11T23:41:19.223487Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-07-20T15:24:07.468468+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T15:24:07.468468+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lubasch, Y","venue":null,"work_id":"ade8bee7-fb7f-40de-b141-7fa9e6c28fbc","year":2025},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:5e02b69a5807efd15993041069f2660e42899dfbf2d24ca1ee785193f1d0fe5f","observation_id":"b15aa50a-c382-4ca2-813b-145a3f01d081","resolution":{"observed_at":"2026-05-27T02:13:25.675171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Preskill,Lecture notes for physics 229: Quantum information and computation, California institute of technology, 16 (1998), pp","venue":null,"work_id":"640601f6-7999-4a65-bd97-bf6fe45d7312","year":1998},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:2157f901429fd27519d230a3e5ee665751dd9a835b1caf09bfcb78dec446a5f5","observation_id":"4be66935-be07-4a7e-a2d5-fec09329092c","resolution":{"observed_at":"2026-05-27T02:13:25.679657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"8b167032-7541-4a9a-9263-ff77464c3625","year":2021},"citing_paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-07T16:25:52.183768Z"},"links":{"citing_paper":"/paper/2604.25825"},"observation_digest":"sha256:abc8fdd128734e03d26330bd93fc9c9bdc7796f3596dc93d3d82bb98a9597f11","observation_id":"d17cf7ce-0140-4d68-8bf4-5b5485488131","resolution":{"observed_at":"2026-05-27T02:13:25.683175Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.25825","last_updated":"2026-04-28T16:33:59Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-07-06T23:11:39.318906Z","submitted_at":"2026-04-28T16:33:59Z","title":"A Quantum Spectral Framework for Solving PDEs"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":4,"verified_fuzzy":7},"total_outbound_references":15},"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":"2026-08-01T06:32:01.292127+00:00","source":"crossref"},{"observed_at":"2026-08-01T06:31:58.492377+00:00","source":"retraction_watch"}],"thesis":"As of 1 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 2 inbound Pith citation observations for arXiv:2604.25825."}