{"as_of":"2026-08-08T14:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8c64ab760a918b576f023088e611b51d24d0ebce9baa1bf39da54e440430610c","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:09:00.101807Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2505.22930/citation-record","integrity":"/paper/2505.22930/integrity","json":"/paper/2505.22930/citation-record.json","paper":"/paper/2505.22930"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:03.300087Z","title":"Semigroups of linear operators , volume 93","venue":null,"work_id":"e5948281-36a6-4c59-8d46-f371de996195","year":2019},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:58.478993Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:57d2e90b2fe5e77566085782076f5a65ee935eda5f90327600821c0d73fa7acd","observation_id":"e0240f39-632f-4770-9148-378f75066137","resolution":{"observed_at":"2026-08-07T13:09:03.477449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:03.051906Z","title":"On twisted Fourier analys is and convergence of Fourier series on discrete groups","venue":null,"work_id":"29099a9f-b803-484b-bd3e-6e7c1e0001a0","year":2009},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:58.578930Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:69480d5df461b3f549315c49f5753b823267a7a56ab8825abb61a85ad78a14b5","observation_id":"f987734d-dbc4-4fcc-9b4e-5c94840d6a89","resolution":{"observed_at":"2026-08-07T13:09:03.166901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:02.786110Z","title":"Fourier series and twiste d C*-crossed products","venue":null,"work_id":"db5b50cb-fc55-42a6-8794-dc2a6b8cfc01","year":2015},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:58.751577Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:1a3a1a2dc20082ffed8444ba1e4d3607eab58c68dbe9705a0f0b4add3c7d84b9","observation_id":"44c7c736-4bd6-4043-8ab2-341480bf2aa6","resolution":{"observed_at":"2026-08-07T13:09:02.935654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:02.450024Z","title":"Heat Properties for Group s","venue":null,"work_id":"d0b3c25d-8061-49b4-87e7-237aecbd829a","year":2024},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:58.862632Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:e4a7fdbbae94e1cc11372a654cebf34ee93c61d68bfe59f8319c42e69d46b3c4","observation_id":"a2f315d6-39d3-4ac1-a353-df5ae6617975","resolution":{"observed_at":"2026-08-07T13:09:02.615577Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:02.182129Z","title":"Operator algebras and quantum statistical mechanics: Volu me 1: C*-and W*-Algebras","venue":null,"work_id":"bd30a2e6-fb4b-425c-a4f9-47ca0e8c61e0","year":2012},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.010753Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:079a241200389673606317208ffafa6c04024c945b285085a1320e07259f6375","observation_id":"f1002843-4299-4ced-9e3d-f635e056f045","resolution":{"observed_at":"2026-08-07T13:09:02.331654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:01.908809Z","title":"Dym and H","venue":null,"work_id":"33cd6f36-3637-452b-acb5-eee59ac79484","year":1972},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.139833Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:d3f76bac0138053bd6202be752eb7e78f663a45b288781868b0b9e691e9b01ee","observation_id":"8ad8e52d-18c6-474f-ada3-1f1a0506046f","resolution":{"observed_at":"2026-08-07T13:09:01.996591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:01.630476Z","title":"One-parameter semigroups for linear evolution equations , volume","venue":null,"work_id":"42d3db08-9a39-44d2-b944-592382fbd441","year":null},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.306707Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:54668f346b3cd0d66a14fd281423e4331d036667590ac3d466ee40417c95d180","observation_id":"c0318be8-1724-454e-8f64-0d654f940ca7","resolution":{"observed_at":"2026-08-07T13:09:01.787939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:01.388516Z","title":"An example of a non nuclear C*-algebra, whi ch has the metric approximation property","venue":null,"work_id":"2d13c5da-0ec7-4b48-950e-a5bdf9ab51d6","year":1978},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.446738Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:57909004f643134cd0fdf4a4b7dec8307a90b29f635cea65376e47a979114652","observation_id":"a11be2f4-633c-4062-8380-d1e305fce723","resolution":{"observed_at":"2026-08-07T13:09:01.504745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:01.101062Z","title":"Abstract harmonic analy sis","venue":null,"work_id":"62243a72-23c2-402f-9d5f-8f5921813e14","year":1997},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.612005Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:cb832ef10281a4e8fe8178e8045fcdae4539d09324c35b36c0bf2c089299e75b","observation_id":"52b4a7a7-232d-4b87-951f-aeb140467a40","resolution":{"observed_at":"2026-08-07T13:09:01.262196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:00.815488Z","title":"The Wave Equation in the Context of Reduced Group C*-Algebra s","venue":null,"work_id":"6216cf15-d867-43ff-b2e8-05b34e3fffbf","year":2025},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.772640Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:0693f9eede8ec117ccd54f4df0bd9fc93ef01da121cbc64154988d69b482e7e1","observation_id":"72117b0b-1560-4ea4-941d-24b34a69a2b5","resolution":{"observed_at":"2026-08-07T13:09:00.944116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:00.522173Z","title":"Unbounded de rivations of group C∗ -algebras","venue":null,"work_id":"6a314a43-0f56-4a17-ba18-9459caf16e94","year":1976},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:59.898978Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:a115f8dd96b045b4c9252c9d197df65d21dab59029bda76f02f9d878338c525c","observation_id":"eaa99101-d483-4510-b20e-a8601de1741d","resolution":{"observed_at":"2026-08-07T13:09:00.677193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:09:00.244510Z","title":"Fourier Analysis: An Introduction , volume 1","venue":null,"work_id":"60b50868-616e-44f9-9aba-87398e2976d6","year":2011},"citing_paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:09:00.101807Z"},"links":{"citing_paper":"/paper/2505.22930"},"observation_digest":"sha256:3fe2cb207bd880d1af0d15e2e66e2f4a0115e638848772a4b131c3601a00f5c4","observation_id":"0932a4d2-ab19-4813-9619-ac26041c48b0","resolution":{"observed_at":"2026-08-07T13:09:00.382412Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}}],"paper":{"arxiv_id":"2505.22930","last_updated":"2025-05-28T23:10:50Z","latest_version":1,"primary_category":"math.OA","snapshot_observed_at":"2026-08-07T12:54:58.323500Z","submitted_at":"2025-05-28T23:10:50Z","title":"The Wave Equation in the Context of Reduced Groups $C^*$-Algebras"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":12},"total_outbound_references":12},"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 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2505.22930."}