{"as_of":"2026-08-21T10:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:670757122d152647fa9a2b21259e4c5f7140ed80bb75fbc8207fe5fcc826c3e8","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:35:10.228510Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2507.08274/citation-record","integrity":"/paper/2507.08274/integrity","json":"/paper/2507.08274/citation-record.json","paper":"/paper/2507.08274"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:35:10.946499Z","title":"D’Abbicco, Small data solutions for the Euler-Poisson-Darboux equation with a power non- linearity","venue":null,"work_id":"9484dcf5-f83c-4d01-a11d-70442fa4d870","year":2021},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.452309Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:d943895059b9d7f81c143d72c6d16e1d67d3ba69076c062f138980c2c9a1f324","observation_id":"57ed109b-4902-4566-830c-2d69772fabcf","resolution":{"observed_at":"2026-08-06T18:35:10.950623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.936146Z","title":"D’Abbicco, The threshold of effective damping for semilinear wave equations","venue":null,"work_id":"851e0593-1754-4817-a739-49e711a47b84","year":2015},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.516995Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:87811ea71647c6b049dc0f24164e671e70abad6c46dd8b014d72f8c8906a221d","observation_id":"85fb2ebf-b2a1-4c02-b66b-4eb1b7813aa7","resolution":{"observed_at":"2026-08-06T18:35:10.939428Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.925247Z","title":"D’Abbicco, S","venue":null,"work_id":"4c8c7e7a-4601-47cc-b39e-6fa1c19d16e7","year":2015},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.572423Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:cc5ea778ced878f6f4529086d62f0526a3525875d7977fddbe8d287214ab19d5","observation_id":"bdbc6f42-0c9f-47f2-aa28-611f4b9d1ee4","resolution":{"observed_at":"2026-08-06T18:35:10.929056Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:35:07.649181Z","title":"Alinhac, The null condition for quasilinear wave equations in two space dimensions I","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.649181Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:20834125b7d5a5f0f67c2c4f9e5363499e1adacbcd384e3e345a6e47fa06e488","observation_id":"8858b66a-67a9-4bf0-9083-06cd689c9269","resolution":{"observed_at":"2026-08-06T18:35:07.649181Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:35:10.908096Z","title":"Alinhac, The null condition for quasilinear wave equations in two space dimensions, II","venue":null,"work_id":"492ee6d2-bacd-4bc2-941b-93f37e7cc1b8","year":2001},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.711072Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:80345109aaf082921b579e2604b481fca0d035dd577232e4e5ee560f698146d4","observation_id":"1579380f-2a2e-4d68-a9c7-b2d3b842d3f4","resolution":{"observed_at":"2026-08-06T18:35:10.911044Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.898447Z","title":"Alinhac, An example of blowup at infinity for a quasilinear wave equations","venue":null,"work_id":"d6db7329-db1c-479e-bc89-2d977a2b8da1","year":2003},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.771726Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:083eb95c8e39099faf629f6159d832d993f94ac8bdd3d9c630e2e6975ad8b6e5","observation_id":"943e9f48-b790-4cab-bc10-8892e54f5617","resolution":{"observed_at":"2026-08-06T18:35:10.901741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.888830Z","title":null,"venue":null,"work_id":"3771886c-69ab-4307-9b6b-6f78fe1b1314","year":2015},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.817452Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:dd3ff7c448bdeab28cf929e82c8e53eecdce45662db60f150733824abdc95dca","observation_id":"7ebe684e-3dbc-49aa-b1c5-3a79d001b579","resolution":{"observed_at":"2026-08-06T18:35:10.892181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.879712Z","title":null,"venue":null,"work_id":"ad648823-b267-4bfc-a62a-bf7eb026ac1c","year":2025},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.857170Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:66e84d3ca27894df9e1b2572eebc8720f5b2b831c05d783ee3f814fcba422fdb","observation_id":"94dfbf5c-27ce-45c6-b45a-b62d9729f5c2","resolution":{"observed_at":"2026-08-06T18:35:10.882630Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.869135Z","title":"Fujita, On the blowing up of solutions of the Cauchy Problem for ut = ∆u + u1+α","venue":null,"work_id":"d0aaa13f-aa50-4413-a60f-d970e4eb32e9","year":1966},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.912376Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:cc9f65112f78791eddf52094bf3052c825f686272a27150f8063457ad2600015","observation_id":"d61bfb64-8c1d-4a5d-8dee-e200f94c0290","resolution":{"observed_at":"2026-08-06T18:35:10.872733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.05268","last_updated":"2025-06-25T09:15:35Z","snapshot_observed_at":"2026-08-15T23:05:55.599214Z","submitted_at":"2025-05-08T14:14:43Z","title":"Morawetz type estimate for damped wave equation in $\\mathbb{R}^n (n\\geq 4)$ and its application","version":2},"cited_work":{"arxiv_id":"2505.05268","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.05268","snapshot_observed_at":"2026-08-06T18:35:10.656081Z","title":"Morawetz type estimate for damped wave equation in $\\mathbb{R}^n (n\\geq 4)$ and its application","venue":"math.AP","work_id":"665d1cd0-bf3d-4e1d-9e0e-58565ba20acb","year":2025},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:07.987585Z"},"links":{"cited_paper":"/paper/2505.05268","citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:bd4746f97a2a6bb09ae7030675d2c598302c34c872d66241e2f705417084bf6e","observation_id":"b3d163b7-0401-43ac-833e-39f7be3d9cc9","resolution":{"observed_at":"2026-08-06T18:35:10.660375Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.19438","last_updated":"2025-07-11T08:57:40Z","snapshot_observed_at":"2026-08-16T12:47:04.382273Z","submitted_at":"2025-03-25T08:29:21Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II","version":2},"cited_work":{"arxiv_id":"2503.19438","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.19438","snapshot_observed_at":"2026-08-06T18:35:10.390880Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II","venue":"math.AP","work_id":"777ce900-7076-459c-a123-6eb2462a4757","year":2025},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.075830Z"},"links":{"cited_paper":"/paper/2503.19438","citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:70323355d2804ce06368e93e6f0390b30f5555bbb68e358b44ed1c01bdf7c714","observation_id":"caa4d2e1-7a8c-4d2e-a8f5-01dd1a2c3ebb","resolution":{"observed_at":"2026-08-06T18:35:10.481131Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.857219Z","title":"Preprint (2025)","venue":null,"work_id":"04d5a245-a31f-492e-9b68-9b9dab495474","year":2025},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.138600Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:239ee717edaa01f96d2c0d153b5da0f9bd5108f744bd8129740aba2027e77c72","observation_id":"c47d68f0-009d-4ae6-a5cc-1cdc8fb7e6dc","resolution":{"observed_at":"2026-08-06T18:35:10.860181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.847392Z","title":"H ¨ormander, Lectures on nonlinear hyperbolic equations","venue":null,"work_id":"1428b21b-8fd4-4360-a97c-5f923bdb85f6","year":1997},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.188640Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:8eeb182d32f01e458aa854d4cb234fc2e8901ae924a33b89d7bf9de3d2c1a432","observation_id":"7501e955-c57a-4bf3-a288-d691daf99253","resolution":{"observed_at":"2026-08-06T18:35:10.850789Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.836770Z","title":"Ikeda, M","venue":null,"work_id":"9a1eca02-5774-4f5c-b009-a6a47cc8c193","year":2018},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.265569Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:2f4b97c7fe7bb83bd3af19eb274a6f209f97db0913cbad2a1865c106874123a3","observation_id":"2efc5884-124e-497e-b5f0-20eb9195cf2d","resolution":{"observed_at":"2026-08-06T18:35:10.840517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.826601Z","title":null,"venue":null,"work_id":"844d2f96-df99-40c8-98da-ca04e4986074","year":2020},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.341290Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:7039019fcc8465b987496bd4a973ddf4619e63a53c331e1a99189547ed614994","observation_id":"c801efe2-f563-41fe-ae4a-4b4b54a8f1aa","resolution":{"observed_at":"2026-08-06T18:35:10.830234Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.816436Z","title":"Klainerman, Uniform decay estimates and Lorentz invariance of the classical wave equation","venue":null,"work_id":"a4c64124-cc80-4cf3-933e-e48955d8ee07","year":1985},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.397510Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:170d39edc443694964af0b892dfdfc6128bd62079d7e1c9f301bc184c5445740","observation_id":"8c78d722-3e09-4131-ab7f-63cdff07c14d","resolution":{"observed_at":"2026-08-06T18:35:10.819925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:35:08.464894Z","title":"Klainerman, G","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.464894Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:a0c88e6113a345f1b702ea0a471d0f29a825c0591bc8100d1ad446e7f3d46fca","observation_id":"7da7105b-795b-4dfd-b0eb-b1385c229b91","resolution":{"observed_at":"2026-08-06T18:35:08.464894Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:35:10.799978Z","title":"Takamura, K","venue":null,"work_id":"0c3fe77e-9086-4749-9a48-1104d6f33e38","year":2017},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.547362Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:d7e9a0435f16ffc4ffb10268ed31dcd7b21f27174b6cf4b2b357c4286c9f9677","observation_id":"e9144965-c0a6-417d-9650-9719941f10b5","resolution":{"observed_at":"2026-08-06T18:35:10.802815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.18677","last_updated":"2025-07-12T00:22:16Z","snapshot_observed_at":"2026-08-21T07:55:30.372165Z","submitted_at":"2025-03-24T13:49:29Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, I","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.18677","snapshot_observed_at":"2026-08-06T18:35:08.624866Z","title":"Preprint (2025), arXiv:2503.18677","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.624866Z"},"links":{"cited_paper":"/paper/2503.18677","citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:47009808efdb6d62765aee2565e850cb59e5564d4e49daf8a633fab16eaa1fb2","observation_id":"e5623b37-d637-4adb-9ffd-305ea1ff7e27","resolution":{"observed_at":"2026-08-06T18:35:08.624866Z","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":"2026-08-06T18:35:08.666619Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.666619Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:aed8533925fabb83133568876451f405f99f3091cf400e399a4312752c152369","observation_id":"0e047762-1963-43d1-8192-323c938a644e","resolution":{"observed_at":"2026-08-06T18:35:08.666619Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:35:10.784592Z","title":null,"venue":null,"work_id":"5560d06e-f0f2-43e9-920c-d9e9b2244e6e","year":1991},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.741360Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:5f6dcd74833c17feda527bfb6b216d35057d1fb8af983162338524bdb41b8fae","observation_id":"b9a3c3e9-5664-4b3d-ad5e-34527b850c30","resolution":{"observed_at":"2026-08-06T18:35:10.787545Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.775552Z","title":"Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data","venue":null,"work_id":"27eca5e7-c124-49d4-bb63-c4a6ef4d3545","year":1990},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.809417Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:45dfb027d307980fb7d88d3946c34417189e31817bb986b20227efdf9c4d069c","observation_id":"18d7203f-f0f0-452e-8f57-04c54c3526f2","resolution":{"observed_at":"2026-08-06T18:35:10.778711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.765673Z","title":"Lindblad, Global solutions of quasilinear wave equations","venue":null,"work_id":"640b8cb2-a8a2-44d5-886d-1885ef677f8d","year":2008},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.821234Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:345b16bdf7ef8ce3bd06d53a39fb63e95dba85c9838e02f824a3f3d69e72fe98","observation_id":"9f5be8eb-eac2-4947-a1ad-e654a5dd96f1","resolution":{"observed_at":"2026-08-06T18:35:10.769167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.755999Z","title":"Olver, D.W","venue":null,"work_id":"05b82238-e875-4559-835e-a2c2528d4c9f","year":2010},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:08.933581Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:cdf57f7886891cff05e0fa1f7a7cd607c740fba0a03099a28a4aaebd60ddd01c","observation_id":"99ea69be-adb0-4761-9035-6654f31adcdc","resolution":{"observed_at":"2026-08-06T18:35:10.759243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.746063Z","title":"Palmieri, On the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equa- tion with power nonlinearity","venue":null,"work_id":"d5413cb1-2f8c-4992-8bbf-185c205371ee","year":2025},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:09.045869Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:f9b0e1f5980b6a9ab058ab132ca91af144c77b0fbbf792033a24b0b5f65f9289","observation_id":"7365b0db-73ff-4453-878c-358b2c8bd6c5","resolution":{"observed_at":"2026-08-06T18:35:10.749430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.735875Z","title":"Palmieri, M","venue":null,"work_id":"bea850e1-23f5-4e1d-843e-e438ea2b5a04","year":2019},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:09.276350Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:b671c4e4de06e792f3f2ca23b4d1d653f26408c9f68043a26b22a51c59074d81","observation_id":"7788326b-eeb7-464d-ad8e-59e874c1dbc7","resolution":{"observed_at":"2026-08-06T18:35:10.739494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.725124Z","title":"Palmieri, Tu Ziheng, A blow-up result for a semilinear wave equation with scale-invariant damping andmass and nonlinearity of derivative type","venue":null,"work_id":"0afe677f-2102-4c0a-aa7a-e10365428910","year":2021},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:09.449449Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:96feb43deebf891cea7b95cb0e9e5c27df0d485b650c3f53c28fb5d989cc3dd8","observation_id":"7a07fa19-f192-4719-85f2-a102fa86c1e4","resolution":{"observed_at":"2026-08-06T18:35:10.728775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.713665Z","title":"Strauss, Nonlinear scattering theory at low energy","venue":null,"work_id":"619da344-d057-4b06-98f9-2f802e922a4e","year":1981},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:09.596224Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:c043504a6eeecf9259047e6f98c8ce2a1b63bc399939bb9e6fe48196b92ae54a","observation_id":"c2ffb2b6-094e-4d30-9048-8f89cfacf170","resolution":{"observed_at":"2026-08-06T18:35:10.717627Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.698670Z","title":"Differential Integral Equations 32 (2019), no","venue":null,"work_id":"e352f89a-d2ab-42f1-9b77-d44fc77fab4f","year":2019},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:09.717473Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:253868ad03c451e8af5c7b2b48d43814b84550f1d75693e2586bcdfc165f6276","observation_id":"156b5700-0a20-4249-8e19-03e753242150","resolution":{"observed_at":"2026-08-06T18:35:10.705400Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.688267Z","title":"Wakasugi, Critical exponent for the semilinear wave equation with scale invariant damping, in: Fourier Analysis","venue":null,"work_id":"27f6b878-0fa9-4bfa-852e-c61a3ae86f43","year":2014},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:09.836490Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:ef0e010ba3490732011a4fea11e04041793665e352af9245f698dfc5de30a575","observation_id":"38ae83aa-a6f6-4db1-9dd2-fff59c495004","resolution":{"observed_at":"2026-08-06T18:35:10.691908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.677928Z","title":"Watson, A treatise on the theory of Bessel functions","venue":null,"work_id":"3024a11a-0f7d-452b-9fcf-2002f805bff9","year":1922},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:10.079585Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:bac9b8af9870b6f2b2a2d2a8d8b812c8a62930e7f418a3b87ab230953125c783","observation_id":"de437692-a17b-481c-ae70-960f26eaeecd","resolution":{"observed_at":"2026-08-06T18:35:10.681513Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-06T18:35:10.667768Z","title":"Wirth, Solution representations for a wave equation with weak dissipation","venue":null,"work_id":"1657c563-ff85-42ba-8ac4-3b5f575ba768","year":2004},"citing_paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T18:35:10.228510Z"},"links":{"citing_paper":"/paper/2507.08274"},"observation_digest":"sha256:7aea2ab214a93f04153bcb86bd2c70e77a8151cdf5e8a7b4f0e475b32fd5b8ce","observation_id":"f7b7091e-171b-4cee-9eb2-2855b155334d","resolution":{"observed_at":"2026-08-06T18:35:10.671350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.08274","last_updated":"2025-07-15T13:35:06Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-06T18:20:16.946346Z","submitted_at":"2025-07-11T02:49:07Z","title":"Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":8,"verified_exact":0,"verified_fuzzy":22},"total_outbound_references":32},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2507.08274."}