{"as_of":"2026-08-21T13:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:892dc586fde330256c0d17c8ee029c8662f1bad175fdce8b8de3d0108eea5477","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T23:18:56.276676Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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":"2026-08-06T18:35:07.987585Z","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":"2026-08-06T18:35:10.656081Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.05268","snapshot_observed_at":"2026-07-11T17:02:26.447669Z","title":"Preprint (2025), arXiv:2505.05268","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.04575","last_updated":"2026-07-06T01:03:03Z","snapshot_observed_at":"2026-08-21T06:24:43.654846Z","submitted_at":"2026-07-06T01:03:03Z","title":"Global existence of small data solutions to 3-D semilinear Euler-Poisson-Darboux equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-11T17:02:26.447669Z"},"links":{"cited_paper":"/paper/2505.05268","citing_paper":"/paper/2607.04575"},"observation_digest":"sha256:567ee4fa1ef654b04bd86736b7280dcffed1fe5445f524ebdade36e8eab2aa34","observation_id":"c8941463-657b-40c9-96d9-6b822a62ff52","resolution":{"observed_at":"2026-07-11T17:02:26.447669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.05268/citation-record","integrity":"/paper/2505.05268/integrity","json":"/paper/2505.05268/citation-record.json","paper":"/paper/2505.05268"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:18:56.814456Z","title":"D’Abbicco, The threshold of effective damping for semilinear wave equations, Math","venue":null,"work_id":"fc6f0e44-df57-4273-ae52-d5a6f99d57e1","year":2015},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.114095Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:57563d462e60b0266570da9328446fa94cba61ca3dd422f1ce74489a12f1d439","observation_id":"fbbe8b9b-caef-49e4-a65b-4ad4232888fd","resolution":{"observed_at":"2026-08-15T23:18:56.818946Z","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":"2026-08-15T23:18:56.800239Z","title":"D’Abbicco, Small data solutions for the Euler-Poisson-Darboux equation with a power non linearity, J","venue":null,"work_id":"9b2ca22f-a2b3-4611-bd6c-8666a93d24f3","year":2021},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.119377Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:b584559ac349b5e095ecd51691619280b914dc1fa9c779e4d18719fca7f33074","observation_id":"84f02bd0-0d9c-42ce-980a-855c11252ca5","resolution":{"observed_at":"2026-08-15T23:18:56.805538Z","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":"2026-08-15T23:18:56.786828Z","title":"D’Abbicco, S","venue":null,"work_id":"8c4b4f8c-a866-44c8-8791-35ac2fada2ad","year":2015},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.123876Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:b6ab5c24bf5a16115de74d5a8383054fc82944dbee39c93ff5ce6e5e5e4fb86c","observation_id":"24351daf-3286-4f62-8ded-08a42a5e37a6","resolution":{"observed_at":"2026-08-15T23:18:56.791089Z","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":"2026-08-15T23:18:56.773947Z","title":"D’Abbicco, S","venue":null,"work_id":"94fa2eee-ca57-4a6e-ae5a-a4a858a05302","year":2015},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.128588Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:24831d440f6016f5b5bcc91623cc220b06a936407a212edbc5ab76e59bd4019f","observation_id":"a866d78a-afca-4322-8bb1-23e4dad5f738","resolution":{"observed_at":"2026-08-15T23:18:56.778177Z","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":"2026-08-15T23:18:56.760291Z","title":"Erdelyi, W","venue":null,"work_id":"06d37557-b161-4795-be7d-0f9fab4f7432","year":1953},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.133010Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:ca0b5e93a46374c395221d13cf8d68c125fc12fd3aaa8ebd4f99b17a521ba396","observation_id":"07cb24fa-66d9-4bb5-abeb-36b10824f0d8","resolution":{"observed_at":"2026-08-15T23:18:56.764738Z","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":"2026-08-15T23:18:56.747172Z","title":null,"venue":null,"work_id":"c6d57c6a-c9c0-4c38-bbcc-25be925e64f9","year":2025},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.137552Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:bb6e5ead07845003faa99cf2c8169f24f4d6aba9cbef98aeca3a0f51dcc78bff","observation_id":"497494da-ce7a-4226-ac97-8b012d928004","resolution":{"observed_at":"2026-08-15T23:18:56.751566Z","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":"2026-08-15T23:18:56.733605Z","title":null,"venue":null,"work_id":"dfd63931-4ff9-4e44-bc2d-2c3f46fa20a9","year":null},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.142309Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:5394658e58f1c0ccc05ccada7d9e9a13f3ef02381e6f10bc4882e46df3f1593a","observation_id":"3c211646-25ef-4e04-b32a-1bdd14e1b146","resolution":{"observed_at":"2026-08-15T23:18:56.738147Z","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":"2026-08-15T23:18:56.718230Z","title":"Fujita, On the blowing up of solutions of the Cauchy Problem for ut = ∆u +u1+α, J","venue":null,"work_id":"7b4b962c-50f4-4734-8222-0c0574a0ff17","year":1966},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.146767Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:fba16b85f933918af76cb99678e96174b61767f5f3f69a197ad43a33c2b5a389","observation_id":"5902175a-c9f2-4362-af2a-f1c0572b1ad0","resolution":{"observed_at":"2026-08-15T23:18:56.723857Z","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":"2026-08-15T23:18:56.704000Z","title":"Georgiev, H","venue":null,"work_id":"450b2cc2-ecd4-49f8-9e4e-1b601a00cbb2","year":1997},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.151088Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:b9d1565604b7d9ef07dd67ddf039f3687c27a4dfc10d57f067eae40bbdf03937","observation_id":"8a6368b4-57ef-431f-8128-44f0cc3b5079","resolution":{"observed_at":"2026-08-15T23:18:56.708519Z","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":"2026-08-15T23:18:56.689922Z","title":null,"venue":null,"work_id":"3fe22201-0d02-4027-9367-5b796ac2d6a4","year":2017},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.155085Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:41f1885e1d780ab16aece6ea4d8039320d95a7e6e4ace7f7c15f972cdc1ab9d9","observation_id":"6f0763b8-cba9-40a4-aa2b-b0ddb53b0c2c","resolution":{"observed_at":"2026-08-15T23:18:56.694572Z","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":"2026-08-15T23:18:56.675700Z","title":null,"venue":null,"work_id":"15a29525-6c70-46ba-a0db-ca9c27e3ddb5","year":2017},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.159254Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:defe06e9e6add581d2a92135c1a89416385c950fb588d7aa818c83837aced38e","observation_id":"90cbcdde-e64b-44de-8942-c41626bd57b9","resolution":{"observed_at":"2026-08-15T23:18:56.680634Z","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":"2026-08-15T23:18:56.661509Z","title":null,"venue":null,"work_id":"f44e16e5-54b8-4617-8aaa-bb145473b586","year":2020},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.163533Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:e7da673b18a02d14246b45168d09089e5bea6369dc5f1ed849c19983487b823d","observation_id":"f4f433bf-8df3-4035-b6a4-bd351a0e4df2","resolution":{"observed_at":"2026-08-15T23:18:56.666069Z","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":"2026-08-15T23:18:56.647885Z","title":null,"venue":null,"work_id":"c278b5d4-1f62-494b-a830-ea964d5944d9","year":2021},"citing_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},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.168478Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:a601bf309cebb865aafd2a47d9bedda68983faeb7b84910e805aa597836aaafe","observation_id":"a64078f8-7c8d-4d25-bd07-08b7f0533500","resolution":{"observed_at":"2026-08-15T23:18:56.652515Z","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":"2026-08-15T23:18:56.634117Z","title":null,"venue":null,"work_id":"d9b9132e-4fb4-440b-903f-529a5c862b38","year":2021},"citing_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},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.173556Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:c89b1998526b9b91ac7726a514348ecb495e8b447cfd19202f7e8abf74f223a4","observation_id":"120d985c-8017-4e73-8c14-7743475d7363","resolution":{"observed_at":"2026-08-15T23:18:56.638562Z","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":{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.19438","snapshot_observed_at":"2026-08-15T23:18:56.178332Z","title":null,"venue":null,"work_id":null,"year":null},"citing_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},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.178332Z"},"links":{"cited_paper":"/paper/2503.19438","citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:643097a7de921fc4d5ff6ac92f0e758ebd826d6da63a9cfb30bd93fa7b63c037","observation_id":"3a68a2c7-6644-4959-adb8-5133fd9f20d0","resolution":{"observed_at":"2026-08-15T23:18:56.178332Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.01670","last_updated":"2025-01-03T07:02:53Z","snapshot_observed_at":"2026-08-16T19:04:14.917866Z","submitted_at":"2025-01-03T07:02:53Z","title":"Global existence for small amplitude semilinear wave equations with time-dependent scale-invariant damping","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.01670","snapshot_observed_at":"2026-08-15T23:18:56.183083Z","title":null,"venue":null,"work_id":null,"year":null},"citing_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},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.183083Z"},"links":{"cited_paper":"/paper/2501.01670","citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:a444394cd561ba983c55f8800537094792eac9f6d88acf743bd9e375ae00d486","observation_id":"1fb2679c-c7cb-4a9a-8670-edb490e3c347","resolution":{"observed_at":"2026-08-15T23:18:56.183083Z","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":"2026-08-15T23:18:56.621638Z","title":"Ikeda, M","venue":null,"work_id":"35620196-4a4e-439c-a145-324bab61197f","year":2018},"citing_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},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.187786Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:00786ff0a9d70f569a5cc4ec0c7263ea91ef57434d77c9435fa88010e5c5439b","observation_id":"8be02d28-6075-4311-8870-863e2e0a3161","resolution":{"observed_at":"2026-08-15T23:18:56.625542Z","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":"2026-08-15T23:18:56.608406Z","title":null,"venue":null,"work_id":"b195bd0d-500e-4861-8bd8-ababc774193e","year":2020},"citing_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},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.192007Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:14c5b8923f9b7e95efc1d20ceeab5499e66efabfa4a8ce9f6979b9fbfce4b95f","observation_id":"a19dcdfd-d055-4586-b279-dba0984bce28","resolution":{"observed_at":"2026-08-15T23:18:56.612873Z","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":"2026-08-15T23:18:56.594801Z","title":"John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math","venue":null,"work_id":"b6ce7af8-6a44-40a1-9b26-a88282522ed9","year":1979},"citing_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},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.196414Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:6a88082497ef4c9a2ce03f6fc3ddbcde0ee8275b960b89d21df8ce78c111e957","observation_id":"3d803db7-3263-495c-befb-2dd7cfcd6e00","resolution":{"observed_at":"2026-08-15T23:18:56.599351Z","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":"2026-08-15T23:18:56.581118Z","title":null,"venue":null,"work_id":"8ae17b17-0f99-4725-a1b2-15114e9d1b88","year":2019},"citing_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},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.200522Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:a0b6fc02dea8aa07bbd0c9968faf43662e4978a0592abd4ea05aa607fc21df41","observation_id":"5f014130-ab6e-485e-8c2c-294a589f3ee4","resolution":{"observed_at":"2026-08-15T23:18:56.585472Z","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":"2026-08-15T23:18:56.567019Z","title":"Lai, Weighted L2-L2 estimate for wave equation in R3 and its applications","venue":null,"work_id":"a2f09619-1fbd-4dce-968a-5443a17c5759","year":2020},"citing_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},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.204534Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:4245425dd4bc9bf1036dea0601e1b81b58c95c5bfce97f5786edc41f8cb9653d","observation_id":"267d26c8-8d3d-41fa-9390-9a647d4e52c4","resolution":{"observed_at":"2026-08-15T23:18:56.571327Z","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":"2026-08-15T23:18:56.554091Z","title":null,"venue":null,"work_id":"4ec01fe4-e651-44b0-9c47-7c4d632a9f16","year":2020},"citing_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},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.208687Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:09cfe73e838ec5f260c622e72d4c64ba9f7c8ed28ec359c43ec4b855ae210d31","observation_id":"1b664550-29af-410d-8fff-3ae3037bd382","resolution":{"observed_at":"2026-08-15T23:18:56.558359Z","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":{"arxiv_id":"2405.16145","last_updated":"2024-05-25T09:29:19Z","snapshot_observed_at":"2026-08-16T13:49:31.070340Z","submitted_at":"2024-05-25T09:29:19Z","title":"A blow-up result for the semilinear Euler-Poisson-Darboux-Tricomi equation with critical power nonlinearity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.16145","snapshot_observed_at":"2026-08-15T23:18:56.212614Z","title":null,"venue":null,"work_id":null,"year":null},"citing_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},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.212614Z"},"links":{"cited_paper":"/paper/2405.16145","citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:b1ed7fb42ffb140d7dfba7eafe74e0ce4b3e1c88527245d8874700bf6d7065b8","observation_id":"5195839d-e8d8-4565-9b9e-f645d2cfc4fe","resolution":{"observed_at":"2026-08-15T23:18:56.212614Z","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":"2026-08-15T23:18:56.540346Z","title":null,"venue":null,"work_id":"621dd37f-45aa-4c7f-9337-26e78948943a","year":2014},"citing_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},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.217182Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:1e3a94bb40ee3572113fc4a8132e4af2c9c9b3c26a1b09acd86e96167253c6c4","observation_id":"faf21a69-9f41-465d-8f98-925a452b4bd3","resolution":{"observed_at":"2026-08-15T23:18:56.544739Z","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":"2026-08-15T23:18:56.527309Z","title":null,"venue":null,"work_id":"bbd22298-129d-4f34-a9c8-544c2b20aa26","year":2021},"citing_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},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.221184Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:9551c127ca3a3259cc266e74ac802f7d44eb2c85e390ec8341503910edc4bb13","observation_id":"b61a8362-1573-4e21-b4da-c6b3cb500d66","resolution":{"observed_at":"2026-08-15T23:18:56.531464Z","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":{"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":"2026-08-15T23:18:56.225225Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.225225Z"},"links":{"cited_paper":"/paper/2503.18677","citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:59dc7c6c269a00d45c9dab6be5c719362992f59b850ba25f3db43d8d5f59234e","observation_id":"94ffd958-5488-4446-9862-5b2cd4370b66","resolution":{"observed_at":"2026-08-15T23:18:56.225225Z","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":"2026-08-15T23:18:56.514028Z","title":null,"venue":null,"work_id":"5452d813-7a5e-4191-aa26-6f24614d58ff","year":2025},"citing_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},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.229821Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:efb98b06cb272fcac6241ea9415a278337af4218f18a9aeb8edc0ebe804caaa9","observation_id":"360799c5-835c-4da8-aa5a-f49fe00fac42","resolution":{"observed_at":"2026-08-15T23:18:56.518240Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:18:56.234310Z","title":"Lindblad, C","venue":null,"work_id":null,"year":1995},"citing_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},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.234310Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:f18b3c92a6c3f5f61ac9a85eb271b2fd391da892f55ddc57bdffff16a43186ca","observation_id":"ab5e2d76-0977-4582-b8d7-1ee58be37f50","resolution":{"observed_at":"2026-08-15T23:18:56.234310Z","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":"2026-08-15T23:18:56.238620Z","title":"Palmieri, A global existence result for a semilinear scale-invariant wave equation in even dimension, Math","venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.238620Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:38326e1832b1e5f01c4659073b09ab387b1af7b4bdc67407228e4980337c90e7","observation_id":"b0df9c01-ff22-4906-8dfe-de8da7843cc6","resolution":{"observed_at":"2026-08-15T23:18:56.238620Z","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":"2026-08-15T23:18:56.481270Z","title":"Palmieri, Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case, Math","venue":null,"work_id":"86e55943-5d33-4f2a-8347-28750e56e07c","year":2021},"citing_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},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.242863Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:311002b85be1271d8b10bba6df59bada507bc4418fa32ea2619457b23806fe6b","observation_id":"e69e6466-cbb5-44d0-b445-31c4c005ee9f","resolution":{"observed_at":"2026-08-15T23:18:56.487005Z","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":"2105.09879","last_updated":"2024-03-19T12:05:21Z","snapshot_observed_at":"2026-08-16T18:23:19.661261Z","submitted_at":"2021-05-20T16:25:47Z","title":"On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.09879","snapshot_observed_at":"2026-08-15T23:18:56.246965Z","title":"Palmieri, On the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity","venue":null,"work_id":null,"year":2024},"citing_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},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.246965Z"},"links":{"cited_paper":"/paper/2105.09879","citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:25d8f04d50dc6e89a5968554272f3da46c3994368caa373f01106e01e939dca3","observation_id":"9209d887-6897-45f0-b5e7-932ba9c0ed74","resolution":{"observed_at":"2026-08-15T23:18:56.246965Z","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":"2026-08-15T23:18:56.465996Z","title":"Sideris, Nonexistence of global solutions to semilinear wave equations in high dimensions, J","venue":null,"work_id":"7636e3df-ffd6-429a-aa63-1d01689313dc","year":1984},"citing_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},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.251511Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:11eff1b8c136db107f6c45fcdea77743d23f34b43dfb9d059dd09849803a53a8","observation_id":"e29cfab1-e65e-4c21-9c73-2b45a91bc18c","resolution":{"observed_at":"2026-08-15T23:18:56.471121Z","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":"2026-08-15T23:18:56.451172Z","title":"Strauss, Nonlinear scattering theory at low energy, J","venue":null,"work_id":"eb53077a-6b90-482e-85c0-7e10868b9a02","year":1981},"citing_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},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.255849Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:cdf313b4dc1de342b7cc63708d413d0c24971dffc7fe240cb4d6b381e300a4bf","observation_id":"81c03c30-c93b-4ad3-88a7-99f409d38b21","resolution":{"observed_at":"2026-08-15T23:18:56.456086Z","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":"2026-08-15T23:18:56.436204Z","title":"Wakasa, The lifespan of solutions to semilinear damped wave equations in one space dimension, Commun","venue":null,"work_id":"ccab0908-78d8-4316-b59f-5ec017b02b90","year":2016},"citing_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},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.259840Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:647172c0380ffc1c7333ab045088ab3bdbeab45e395fd99814eeb1b2bba02750","observation_id":"7d148782-fab5-4e50-b539-d1ae51c91db7","resolution":{"observed_at":"2026-08-15T23:18:56.440618Z","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":"2026-08-15T23:18:56.422289Z","title":"Wakasugi, Critical exponent for the semilinear wave equation with scale invariant damping, in: Fourier Analysis, Birkh¨auser, Cham, 2014, pp","venue":null,"work_id":"3adee59d-a36a-4fdd-9be2-b0c4f79dd764","year":2014},"citing_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},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.263850Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:51c7d157bfec24e66d626d4be21c4fa1c5deac0b4fcf19bd3ac03dc923fde194","observation_id":"a6dbc3a8-fe8c-48ef-a13d-c48779d6c0b0","resolution":{"observed_at":"2026-08-15T23:18:56.426753Z","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":"2026-08-15T23:18:56.407569Z","title":"Wirth,Solution representations for a wave equation with weak dissipation, Math","venue":null,"work_id":"cda2b25f-4e16-4541-a6cc-40174b05d03a","year":2004},"citing_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},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.267995Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:fd22ea1958eb5b5c84d37530f03b55754067ad6fdcbf276f76b7f2422ba9e8ac","observation_id":"9d4c4f25-f674-45fd-a8ae-62d338e383fd","resolution":{"observed_at":"2026-08-15T23:18:56.412645Z","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":"2026-08-15T23:18:56.393274Z","title":"Yordanov, Q","venue":null,"work_id":"235e3aae-ce1b-4ee9-a0c9-6e17725dd816","year":2006},"citing_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},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.272677Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:29244b25b31d6bb3fbda312d2725720c3374b8b20611994a7e77e7c472516124","observation_id":"0dfbe52b-c7af-4a37-9e57-54d53b7a5e9a","resolution":{"observed_at":"2026-08-15T23:18:56.397710Z","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":"2026-08-15T23:18:56.377015Z","title":"Zhou, Blow up of solutions to semilinear wave equations with critical exponent in high dimensions, Chinese Ann","venue":null,"work_id":"65db63bb-cc0d-4f06-836e-e6f8ec7ec783","year":2007},"citing_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},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T23:18:56.276676Z"},"links":{"citing_paper":"/paper/2505.05268"},"observation_digest":"sha256:84da535f1d53c1dc6219eece714106e0dbff3ed170c83885a0a887d6a82e81ee","observation_id":"6d5f641b-0da6-4b25-8d17-ebca52872507","resolution":{"observed_at":"2026-08-15T23:18:56.383613Z","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":"2505.05268","last_updated":"2025-06-25T09:15:35Z","latest_version":2,"primary_category":"math.AP","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"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":0,"verified_fuzzy":18},"total_outbound_references":38},"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 38 of 38 outbound references and 2 inbound Pith citation observations for arXiv:2505.05268."}