{"as_of":"2026-08-16T07:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6aec0f0f978260063e1850a61f91e30f1634b269e85874f100000f7188318b0f","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:37:10.145987Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.02989/citation-record","integrity":"/paper/1908.02989/integrity","json":"/paper/1908.02989/citation-record.json","paper":"/paper/1908.02989"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:37:10.575084Z","title":null,"venue":null,"work_id":"725b05b1-1705-402d-84b8-ae14840fe006","year":2005},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.058654Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:21c32c9de32465c1ca107b6d4ac349e03ac07a98652c6f76880494fe8e573119","observation_id":"5f22d62c-68b8-45d6-a71c-a3f140cb4717","resolution":{"observed_at":"2026-08-14T14:37:10.579249Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.562013Z","title":null,"venue":null,"work_id":"c544b6ab-ce48-41f0-99ae-f6cf9f590e7d","year":2009},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.063777Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:9e76b22c72c8f15e23b014e3b56acfc434135edb33a201267f68340bbd102b75","observation_id":"5cc6b78a-d40e-4d09-acb5-b00a79993ddf","resolution":{"observed_at":"2026-08-14T14:37:10.566342Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.548807Z","title":null,"venue":null,"work_id":"9a161647-4afb-4210-9e66-fc8328e860a4","year":1999},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.068100Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:39d7a0659636e004b4a91aadf6217f6a78c262bf01449f362aedd5c648b9a3a0","observation_id":"d90419d0-f9b4-4c24-98b0-a75778c13b5b","resolution":{"observed_at":"2026-08-14T14:37:10.552969Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.535496Z","title":null,"venue":null,"work_id":"b688875f-5cb5-40ae-8116-acc68130e7e1","year":1956},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.072510Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:9c82cb5d944ca08e6ed35fc3f67fddda46818f6f6bcee52dc2a9ae1dab7e94d8","observation_id":"7bd01792-041a-428d-9db2-3ca27b7b04db","resolution":{"observed_at":"2026-08-14T14:37:10.539701Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.522701Z","title":"Theory Adv","venue":null,"work_id":"b7360590-c3c5-4a3b-a301-3654b2cb00e9","year":2013},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.077296Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:5601440f6e6daef41e27c26a00ab20e48977793b027720481567e214440e41a0","observation_id":"bcfae663-5dea-4654-a357-8b06d7726d3d","resolution":{"observed_at":"2026-08-14T14:37:10.526975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00033-019-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:37:10.174662Z","title":null,"venue":null,"work_id":"cb019595-5863-4312-b2d7-1d7fecd2ae06","year":2019},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.081777Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:fb853bd57c41f94a8ee79bceae71c61001b05270fcc3747f6afa76939d0f5372","observation_id":"3ffc9da7-77fd-455e-8b60-8ab53d49e5c4","resolution":{"observed_at":"2026-08-14T14:37:10.180308Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.509554Z","title":null,"venue":null,"work_id":"574ffa86-3b3a-4a0e-9b75-26cfa57e870a","year":2015},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.086691Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:b4fdbc06ef04f8fa09316dfed3ab87eede9eb38867c9ceb08bd6d069a0f0f51d","observation_id":"b4eadd6f-ada5-4867-a595-6acb99c31c40","resolution":{"observed_at":"2026-08-14T14:37:10.513697Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.496193Z","title":"B, 34 (2013), 345-380","venue":null,"work_id":"f43a76c9-5291-42fc-8df9-1c7408a8de67","year":2013},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.090858Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:ff0779f0695c2cd26c64d34aefd065dc068616460ecbd53133c31737d2a708a3","observation_id":"424e797d-7952-4f6b-858f-23ccea013e04","resolution":{"observed_at":"2026-08-14T14:37:10.500512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.481715Z","title":"Qualitative pr operties of solutions, phase space analysis, semilinear models, Birkh¨ auser, Basel, 2018","venue":null,"work_id":"e7937b7b-7df2-41d8-b2be-9977c9936bac","year":2018},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.094837Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:0b4bc6fb69b734f01d1f7ecb3ba2f5752805152120705c6b277944ee8be3ebe4","observation_id":"59e7188c-3e03-4f4e-8324-a305715de1ce","resolution":{"observed_at":"2026-08-14T14:37:10.486837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1905.05696","last_updated":"2019-05-14T16:18:53Z","snapshot_observed_at":"2026-08-14T16:32:25.983527Z","submitted_at":"2019-05-14T16:18:53Z","title":"Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg group","version":1},"cited_work":{"arxiv_id":"1905.05696","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.05696","snapshot_observed_at":"2026-08-14T14:37:10.235860Z","title":"Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg group","venue":"math.AP","work_id":"6d4ebe42-475c-4a61-8548-6771c7eddc51","year":2019},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.099236Z"},"links":{"cited_paper":"/paper/1905.05696","citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:41e88476de1d451bf61f3353afeb17b4ae9696beef2b2f2cba8de75f030ed502","observation_id":"206a29b5-0ce5-47a7-aa36-8c2a26b86f8e","resolution":{"observed_at":"2026-08-14T14:37:10.347950Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.468865Z","title":null,"venue":null,"work_id":"ea5d657e-2115-45fc-8ad4-7fa7bdf1a253","year":null},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.103862Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:fa8dbf27ecd57cf0e933e079ce0d7f084e6956adf608a9440dff6bcafad034cc","observation_id":"c066e18d-7cb2-4029-ac4c-308e04de4f71","resolution":{"observed_at":"2026-08-14T14:37:10.473082Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.455431Z","title":"61(7) (2005), 1189-1208","venue":null,"work_id":"31130600-0ade-4087-92b1-1ba476764d4e","year":2005},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.108128Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:554192b5b876639eca89bb7cc867263415e4017b95c124bbe19922983159fe44","observation_id":"660e4edd-4629-418a-bb53-b0ac699fcaf1","resolution":{"observed_at":"2026-08-14T14:37:10.459827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.442122Z","title":null,"venue":null,"work_id":"9e1b8e11-b9bd-460b-9e92-1676a9397547","year":1976},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.112392Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:a41fd991ca5db4fb206a711dffa3ff42ab4827a19dc47ca4d5b1f0f59b31762f","observation_id":"c991c4cd-e824-4168-b177-8ef42041c8d9","resolution":{"observed_at":"2026-08-14T14:37:10.446237Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.428733Z","title":"Steklov Inst","venue":null,"work_id":"d578c257-f336-4c5a-8fda-117c6b75f7f0","year":2001},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.116492Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:6fd25c73e8eb91d7a5ba3af62fd992da4a68402b45a32767a41bf51ccddfdb4b","observation_id":"68a86896-cd42-4fb8-9bdf-a25a68b487ce","resolution":{"observed_at":"2026-08-14T14:37:10.433047Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.414826Z","title":null,"venue":null,"work_id":"acea10dc-7c15-48bd-a65b-55fdf005faee","year":2017},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.120603Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:2efc85a51301357954dd8fad5ba6fa0a42c073d22c7f430537407e8ec4e77b55","observation_id":"832f26bc-389d-4ade-b0c0-8c49d32a23fe","resolution":{"observed_at":"2026-08-14T14:37:10.419102Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.400987Z","title":null,"venue":null,"work_id":"4b742b22-9d14-4caa-8096-50fa64eaf124","year":2018},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.124689Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:c509734ffc9f944801372da8920c5d9ef39537cc16f859b1f199e2c3fbb6f7f4","observation_id":"4adbfb1f-c8e9-49ac-907a-794ba2978af7","resolution":{"observed_at":"2026-08-14T14:37:10.405384Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02657","last_updated":"2019-08-07T14:28:58Z","snapshot_observed_at":"2026-08-14T14:36:11.074009Z","submitted_at":"2019-08-07T14:28:58Z","title":"Decay estimates for the linear damped wave equation on the Heisenberg group","version":1},"cited_work":{"arxiv_id":"1908.02657","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.02657","snapshot_observed_at":"2026-08-14T14:37:10.216398Z","title":"Decay estimates for the linear damped wave equation on the Heisenberg group","venue":"math.AP","work_id":"d31b9905-5d15-4728-954a-197a6a9ddfa2","year":2019},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.128752Z"},"links":{"cited_paper":"/paper/1908.02657","citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:ce45d1a4266a5f1c53f92588d5b4cbcce7cf0e9c44dc8c8e602c3d2b9916e787","observation_id":"badfdb08-2ea0-4900-b228-282a5f20fa94","resolution":{"observed_at":"2026-08-14T14:37:10.220942Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.387500Z","title":"Partial Differential Equations , 19(3/4) (1994), 655-676","venue":null,"work_id":"a90fec88-134c-4e13-8160-917705927a53","year":1994},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.132979Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:05153d6c4dd24d898acc05fd7d8c2623f89327d8d53f5c370b92caa81854d5ce","observation_id":"1e10e701-5639-45e1-80a3-4b73ee7b8cf9","resolution":{"observed_at":"2026-08-14T14:37:10.391855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.372466Z","title":"Differential Equations 265 (2018), 5212-5236","venue":null,"work_id":"39c29d7f-8919-4aad-b938-b920fa724aba","year":2018},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.137129Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:4ce191ac4c12a3cb0da007592c08b6664b12f504df8442a076846ccfc38ab44a","observation_id":"9cc9f5cf-ca8c-49f0-afa7-8b6613cf0930","resolution":{"observed_at":"2026-08-14T14:37:10.377510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.01933","last_updated":"2021-11-15T15:25:46Z","snapshot_observed_at":"2026-08-14T22:45:55.786757Z","submitted_at":"2018-12-05T11:57:35Z","title":"Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups","version":3},"cited_work":{"arxiv_id":"1812.01933","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.01933","snapshot_observed_at":"2026-08-14T14:37:10.195813Z","title":"Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups","venue":"math.AP","work_id":"444ee056-53f5-4fac-94fa-0546fc5c5283","year":2018},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.141193Z"},"links":{"cited_paper":"/paper/1812.01933","citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:9e8f9692d3ffc60540cabcb8c5657e1f505cd3adfc65eb92c04e3a13ec788939","observation_id":"181a76a6-057a-41b7-b37a-9a36763b44af","resolution":{"observed_at":"2026-08-14T14:37:10.201824Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:37:10.358133Z","title":"Differential Equations 174(2) (2001), 464-489","venue":null,"work_id":"fd3da453-aec2-4dae-a93e-07342d92dfc7","year":2001},"citing_paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:37:10.145987Z"},"links":{"citing_paper":"/paper/1908.02989"},"observation_digest":"sha256:6fb8af7aadf41751c10780d75b0571abc196df242df221ce88736b61fbebc44d","observation_id":"432f8c74-5a62-41d3-aa7e-2f606e1094f9","resolution":{"observed_at":"2026-08-14T14:37:10.362838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.02989","last_updated":"2019-08-08T09:47:43Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-16T03:37:53.514262Z","submitted_at":"2019-08-08T09:47:43Z","title":"Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":4,"verified_fuzzy":8},"total_outbound_references":21},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:1908.02989."}