{"as_of":"2026-08-15T06:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:feb2290c941ada3101526535c530aed2aaafcdbccb6a2c810da04832160f806c","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T04:59:49.896389Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/1909.02350/citation-record","integrity":"/paper/1909.02350/integrity","json":"/paper/1909.02350/citation-record.json","paper":"/paper/1909.02350"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T04:59:50.568901Z","title":"Ashbaugh, R","venue":null,"work_id":"7516d212-9093-4eb3-9277-a341783e203b","year":1995},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.695760Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:da3dc6e3d177e10fa0001b69f00ea14ff57e9f806037981c81668f3fea148229","observation_id":"667160b8-777c-4dfa-b9c9-bca85ffb4597","resolution":{"observed_at":"2026-08-14T04:59:50.573383Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.555033Z","title":"Ashbaugh, R.S","venue":null,"work_id":"5e7b6664-dd73-445c-b423-435a2495e461","year":1996},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.701742Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:07637c5a05cd92b992ce3c5314259681b32aae702c960554c92a57d75156fad5","observation_id":"6ce9e30c-78f0-41a8-9c4d-a5ad7e9f8b9a","resolution":{"observed_at":"2026-08-14T04:59:50.559495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.540877Z","title":"Bauer, E","venue":null,"work_id":"d4b1cf19-1da0-46a5-aa8c-493d2a1734a2","year":1972},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.706571Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:250fe64cae77d8f4f88a78b1e108fb3413f4b3395717cbe813c27c51e22c3fb8","observation_id":"0b2ad4af-f4f8-4b97-8928-a0745c9a0d4d","resolution":{"observed_at":"2026-08-14T04:59:50.545604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.525926Z","title":"Bishop, R.J","venue":null,"work_id":"4ee8886d-bd96-4b6d-a6ba-447fe69c0d3e","year":1964},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.711203Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:242bbdc9f94b26c49cf22771e3d40b67929dcbb55bc086fe17ba8750fcce6ce4","observation_id":"5b409fba-4d30-4863-8de6-019b5e377193","resolution":{"observed_at":"2026-08-14T04:59:50.531236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.511561Z","title":"Bol, Isoperimetrische Ungleichungen f¨ ur Bereiche auf Fl¨ achen.Jber","venue":null,"work_id":"bf1d42ce-db44-4f3d-831e-5c6011868010","year":1941},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.715719Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:41c7817c72f5045340e1ac0152d2bee7746398b6e53a5d9e29b5464a5f05ac16","observation_id":"9c0a7231-4e2f-4b18-b758-c30a4ee28fe6","resolution":{"observed_at":"2026-08-14T04:59:50.516365Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1811.06423","last_updated":"2018-11-15T15:17:45Z","snapshot_observed_at":"2026-08-14T17:58:42.358587Z","submitted_at":"2018-11-15T15:17:45Z","title":"On Clamped Plates with Log-Convex Density","version":1},"cited_work":{"arxiv_id":"1811.06423","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.06423","snapshot_observed_at":"2026-08-14T04:59:49.997779Z","title":"On Clamped Plates with Log-Convex Density","venue":"math.SP","work_id":"de78c45e-b86e-4619-b8dd-f807ed062bf4","year":2018},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.720385Z"},"links":{"cited_paper":"/paper/1811.06423","citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:b14e1687ddff48e67e830588ff7d6d5f12def03f5ead7e6f05d079d5443d8a44","observation_id":"37a33e43-77e7-4a59-b0f3-a9aef759c4c9","resolution":{"observed_at":"2026-08-14T04:59:50.003520Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.497529Z","title":"Chasman, J.J","venue":null,"work_id":"add46c0d-a26b-4150-80f0-17548df27f4d","year":2016},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.726341Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:227b5a8e275396fc8435ed24355a3d97a58f34b693f2d46b6456eb51a728b8ac","observation_id":"612e6eb8-a763-44ae-a661-f5b728f69e5d","resolution":{"observed_at":"2026-08-14T04:59:50.501981Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.483608Z","title":"Chavel, Eigenvalues in Riemannian geometry","venue":null,"work_id":"4569783a-bcea-4912-9399-f33fa25aa3de","year":1984},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.730885Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:8768609f771c10ffddc14d7dfdaee694fe76734fb7a41f3ed80e673d45e0dfa2","observation_id":"e236da4d-9edd-4209-bf54-613aaf70ae5d","resolution":{"observed_at":"2026-08-14T04:59:50.488144Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.469741Z","title":null,"venue":null,"work_id":"447fa7c0-ce3e-43cd-b340-2366345a56e6","year":2012},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.735601Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:3e6e2a2338a9aec2a681cddfc1bbc844a2b0765a7dbc94cdc34cadc5906e45b9","observation_id":"abe9ace5-6896-4249-aaeb-a71da14331fc","resolution":{"observed_at":"2026-08-14T04:59:50.474055Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.455989Z","title":"Cheng, T","venue":null,"work_id":"3c6e0525-850d-41a3-abd7-80c4e331eba8","year":2010},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.740375Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:d4828b4addd9bf761a261c658b11f959665e5b5878fde1e82baacb7f5316c5e8","observation_id":"bb6c7f21-466f-4768-8046-b9e43df0b736","resolution":{"observed_at":"2026-08-14T04:59:50.460553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.442561Z","title":"Cheng, H","venue":null,"work_id":"027d7bb5-1ea6-4861-a76e-5f881483923b","year":2011},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.744930Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:812f62a022d1104a5548d16d2d596855837f4fae5c6c77b71561d6bfc272fc85","observation_id":"9ebb342d-80a3-44ee-9077-b97873e5770c","resolution":{"observed_at":"2026-08-14T04:59:50.446917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.428462Z","title":"Cheng, H","venue":null,"work_id":"174fee8a-0d0c-4246-af65-343d720e73a5","year":2009},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.749359Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:ada580b95955928bdfad04fa907745875e8b1a7f8e5fe46b48d42e1b5e0785fc","observation_id":"a5ff33a0-aebe-4a46-ba91-e345d8f18a17","resolution":{"observed_at":"2026-08-14T04:59:50.433266Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.414337Z","title":"Cheng, H","venue":null,"work_id":"86505bbe-8d67-428c-8a86-e1327d77dae8","year":2006},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.753848Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:82b03a6ce56bcefc136d5f399324ea36c7ffb46ce50d93ef4ca7ea590f3056a9","observation_id":"cbe58a52-bc57-4788-b24d-8ec1c408643d","resolution":{"observed_at":"2026-08-14T04:59:50.418957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.400444Z","title":"Croke, A sharp four-dimensional isoperimetric inequality","venue":null,"work_id":"e5a5ce83-889f-437e-9952-daccf271c938","year":1984},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.758440Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:c536f88c13dec75736254f3c496412d7b03c8246afccdd5197de78eaf4cdb626","observation_id":"35e45b21-fab9-4ae3-b202-9836ecc2b835","resolution":{"observed_at":"2026-08-14T04:59:50.404991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.386079Z","title":"Coffman, On the structure of solutions to ∆ 2u =λu which satisfy the clamped plate conditions on a right angle","venue":null,"work_id":"20f7e46e-5e88-47ba-82c2-578d62368536","year":1982},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.762795Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:c584b5e83b6917d79b998af90722a1bbe0aa392e2ef26fb2151cc4781830bfb3","observation_id":"95965e84-4591-4a38-9f4a-18915f626595","resolution":{"observed_at":"2026-08-14T04:59:50.390934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.371831Z","title":"Coffman, R.J","venue":null,"work_id":"2d994b6e-791e-43c5-9ca5-ece18ebefc2a","year":1978},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.767301Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:6ab3a96797e24b79718ed77184277315d5c62d37063e98dd67334d41a88cadaf","observation_id":"134c767b-44ac-4e6b-954f-ed58603dab80","resolution":{"observed_at":"2026-08-14T04:59:50.376418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.357721Z","title":"Cuyt, V.B","venue":null,"work_id":"598ce4bb-11e4-4b3d-b863-28d4cd0508b1","year":2008},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.771823Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:1795a4f81930da0f2ba4b4d49129a23bf9f21304cca05e1f0a1b4e0b53760bae","observation_id":"0dc44351-42ec-4bd1-9a19-a7c43b9338f2","resolution":{"observed_at":"2026-08-14T04:59:50.362399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.342923Z","title":"Dinghas, Einfacher Beweis der isoperimetrischen Eigenschaft der Kugel in Riemannschen R¨ aumen kon- stanter Kr¨ ummung.Math","venue":null,"work_id":"c571208d-6669-4050-9e96-649c79f1c965","year":1949},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.776683Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:b4d6db03a348491c2a21f4238ca908fb937c19be190e139e792bd0b9aacc8a1b","observation_id":"d93548c7-67f8-4556-8d00-56e60cd14e84","resolution":{"observed_at":"2026-08-14T04:59:50.347706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.328589Z","title":"Duffin, Nodal lines of a vibrating plate","venue":null,"work_id":"19eaaa90-14a5-489d-8631-2ab3e67e99e2","year":1953},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.781465Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:652b30dd2e99fd41aab838ae917ac317c488a8037b3ee6b1cdce2f24b2ea56bc","observation_id":"c435c5e6-1df2-4085-9fb1-614a3b6cf031","resolution":{"observed_at":"2026-08-14T04:59:50.333255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.09814","last_updated":"2021-09-23T16:44:29Z","snapshot_observed_at":"2026-08-14T10:58:39.703678Z","submitted_at":"2019-08-26T17:36:07Z","title":"Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds","version":7},"cited_work":{"arxiv_id":"1908.09814","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.09814","snapshot_observed_at":"2026-08-14T04:59:49.976847Z","title":"Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds","venue":"math.DG","work_id":"4d48c516-ab3c-4d5a-833c-f5f3c17d4698","year":2019},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.786136Z"},"links":{"cited_paper":"/paper/1908.09814","citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:362db367615c7ba85f4784c0829e900e426933441dbf6becba522e1c3fdf7c23","observation_id":"2fe06e0b-772a-4c9c-bd1b-b2dbf9e3ad84","resolution":{"observed_at":"2026-08-14T04:59:49.981711Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.313981Z","title":"Grunau, F","venue":null,"work_id":"69528d70-556c-4ee3-bf21-4483b63dd387","year":2010},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.790761Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:6bf60f9eb45a3e4a4483a31d95fdbc7484b4121872510c219a7c264211767349","observation_id":"d2fc4180-24ad-4d89-a758-cb5df9ab2040","resolution":{"observed_at":"2026-08-14T04:59:50.318675Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.299347Z","title":"Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities","venue":null,"work_id":"bf0d6eef-2e61-4494-96bd-99a59db11f90","year":1999},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.795189Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:821713c4b6821650629e65b27983e48c25ffa84efd2c11862a4b5748c1c3d5a6","observation_id":"d89730ab-c86d-4532-bfaf-1b60e6567b78","resolution":{"observed_at":"2026-08-14T04:59:50.304197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.284981Z","title":"Hille, Non-oscillation theorems","venue":null,"work_id":"8ba55979-5271-4ad2-a4fa-0cd01988836e","year":1948},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.799829Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:5f71ca8256cdb63bdd2efbd2a4a8221949cdaf23067cbc4e782bf83cff10854a","observation_id":"32a99577-6c8a-4d10-8115-69940ebb8146","resolution":{"observed_at":"2026-08-14T04:59:50.289818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.269977Z","title":"Karp, private communication & manuscript in preparation","venue":null,"work_id":"88436bb2-743a-45b6-b274-f3e2c746bb17","year":null},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.804418Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:ccf6c6b89ab26fa044d7b0d2c9d29d4ebd60951e1037e73b01b6568b1862a179","observation_id":"1319e0da-5729-405e-a3c1-882749e77f07","resolution":{"observed_at":"2026-08-14T04:59:50.274882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.255406Z","title":"Karp, S.M","venue":null,"work_id":"c8a0481a-2b11-441a-a471-f18d5ff6da60","year":2009},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.809393Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:c0e0e7c6040364c13b8f25fdc5835ad5b2cba82dcbe3fe933e16188761933056","observation_id":"5923f418-9111-4894-933d-fc41a5672624","resolution":{"observed_at":"2026-08-14T04:59:50.259949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.241074Z","title":"Kleiner, An isoperimetric comparison theorem","venue":null,"work_id":"7771eeab-d7eb-4efe-9057-01db3036ea00","year":1992},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.815083Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:4980e9bac6a06884d9f70af198dd0ad86dbb04c1d114dd1dc4d6ef47626625ab","observation_id":"ae754165-7c50-4f1d-8196-95a667f83316","resolution":{"observed_at":"2026-08-14T04:59:50.245691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.226846Z","title":"Klingenberg, Riemannian geometry","venue":null,"work_id":"faaada98-dd58-4725-a5c2-13b231f55f90","year":1995},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.819936Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:a16d2d866fe810334a350d6dcadb65d4a3f920ec878337f07f9e08b10982d136","observation_id":"3ebc469f-2ee7-40f4-9e5b-6ac064d90095","resolution":{"observed_at":"2026-08-14T04:59:50.231224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1303.3115","last_updated":"2017-02-13T13:11:22Z","snapshot_observed_at":"2026-08-15T00:25:23.312006Z","submitted_at":"2013-03-13T09:45:13Z","title":"The Cartan-Hadamard conjecture and The Little Prince","version":3},"cited_work":{"arxiv_id":"1303.3115","doi":null,"metadata_source":"pith","pith_arxiv_id":"1303.3115","snapshot_observed_at":"2026-08-14T04:59:49.956021Z","title":"The Cartan-Hadamard conjecture and The Little Prince","venue":"math.DG","work_id":"ec330de4-42cd-4472-927b-826bca25d0c2","year":2013},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.824793Z"},"links":{"cited_paper":"/paper/1303.3115","citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:68142e524558ee236174e0886fc63e8f148d0651edc4867d2826e0f5e2be1dc8","observation_id":"ec4ff047-ad8d-4b09-a470-8a156b23d9e0","resolution":{"observed_at":"2026-08-14T04:59:49.961197Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.06487","last_updated":"2018-10-15T15:55:03Z","snapshot_observed_at":"2026-08-14T18:14:29.143524Z","submitted_at":"2018-10-15T15:55:03Z","title":"New features of the first eigenvalue on negatively curved spaces","version":1},"cited_work":{"arxiv_id":"1810.06487","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.06487","snapshot_observed_at":"2026-08-14T04:59:49.932286Z","title":"New features of the first eigenvalue on negatively curved spaces","venue":"math.AP","work_id":"6d4bd06b-ed97-443e-a6c8-a38d0299fb4d","year":2018},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.829717Z"},"links":{"cited_paper":"/paper/1810.06487","citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:e5f66776def51e3c68bb37374c4e0b81f062f44fae222c42cd40e34b5f5f7243","observation_id":"9299c6cc-dda4-416f-b80c-46dc331aab40","resolution":{"observed_at":"2026-08-14T04:59:49.939244Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.211705Z","title":"McKean, An upper bound to the spectrum of ∆ on a manifold of negative curvature","venue":null,"work_id":"a7b9c726-0e45-483b-a1bb-f379bf2401bc","year":1970},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.834745Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:728c1a81f0ba92f4f2b055b5a36f9e63a028722e8657c2f633f5daa38826ea03","observation_id":"197f6802-a37f-427c-b3a6-c09c245839e7","resolution":{"observed_at":"2026-08-14T04:59:50.217500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.197225Z","title":"Nadirashvili, New isoperimetric inequalities in mathematical physics","venue":null,"work_id":"f76e9f8f-fbb8-4fb7-8da4-61f7036233ae","year":1992},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.839758Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:8a18296427cc9a346fbbee0baccd71016eea24e1a1fe3d37e576260339994544","observation_id":"9c4c5487-eb52-4d89-90a5-f04438c58115","resolution":{"observed_at":"2026-08-14T04:59:50.202192Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.181993Z","title":"Nadirashvili, Rayleigh’s conjecture on the principal frequency of the clamped plate","venue":null,"work_id":"945d859d-0acf-4197-a18b-c203f001ac81","year":1995},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.844328Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:45d4c886024b3f5958fb1615431963826e9b1a8aceefe58028eb81bd29d65162","observation_id":"de766803-3e62-48ed-8e9f-946905888d9a","resolution":{"observed_at":"2026-08-14T04:59:50.187449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.167174Z","title":"Olver, D.W","venue":null,"work_id":"6a403662-7953-416f-9e62-38b67ba4febb","year":2010},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.849404Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:1501e7e9e8bd2f6c38b16c0538fd7e87038523f3576f008f95b5b7f4f2c0dca8","observation_id":"b1e2f8ec-d3ba-4102-ada8-3308990a52b5","resolution":{"observed_at":"2026-08-14T04:59:50.172336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.151941Z","title":"Palais, The principle of symmetric criticality","venue":null,"work_id":"9b8bd6c1-17d8-4a0c-a81d-56248e6044e9","year":1979},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.854324Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:494d9f56fd5ffbc3d70ac52373f36bce2fa2e3547a1f9af2b1595e46ea07c963","observation_id":"c7e419c0-0228-4023-a484-0c0aa2e82d61","resolution":{"observed_at":"2026-08-14T04:59:50.156628Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.137771Z","title":"Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics Vol","venue":null,"work_id":"74ff0c1c-97ef-4bb5-ac3d-dbd323799b60","year":1986},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.858921Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:e6251e3042591b825c50e825d76faa40128004c50207cd5f37feb62fdf5b57bf","observation_id":"fdbcd6c6-20ab-4109-a5a4-ff51f8f17b17","resolution":{"observed_at":"2026-08-14T04:59:50.142479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.123247Z","title":"Rayleigh, The Theory of Sound","venue":null,"work_id":"06408f79-061d-49e1-b6f1-fd2c2928785a","year":null},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.863526Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:c727f0de478ce8307b919cf6d52228c53dab8d0c57814c0859e74b765307f874","observation_id":"5aee9c7a-9d93-459b-88fb-1b60bc9444aa","resolution":{"observed_at":"2026-08-14T04:59:50.127894Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.092859Z","title":"Robin, Fonctions sph´ eriques de Legendre et fonctions sph´ ero¨ ıdales","venue":null,"work_id":"06b572ee-e596-46b1-b631-17d1c09a669e","year":1959},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.873507Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:f1909615b87747a32b2ac9b729998cde24b1626eb5cdef2766befbe30affc14d","observation_id":"341c9dc8-f33a-410a-95b3-2c4d9b075968","resolution":{"observed_at":"2026-08-14T04:59:50.098233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.077829Z","title":"Szeg˝ o, On membranes and plates.Proc","venue":null,"work_id":"60257f28-c7f9-4b94-8726-46f9e5ab06c8","year":1950},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.877882Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:cb1152012e5371a013488b20ec5cb51f29edad3a619ca9a0bbdf53644a876b81","observation_id":"03caf147-3bfc-4017-a655-b6e9dc146c9a","resolution":{"observed_at":"2026-08-14T04:59:50.082696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.062928Z","title":"Sugie, K","venue":null,"work_id":"efbe915d-b80f-4f05-b713-05d792d61bf1","year":2002},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.882474Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:2dca93867d8442d38a86d938dd267d466083b217cac764c972429d1880d44986","observation_id":"40124701-fc31-40e3-925f-2811916d6216","resolution":{"observed_at":"2026-08-14T04:59:50.067657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.047515Z","title":"Talenti, On the first eigenvalue of the clamped plate","venue":null,"work_id":"35c2127c-44b5-4504-b4cb-8fdf5b5cc0f0","year":1981},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.886957Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:f583336a4757d50f2e983418fd7ca3a5ae0756126e377402523d4f99c5e2ab77","observation_id":"fa6363d4-1fa7-4a47-934f-cc7403793d1f","resolution":{"observed_at":"2026-08-14T04:59:50.052326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.030952Z","title":"Zhurina, L","venue":null,"work_id":"61f1b478-a366-4ba1-b85e-f71c7a254a8e","year":1966},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.891849Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:3374fbfea0582c051a083434c89b66f1bc210748778fc779e399bd5cf66450a5","observation_id":"babf5d0b-0bf7-4d73-b24a-9b7a72ea04ba","resolution":{"observed_at":"2026-08-14T04:59:50.036334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.014876Z","title":null,"venue":null,"work_id":"752ea076-f4e6-41e4-ac9a-50b17571f1d6","year":2007},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.896389Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:ffde618cfb9b3ac30d142eb86a3532815205646289241445a07a3134f1286f14","observation_id":"9761788f-844e-4648-8a88-3a4add6eafac","resolution":{"observed_at":"2026-08-14T04:59:50.020293Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-14T04:59:50.108328Z","title":null,"venue":null,"work_id":"df7212de-5373-4640-b9a7-50173af92f1e","year":null},"citing_paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces","version":2},"reference_index":1926,"source":"pdf_text","source_observed_at":"2026-08-14T04:59:49.868196Z"},"links":{"citing_paper":"/paper/1909.02350"},"observation_digest":"sha256:2b524aa9124605bdd30efbb1590195248646320883041849924dc5dd18d5190a","observation_id":"7a87b559-fd16-4a3b-8010-fb9573d1dcb6","resolution":{"observed_at":"2026-08-14T04:59:50.113050Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1909.02350","last_updated":"2020-03-14T14:16:01Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T02:40:31.943046Z","submitted_at":"2019-09-05T12:09:32Z","title":"Fundamental tones of clamped plates in nonpositively curved spaces"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":4,"verified_fuzzy":36},"total_outbound_references":43},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1909.02350."}