{"as_of":"2026-08-15T08:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a4a43161320d562c3862edcb65e7dc835cac56e747061539fef7b414f7f2a6a0","coverage":[{"denominator":17,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":17,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T04:58:54.625248Z","state":"measured"},{"denominator":18,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":18,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T05:02:54.285412Z","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":"2026-08-14T05:02:54.373097Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"cited_work":{"arxiv_id":"1909.02388","doi":null,"metadata_source":"pith","pith_arxiv_id":"1909.02388","snapshot_observed_at":"2026-08-14T05:02:54.373097Z","title":"Concentration of Small Hawking Type Surfaces","venue":"math.DG","work_id":"8e2efacc-2ba4-4497-a507-e2f181bf8b75","year":2019},"citing_paper":{"arxiv_id":"1909.02381","last_updated":"2019-09-06T09:25:46Z","snapshot_observed_at":"2026-08-14T04:49:14.329930Z","submitted_at":"2019-09-05T13:12:57Z","title":"Minimizers of Generalized Willmore Functionals","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T05:02:54.285412Z"},"links":{"cited_paper":"/paper/1909.02388","citing_paper":"/paper/1909.02381"},"observation_digest":"sha256:1b4b9adc277e0e6d2dd0c4fd895f737ce917a4487a37bb471bd328baa6bdede4","observation_id":"1db7e3cd-4106-4431-a706-1d4756054088","resolution":{"observed_at":"2026-08-14T05:02:54.379372Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/1909.02388/citation-record","integrity":"/paper/1909.02388/integrity","json":"/paper/1909.02388/citation-record.json","paper":"/paper/1909.02388"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T04:58:54.856175Z","title":"Bubble tree of a class of confo rmal mappings and applications to Willmore functional","venue":null,"work_id":"b8279447-af78-42dd-b44e-e797c5f29e12","year":2014},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.563960Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:7b74021cfec1fe3c9c6bdb706384a403265a048cc5952b5d34b5c5ffecee063e","observation_id":"f27ae533-9728-433d-9e12-f801421a036e","resolution":{"observed_at":"2026-08-14T04:58:54.859921Z","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":"2026-08-14T04:58:54.844725Z","title":"Optimal rigidity es timates for nearly umbilical surfaces","venue":null,"work_id":"a943007d-1a4d-4540-ad0f-2ee8471efc0a","year":2005},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.568384Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:133be9a115bb42c0d5155056b272c3bfb422ca6f44df505e5b8e8e78480423c3","observation_id":"194a8867-98ac-45bb-b509-2d7f943f5ecf","resolution":{"observed_at":"2026-08-14T04:58:54.848553Z","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":"2026-08-14T04:58:54.833031Z","title":"A C 0 estimate for nearly umbilical surfaces","venue":null,"work_id":"f1b03867-d740-461c-906e-4b2e4f4ab440","year":2006},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.572353Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:ff926b6f5d4113d9ecf41e6788ec0a3014b6f90a9c81babe4d7686168802db95","observation_id":"23c1d804-3894-4a81-81a4-ef4b877c3d69","resolution":{"observed_at":"2026-08-14T04:58:54.836775Z","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":"2026-08-14T04:58:54.821274Z","title":"Normally Hyperbolic Invariant Manifolds - The Noncompact C ase","venue":null,"work_id":"722d3ab2-ce32-43a4-8e9e-c6532fb80897","year":2013},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.577088Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:45d597755b917a1b2da9e1d21856c7eaa3ed5fbebc1872d384fe913e4b7db810","observation_id":"e9c382d9-95fa-4fd8-bef7-6540bfe28601","resolution":{"observed_at":"2026-08-14T04:58:54.825442Z","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":"1909.02381","last_updated":"2019-09-06T09:25:46Z","snapshot_observed_at":"2026-08-14T04:49:14.329930Z","submitted_at":"2019-09-05T13:12:57Z","title":"Minimizers of Generalized Willmore Functionals","version":2},"cited_work":{"arxiv_id":"1909.02381","doi":null,"metadata_source":"pith","pith_arxiv_id":"1909.02381","snapshot_observed_at":"2026-08-14T04:58:54.705558Z","title":"Minimizers of Generalized Willmore Functionals","venue":"math.DG","work_id":"52d3d93d-364e-4eab-a65e-8bbdbce3e402","year":2019},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.580924Z"},"links":{"cited_paper":"/paper/1909.02381","citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:e35f7994490ca9e47d67e768a80c7ba552eb0dcd35fbb7df0e547cabe816033c","observation_id":"99f9362d-aff4-48af-b741-ff0d53d522e6","resolution":{"observed_at":"2026-08-14T04:58:54.709418Z","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":"2026-08-14T04:58:54.809895Z","title":"Horowitz and B.G","venue":null,"work_id":"32d01d81-d181-4ed3-bec5-2923d4b8e4d6","year":1982},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.584731Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:f7b539a2a809fb90c361c35e03adf3289f11f4306b50dc80f3281033b6aba305","observation_id":"6bd3a261-28b8-419e-b513-d03345424d41","resolution":{"observed_at":"2026-08-14T04:58:54.813825Z","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":"2026-08-14T04:58:54.798717Z","title":"Geometric evolut ion equations for hypersurfaces","venue":null,"work_id":"cafae518-c6c7-4e08-9e89-57c0edfb5242","year":1999},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.588566Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:877cd3484b3e12b9c8c8a7b11bf28712f42387d8e1df4800eb498fd9810722ec","observation_id":"62fa2b37-c526-4e74-93d7-3141a292d590","resolution":{"observed_at":"2026-08-14T04:58:54.802597Z","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":"2026-08-14T04:58:54.786784Z","title":"W 2, 2-conformal immersions of closed Riemann surfaces into Rn","venue":null,"work_id":"3d62248e-e293-4588-8467-368090eeeb92","year":2012},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.592082Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:7b386b6093d68f6ed191417bbec9872a2c4f0a9bc94c00ffdfd224da5df0c409","observation_id":"3150f090-dd46-4c4f-99b5-a96f4eba77d1","resolution":{"observed_at":"2026-08-14T04:58:54.791301Z","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":"2026-08-14T04:58:54.775788Z","title":"Removability of point singul arities of Willmore surfaces","venue":null,"work_id":"17d60635-7be3-4acd-93af-d28a7cb0739f","year":2004},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.596013Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:f32fd58312f92fc50fd065d3a50c7c9ebd95115fb5e331c7a1fe781770cd3d29","observation_id":"84db8a12-d032-4c45-96b3-89d2b90ece20","resolution":{"observed_at":"2026-08-14T04:58:54.779475Z","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":"0909.0590","last_updated":"2009-09-24T09:15:40Z","snapshot_observed_at":"2026-08-15T05:39:58.745396Z","submitted_at":"2009-09-03T08:29:49Z","title":"Small surfaces of Willmore type in Riemannian manifolds","version":2},"cited_work":{"arxiv_id":"0909.0590","doi":null,"metadata_source":"pith","pith_arxiv_id":"0909.0590","snapshot_observed_at":"2026-08-14T04:58:54.689808Z","title":"Small surfaces of Willmore type in Riemannian manifolds","venue":"math.DG","work_id":"e2996497-c06f-4322-a346-6f0639fabb8b","year":2009},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.599531Z"},"links":{"cited_paper":"/paper/0909.0590","citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:38f06d27914bd5e46e92ba36e416988b33626e8949fb230b7875b56d800d2bf2","observation_id":"d269feed-602a-4436-9645-5468f7258af5","resolution":{"observed_at":"2026-08-14T04:58:54.693901Z","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":"1201.1887","last_updated":"2012-01-10T16:07:20Z","snapshot_observed_at":"2026-08-15T04:22:57.795905Z","submitted_at":"2012-01-09T19:54:49Z","title":"Minimizers of the Willmore functional with a small area constraint","version":2},"cited_work":{"arxiv_id":"1201.1887","doi":null,"metadata_source":"pith","pith_arxiv_id":"1201.1887","snapshot_observed_at":"2026-08-14T04:58:54.673777Z","title":"Minimizers of the Willmore functional with a small area constraint","venue":"math.DG","work_id":"ebcf07c1-91f9-4310-85b0-b9ee33e789a6","year":2012},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.603482Z"},"links":{"cited_paper":"/paper/1201.1887","citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:35967432a1bf1d702a72bb87d01b8dfab4979f5b926792f08a9f12a4649c5281","observation_id":"fdfd6e22-fdbe-4406-bd34-bbee464de0c2","resolution":{"observed_at":"2026-08-14T04:58:54.678028Z","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":"2026-08-14T04:58:54.764224Z","title":"A New Conformal Invariant an d Its Applications to the Wilmore Con- jecture and the First Eigenvalue of Compact Surfaces","venue":null,"work_id":"e12cccdf-3ff9-4b8a-9852-1b2acc4597c3","year":1982},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.607192Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:6a35f513e82f56dd999f3a3568dc30861c1ec79524c276f7026ac189ce3cfa88","observation_id":"6b8cfe51-48e3-4d32-ab6a-4378e8eb6fff","resolution":{"observed_at":"2026-08-14T04:58:54.768082Z","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":"1908.11577","last_updated":"2019-08-30T07:54:59Z","snapshot_observed_at":"2026-08-14T10:09:24.563918Z","submitted_at":"2019-08-30T07:54:59Z","title":"Refined position estimates for surfaces of Willmore type in Riemannian manifolds","version":1},"cited_work":{"arxiv_id":"1908.11577","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.11577","snapshot_observed_at":"2026-08-14T04:58:54.655165Z","title":"Refined position estimates for surfaces of Willmore type in Riemannian manifolds","venue":"math.DG","work_id":"16cb380f-fdf5-4295-881e-c097f1d38b94","year":2019},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.610739Z"},"links":{"cited_paper":"/paper/1908.11577","citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:d76c1596776e4ee4677f3485c64f4b819919d4eb5a7f045555522dde9efdc342","observation_id":"e0cafef6-4e1b-4b8a-8b1e-08d164c6ca96","resolution":{"observed_at":"2026-08-14T04:58:54.661276Z","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":"2026-08-14T04:58:54.752608Z","title":"Some results about the existence of cri tical points for the Willmore functional","venue":null,"work_id":"d397c157-65b0-418b-a3c2-99a0adf06214","year":2010},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.614801Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:25ac20bf34d59cfdc8c55a0c4ea9dd7350c568c582065c6bcde34870d88cef9d","observation_id":"c9d887e3-d22d-4d3b-9b07-5d6a8bfaf691","resolution":{"observed_at":"2026-08-14T04:58:54.756562Z","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":"2026-08-14T04:58:54.741023Z","title":"Willmore spheres i n compact Riemannian manifolds","venue":null,"work_id":"9d9f76b1-0b8e-45c5-a8b8-c2f055347129","year":2013},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.618461Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:b4dc14c00172565edf1e0dc1af3608e8844bfb47d061fa9209cf0c7077e8c85f","observation_id":"b9d5c37e-f4eb-4354-b9ca-bed0be065f14","resolution":{"observed_at":"2026-08-14T04:58:54.744893Z","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":"2026-08-14T04:58:54.728764Z","title":"Szabados","venue":null,"work_id":"648adba2-6fa8-49c3-81dc-5cf96d480d4b","year":2004},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.621764Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:57e23c9f52bf09e2aa04f856815b09b45aa1d440f618c43bb5a658f12f2ef5ea","observation_id":"232785e1-f67c-4597-92ff-35d64cfad9db","resolution":{"observed_at":"2026-08-14T04:58:54.733256Z","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":"2026-08-14T04:58:54.717272Z","title":null,"venue":null,"work_id":"e4d1298d-0c5c-4931-8b64-938b573a7eca","year":1968},"citing_paper":{"arxiv_id":"1909.02388","last_updated":"2019-09-06T09:28:59Z","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T04:58:54.625248Z"},"links":{"citing_paper":"/paper/1909.02388"},"observation_digest":"sha256:9fc8bb4f273b476c6d37835cff5af60904a4f2e2e27f740de3825c42cb846888","observation_id":"08aba963-4667-40a6-8f6c-fa33d2312445","resolution":{"observed_at":"2026-08-14T04:58:54.720914Z","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":"1909.02388","last_updated":"2019-09-06T09:28:59Z","latest_version":2,"primary_category":"math.DG","snapshot_observed_at":"2026-08-15T06:26:14.351467Z","submitted_at":"2019-09-05T13:23:50Z","title":"Concentration of Small Hawking Type Surfaces"},"reference_resolution":{"displayed":17,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":4,"verified_fuzzy":12},"total_outbound_references":17},"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 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:1909.02388."}