{"as_of":"2026-08-09T05:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2bf86412082c9a7f3b14fd4e19cd7e5d30c8503e24ee5498ba4a0c2d6d51e1bd","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:24:08.522918Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2505.22439/citation-record","integrity":"/paper/2505.22439/integrity","json":"/paper/2505.22439/citation-record.json","paper":"/paper/2505.22439"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:24:13.508726Z","title":"Alikakos and Giorgio Fusco, The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions, Indiana Univ","venue":null,"work_id":"ce8472e2-b434-475e-91d4-8f0ce36d7af7","year":1993},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.335269Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:432f753aa883b7b40c7c77cda9ebaf0a8d8f304b2c22de2159a7253ddaf5460b","observation_id":"2a7803fc-2d76-402a-ad3c-536ff8da51e0","resolution":{"observed_at":"2026-08-07T13:24:13.618437Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:13.135323Z","title":"211 (2013), no","venue":null,"work_id":"8af4a482-f3fc-43ed-880b-3822896861b2","year":2013},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.401414Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:9ee251fd8c2281d0b8c56db063aa60b094af2e14e76e0f56845a25659eb04647","observation_id":"0cf7f2f5-b9f9-44ea-a4bb-d8ca7843d441","resolution":{"observed_at":"2026-08-07T13:24:13.313755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:12.942101Z","title":null,"venue":null,"work_id":"b9b552ef-5bbe-4f77-8626-3d3dc339107c","year":1968},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.450769Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:74ed00fc2329621a4347395e1b288284915fe98f6eedfc406787954f0546c030","observation_id":"b0790820-97ef-4354-822e-3ba017c6a7d6","resolution":{"observed_at":"2026-08-07T13:24:13.012072Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:12.819773Z","title":null,"venue":null,"work_id":"200ff57f-c5ba-4ca0-ac99-0cc99bc6ef17","year":2006},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.547460Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:3952a379d11f99827611eac41c8fba821ce294b3896d9534975b2a8920880708","observation_id":"78169afe-fbb3-4434-8d7e-d401ee9339ec","resolution":{"observed_at":"2026-08-07T13:24:12.882334Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:12.673447Z","title":null,"venue":null,"work_id":"a720dc50-3e4d-4e9c-975d-7637ae30a84b","year":1984},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.648977Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:b0e0c7dfa0a26a78d58f582d3e69dad84bcbd6cafae69ef91b0e3824734bd1f3","observation_id":"b7cfb19f-0ea3-4a21-8947-eb105050b6ed","resolution":{"observed_at":"2026-08-07T13:24:12.744256Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:12.522873Z","title":null,"venue":null,"work_id":"6c3ce342-2890-430e-b552-96b58e53fc44","year":2000},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.745265Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:372d3b99da62aabfc0e561d4410ac442d28f1c679791adf95c54bf59920ea5fa","observation_id":"35574318-28f0-4b00-9d85-98fd6bb88ce7","resolution":{"observed_at":"2026-08-07T13:24:12.599993Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:12.378158Z","title":null,"venue":null,"work_id":"e6aa9ded-394a-478f-912d-f2f1cc0ed24f","year":2000},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.803469Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:39e9d6b40901169ce3908606d915729641a03b113a74b875972479183180d11d","observation_id":"bea06fd7-d188-4445-9a4a-ef29e6543470","resolution":{"observed_at":"2026-08-07T13:24:12.443743Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:12.145996Z","title":"Harrell, II and Michael Loss, On the Laplace operator penalized by mean curvature, Comm","venue":null,"work_id":"4731dcf1-a64e-42c6-86b8-2e064508f95f","year":1998},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.879863Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:742cce5955fdfd99990e303368bfb40ed0a6bf25f5a734ae9b60632816dc0308","observation_id":"54e065d5-21e0-4cee-9fc2-dc8a54e211de","resolution":{"observed_at":"2026-08-07T13:24:12.227946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:11.947668Z","title":null,"venue":null,"work_id":"c97f48a5-045f-44f3-a1dd-b4e087d81d0d","year":1970},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:06.962548Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:c78d879a18091df3a4042c26bfdbdff2889d638ac74d20dd5b5b04c789003562","observation_id":"34c8edc5-9b24-468b-abd0-c903a302d706","resolution":{"observed_at":"2026-08-07T13:24:11.997629Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:11.710784Z","title":null,"venue":null,"work_id":"3721061a-abe0-4c56-b9d0-bf60c22eed7c","year":2006},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.060976Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:670c2d5ad35d0b02754f882ef1353c12cb696bee7f0f1a635460ec4a979e3614","observation_id":"501afe34-3614-46ab-84be-8aeb981189d0","resolution":{"observed_at":"2026-08-07T13:24:11.826500Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:11.413868Z","title":null,"venue":null,"work_id":"1cb18cd3-c81e-44d6-97e8-494561f6e252","year":2016},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.171540Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:e7c8e08b6fab5022125a6557b70510497033b7ef79529f175b64ac21933abfba","observation_id":"6e98d0bd-b509-41a0-bbdc-ffe2cc2a706c","resolution":{"observed_at":"2026-08-07T13:24:11.566166Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:11.103997Z","title":null,"venue":null,"work_id":"9bab4ef3-8132-498a-a5d0-0a8064fea1be","year":2019},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.267652Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:699f3466dbccd968a86fa84073e5b53b37de559389cc1e444bf3edb25a108dd2","observation_id":"35a5c960-8ff4-46f0-9dce-e56b27c52608","resolution":{"observed_at":"2026-08-07T13:24:11.201208Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.05293","last_updated":"2025-05-08T14:32:24Z","snapshot_observed_at":"2026-08-07T15:48:46.729603Z","submitted_at":"2025-05-08T14:32:24Z","title":"Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces","version":1},"cited_work":{"arxiv_id":"2505.05293","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.05293","snapshot_observed_at":"2026-08-07T13:24:08.596585Z","title":"Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces","venue":"math.DG","work_id":"071e9666-3cd1-4fb1-839d-e08939296a8d","year":2025},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.369903Z"},"links":{"cited_paper":"/paper/2505.05293","citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:905a17b704b9624af69da3db0756257190a62119e0ff2a97ed36ac9e09e19f72","observation_id":"959f912d-90e2-4833-801e-6b0d2e2546bd","resolution":{"observed_at":"2026-08-07T13:24:08.647011Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:10.895442Z","title":"Differential Geom","venue":null,"work_id":"15f71eab-e8c3-481f-a732-a60792f379f0","year":1993},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.482337Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:1377602aae00051b7631e9e85cebe6dd2ed0d0bc2d112b0a2df5e5c2cef36d80","observation_id":"47ae4d33-377b-48bb-bcc1-9fa5ba3db4e3","resolution":{"observed_at":"2026-08-07T13:24:10.997335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:10.663087Z","title":null,"venue":null,"work_id":"f88dc87f-cf26-4ea9-b7d5-8c48f29233d2","year":2008},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.581092Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:ce4bbe1df0b55dfad042490465f6e9210160d757212c46fd2695392a5c57bc3a","observation_id":"e54189c1-8c3d-410a-9f4d-8ac684e12c27","resolution":{"observed_at":"2026-08-07T13:24:10.795207Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:10.457883Z","title":"Blaine Lawson, Jr., Complete minimal surfaces in S3, Ann","venue":null,"work_id":"f5dfc0c6-e5db-4537-b481-8b416a1b1d77","year":1970},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.673821Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:dac0c3bdb4294da59dd9cb88800620eb180fea88772b0c1ef980e878b5c0afe7","observation_id":"80386821-6b2d-461d-a987-f0db8dac2532","resolution":{"observed_at":"2026-08-07T13:24:10.542141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:10.311929Z","title":"Lee, Introduction to Riemannian manifolds, 2nd edition ed., Grad","venue":null,"work_id":"88a7d4f5-95c4-4af7-a53a-76dfe2ff79d4","year":2018},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.769979Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:87d2dccf81618315f54978aa614c5e59643fc5ec73ad6261b97f0fb2d1c6188a","observation_id":"595727a6-4968-4f60-a3bc-e39e8a95414c","resolution":{"observed_at":"2026-08-07T13:24:10.380402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:10.113625Z","title":null,"venue":null,"work_id":"3104a872-f013-45e2-9c8f-e37e0ba13ec4","year":1982},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.846922Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:b36b3fbe35d8eeb4bb763c926876a1d390e219963f1d414683f5a262b9499971","observation_id":"62633534-f744-418f-a163-47e7b5b45ee1","resolution":{"observed_at":"2026-08-07T13:24:10.214086Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.874033Z","title":"Manzano, Julia Plehnert, and Francisco Torralbo, Compact embedded minimal surfaces in S2 × S1, Comm","venue":null,"work_id":"d4939fe2-069b-4085-a4fc-04d0b0c58e59","year":2016},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:07.941958Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:a81d832bab7785f61fd11c7d7e9794db2189e4a729f492e1a310b700ac208e48","observation_id":"41a1336c-da9f-4e61-aed5-3787b9d116a1","resolution":{"observed_at":"2026-08-07T13:24:09.986483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.666200Z","title":"Marques and Andr´ e Neves,Min-max theory and the Willmore conjecture, Ann","venue":null,"work_id":"9b4d5f12-1e0e-4823-991c-9f1f20417433","year":2014},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.010911Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:afad20be313272cb5212175fc9123becd34ef33534a5ac44225a03d8da33f194","observation_id":"8ae92322-0ed6-4290-8e28-0365ed40f191","resolution":{"observed_at":"2026-08-07T13:24:09.764278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.491099Z","title":null,"venue":null,"work_id":"026efa5a-6d70-4f65-9ef7-e7a775604e28","year":2019},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.068850Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:f67076fc4b34b7bd7f37675b190b77a3917b41a62cccef3eacbedcbbbe4f0fc5","observation_id":"ff391b60-18a0-4cb5-bdb6-83ea059660e3","resolution":{"observed_at":"2026-08-07T13:24:09.568847Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.364342Z","title":null,"venue":null,"work_id":"5cbb1dfb-f69d-43af-9e76-e92a38b47e6f","year":1986},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.149245Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:1adcc0cc517cceb0e40c547c995cc81844498b21d8bf941cce694da74718c55e","observation_id":"8552d050-cae5-4880-a9eb-bd9b999d5c86","resolution":{"observed_at":"2026-08-07T13:24:09.412937Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.272851Z","title":"Nadirashvili, Berger’s isoperimetric problem and minimal immersions of surfaces, Geom","venue":null,"work_id":"b885b9a6-3882-4d3d-a53f-bf6001a55b96","year":1996},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.236288Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:448beab5a9a58ef09322d76852564f92e20ed88afb791f24ca4315d6e608d3ce","observation_id":"718f940f-8fa0-4e56-89a9-4d05ab146bb1","resolution":{"observed_at":"2026-08-07T13:24:09.310472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.125795Z","title":null,"venue":null,"work_id":"2cfcac0b-ba39-4254-aa49-2fe78a8ef135","year":1962},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.316132Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:cb90df64242fd3aa6e54aa898082aed16b6f068847ecc8edcc30924fd81fa55d","observation_id":"a18a079b-4c03-483b-94d4-2a882a3cf173","resolution":{"observed_at":"2026-08-07T13:24:09.202968Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:09.008492Z","title":null,"venue":null,"work_id":"980e493c-2301-4273-9441-a40478ae8bcd","year":1990},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.362701Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:1b3803200f3eea0347bb1acc87d18c7fac8fa06153233bd8a210175dea5ab4f3","observation_id":"98bc9ad1-aebd-48ff-a561-ab79da3f87bb","resolution":{"observed_at":"2026-08-07T13:24:09.066120Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:08.871554Z","title":null,"venue":null,"work_id":"aa09d772-49fa-49b4-9533-0084bc5b5ed7","year":2013},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.442675Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:6da663ba925e5e31edc9efa4770f4370130cdbf21cb909c52a63613528b7b852","observation_id":"7d93f99c-c890-4b54-b62d-ac9741043a11","resolution":{"observed_at":"2026-08-07T13:24:08.949609Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:24:08.730485Z","title":"Yang and Shing Tung Yau, Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann","venue":null,"work_id":"952bd02f-db35-4cfd-bd93-5207b5aab8be","year":1980},"citing_paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:08.522918Z"},"links":{"citing_paper":"/paper/2505.22439"},"observation_digest":"sha256:eb1e73c2bad0712481aa0fcd014a85ba408238c0a05c0920f236e6546600fcd0","observation_id":"ce4aba27-5ebe-41da-b021-464f5c91b8ae","resolution":{"observed_at":"2026-08-07T13:24:08.813730Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.22439","last_updated":"2025-05-28T15:04:30Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-08T16:00:11.264072Z","submitted_at":"2025-05-28T15:04:30Z","title":"Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":1,"verified_fuzzy":10},"total_outbound_references":27},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2505.22439."}