{"as_of":"2026-08-17T18:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c0ef8b17bec7b9f2dc18b6aa74e57c759f42d310cdc197ca6967eb13a1fe6515","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T14:28:11.128105Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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/2608.10518/citation-record","integrity":"/paper/2608.10518/integrity","json":"/paper/2608.10518/citation-record.json","paper":"/paper/2608.10518"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.525917Z","title":"Catino, P","venue":null,"work_id":"062c0417-2fc9-4a44-9162-4f225a7ef69b","year":2024},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.014275Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:c0f3635c3d3da76ab81b95e01dc467abb5655f7ff0afb5d40343a21db551e876","observation_id":"6e4bdd09-b585-4a99-95ca-bf95c2f86aff","resolution":{"observed_at":"2026-08-15T14:28:11.531611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.508906Z","title":"Chodosh and C","venue":null,"work_id":"5b4fd76e-0dc3-4f74-b135-c1f8118c60d5","year":2024},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.019433Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:4b16ccd07c5f8fa055feb65cee7c99dab740cfbb79720be99f6f640aa6ef5838","observation_id":"1bfb86df-63ba-4be1-a2c7-8223336aaf71","resolution":{"observed_at":"2026-08-15T14:28:11.513582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.01492","last_updated":"2025-11-05T18:37:28Z","snapshot_observed_at":"2026-08-14T22:25:31.993527Z","submitted_at":"2024-01-03T01:37:54Z","title":"Stable minimal hypersurfaces in $\\mathbf{R}^5$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.01492","snapshot_observed_at":"2026-08-15T14:28:11.024138Z","title":"Chodosh, C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.024138Z"},"links":{"cited_paper":"/paper/2401.01492","citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:19b9ce30d3cebbbbd361947d27e49dbab7bd14481f9a059f2d5e91486e084c62","observation_id":"2bf8336c-9891-4fa2-a31c-d1370ad732fc","resolution":{"observed_at":"2026-08-15T14:28:11.024138Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.492434Z","title":"Cohn-Vossen,K¨ urzeste Wege und Totalkr¨ ummung auf Fl¨ achen, Composi- tio Math.2(1935), 69–133","venue":null,"work_id":"e9319d6f-4f08-462f-b844-e54c889a2335","year":1935},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.029305Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:e9745f63ff6bbe97b56636b91b63006e069938e7fabc9180b593979d303a5d00","observation_id":"21df7b85-9816-41d7-82fc-117f085b4449","resolution":{"observed_at":"2026-08-15T14:28:11.497754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.477004Z","title":"Cohn-Vossen,Totalkr¨ ummung und geod¨ atische Linien auf einfach zusam- menh¨ angenden offenen volst¨ andigen Fl¨ achenst¨ ucken, Recueil Math","venue":null,"work_id":"2e057760-17e2-48e1-a3a8-6189eb6a532b","year":1936},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.034178Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:a339ca9db90065b0e430b019c71f9bb480a405893bd57c1a363b41f8936b4e0a","observation_id":"afac2746-d8de-4fb9-acb9-ac5cace669d6","resolution":{"observed_at":"2026-08-15T14:28:11.482151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.461512Z","title":"do Carmo, Riemannian Geometry, Birkh¨ auser, Boston, MA, 1992","venue":null,"work_id":"ba15902b-3f84-4504-9554-4f31935a528b","year":1992},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.039022Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:6964a0274064e9bd8cdd6bdc16559fb6e76cb9c1400ca38884c7eeb397a65b86","observation_id":"f3fb79d3-ee24-4372-b877-4c6904716ea3","resolution":{"observed_at":"2026-08-15T14:28:11.466427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.444491Z","title":"do Carmo and C.K","venue":null,"work_id":"70762657-ee68-469a-809e-502a88c55168","year":1979},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.043672Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:46b5880c10777f5720e84ac241ba82197c0f7ce650dc40fda561c9b179c60abc","observation_id":"27e62eb9-2331-40f3-b6c6-f8b2bc095e3d","resolution":{"observed_at":"2026-08-15T14:28:11.450182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.048537Z","title":"Fischer-Colbrie,On complete minimal surfaces with finite Morse index in three-manifolds, Invent","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.048537Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:e1815f6949c2f98b847d35481fce2a10d528891be363d19af630a3049abbf31b","observation_id":"0585aaba-4ab3-4598-8b9c-9a48cb94ebc5","resolution":{"observed_at":"2026-08-15T14:28:11.048537Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.419978Z","title":"Fischer-Colbrie and R","venue":null,"work_id":"46ac608b-f45a-4c73-9c4b-80bb41e42f4a","year":1980},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.052852Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:9ea36f5f770abef0e02da8a3e26232eef98d61dc5ac1cabecf84b1e4a1c4afae","observation_id":"be42e3f2-b4c7-4d25-814e-baaed4fd7afa","resolution":{"observed_at":"2026-08-15T14:28:11.424829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.405322Z","title":"Grove and K","venue":null,"work_id":"8d614a7c-634c-48e2-9b5f-6c641230aa04","year":1977},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.057396Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:8a5829f8e99467b77d0bf11e3f89847361440646c916a28b665b319a2392d815","observation_id":"6cf8b750-2539-4b34-8233-1ea395fe37cc","resolution":{"observed_at":"2026-08-15T14:28:11.409838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.390186Z","title":"Harumoto,Topology of complete non-compact surfaces with the finite in- dex of the Schr¨ odinger operator, Master’s thesis, Okayama University, 2026","venue":null,"work_id":"ddb39c93-69a5-4002-8da0-a90986957484","year":2026},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.061682Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:81369ff9eb1b96d1d9f494b95c87252152361ac6ff21d1aae0ba0b9246c7f90c","observation_id":"e3ac1809-2d88-4f90-add5-c27f24cee982","resolution":{"observed_at":"2026-08-15T14:28:11.395166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.066022Z","title":"Huber,On subharmonic functions and differential geometry in the large, Comment","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.066022Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:abff087538083715894ef34baff5ccd5960c346f8736ef5cc2e18e9f17a411bb","observation_id":"2ccbb360-ad19-4e56-96a4-8fd98c14754b","resolution":{"observed_at":"2026-08-15T14:28:11.066022Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.365554Z","title":"Itoh and M","venue":null,"work_id":"691f9aaa-27ff-4b05-909c-810efa1d1eb8","year":2001},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.070889Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:3b9af630467e5b1a32498157ac7665354afa308d870e785a60b46745832eb0d8","observation_id":"ee04d05c-532e-4575-a147-bedeb2ba571f","resolution":{"observed_at":"2026-08-15T14:28:11.370837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.351391Z","title":null,"venue":null,"work_id":"186a01fe-ca43-402e-b084-b43085bab8d8","year":2002},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.075103Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:58540ab40460192c928c4b6b23859130450259592e9358fc5b6ca4c63a4d78fa","observation_id":"1e602f3a-667f-4bc1-a1bc-0383d9d8befc","resolution":{"observed_at":"2026-08-15T14:28:11.355815Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.337302Z","title":"Kondo and S","venue":null,"work_id":"ad1c01b2-0779-4af6-a591-bcc5696be694","year":2007},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.079294Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:db3aafe50476d5ffd76a04c2252f2e41b93e12b83c378432dc9e32a3ed1de279","observation_id":"bfcb7b4e-3074-4413-b209-5a58cee12e8c","resolution":{"observed_at":"2026-08-15T14:28:11.341893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.323355Z","title":"Kondo and M","venue":null,"work_id":"654735e0-cd74-4cc3-a6ea-eb1df22278ba","year":2010},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.083592Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:326a34735813fd3683e4048d94beb497b237ae7ef6ad259a93f145ca96c49a57","observation_id":"34be71fa-4b92-438c-9804-fe4fd0c49a14","resolution":{"observed_at":"2026-08-15T14:28:11.327732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.308452Z","title":"Kondo and M","venue":null,"work_id":"00ada8ff-ded2-4622-a1bf-962767e04e45","year":2011},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.087889Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:0a9a5b7040d035ad85fc0c34b2aefa8890f6c54453ca19da1ec9719750fc0b54","observation_id":"fbd7f6d1-279e-4748-a8a6-c72291a276ff","resolution":{"observed_at":"2026-08-15T14:28:11.313364Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.293793Z","title":"Kondo and M","venue":null,"work_id":"d33ef4c5-e634-4f19-bca5-dcfae3ee9b54","year":2011},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.091964Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:728e9f702446df715455e6570ebf3fad5d6d78fc3d537aa82e4354be9b548b46","observation_id":"bd77aa45-06fe-4a2f-bb9e-07a8720fa85f","resolution":{"observed_at":"2026-08-15T14:28:11.298373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.279747Z","title":"Mao,Volume comparison theorems for manifolds with radial curvature bounded, Czechoslovak Math","venue":null,"work_id":"410fb519-faed-462a-9c55-1bc198234a5c","year":2016},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.096498Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:1c4145fc6ecf922162a526d2a0d60c08da70ce37e5c81db3c2d8167303d84b04","observation_id":"82860638-3c43-4e36-92c2-defd990dc713","resolution":{"observed_at":"2026-08-15T14:28:11.284149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.14676","last_updated":"2024-05-23T15:11:53Z","snapshot_observed_at":"2026-08-16T13:50:09.216012Z","submitted_at":"2024-05-23T15:11:53Z","title":"Stable minimal hypersurfaces in $\\mathbb R^6$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.14676","snapshot_observed_at":"2026-08-15T14:28:11.100863Z","title":"Mazet,Stable minimal hypersurfaces inR 6, arXiv:2405.14676","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.100863Z"},"links":{"cited_paper":"/paper/2405.14676","citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:04dfa97b9e2c2dbe095f73bf9d7c0107784d4af7d927a2fb92a339b447f22666","observation_id":"b8c0d1b2-19c1-4d42-bb21-e577cfd88c17","resolution":{"observed_at":"2026-08-15T14:28:11.100863Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:28:11.264057Z","title":"Shiohama,The role of total curvature on complete noncompact Rieman- nian2-manifolds, Illinois J","venue":null,"work_id":"f41bcb88-aa68-47da-a17c-e44a90828e6b","year":1984},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.106041Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:8cb36408f7ac44780e9c90d993e070fc4b07fd2101502417acd51ba725b31ccc","observation_id":"87c65439-8cdc-41c4-b213-e1b95688c252","resolution":{"observed_at":"2026-08-15T14:28:11.269164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.248574Z","title":"Shiohama, T","venue":null,"work_id":"a11b36d6-60a0-4917-b5ef-789600138502","year":2003},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.110480Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:58924f79c2b15c5f98e373a555883b1fc32e2f9dbf8cd3505e0cc428bb0100e5","observation_id":"f409cb0f-bf5d-491a-8c15-4867929dfea3","resolution":{"observed_at":"2026-08-15T14:28:11.253114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.234322Z","title":"Shiohama and M","venue":null,"work_id":"9420c061-031d-42fb-a593-8216badfe751","year":2002},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.114873Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:e58a3306c9119f17b580a33a4bae5debbb4fc0ae38bc62b627b85d498e15d80d","observation_id":"1faddb92-9844-4323-9898-b9840020b12b","resolution":{"observed_at":"2026-08-15T14:28:11.238775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.219701Z","title":"Shioya,The ideal boundaries of complete open surfaces, Tohoku Math","venue":null,"work_id":"194616a1-1f70-4176-8703-df72f6601b50","year":1991},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.119192Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:4cf7e771ae06a45df5045ce8b1e94e1fef3c065c369a98bff7957be456cb9ca5","observation_id":"6c9302e5-823b-4f77-ac05-3b0b0e96ec3b","resolution":{"observed_at":"2026-08-15T14:28:11.224259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.204197Z","title":"Tanaka,On the cut loci of a von Mangoldt’s surface of revolution, J","venue":null,"work_id":"829e8b10-1217-40ec-8e0a-fbb5235a1400","year":1992},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.123610Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:badba5a726f25c5927bf8ed88fe68024993d32750286fadf7b0f5f5ddf42589b","observation_id":"0118dbd6-ac21-497c-a8f8-7fbb760b870a","resolution":{"observed_at":"2026-08-15T14:28:11.209725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T14:28:11.189066Z","title":"Tanaka and K","venue":null,"work_id":"b77dda4a-1797-4e51-88c7-1324a8ae1dc7","year":2013},"citing_paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T14:28:11.128105Z"},"links":{"citing_paper":"/paper/2608.10518"},"observation_digest":"sha256:01ae55792e805a8538eabdb3660cf0e4580365c084d7affe383d72de0a242fb8","observation_id":"2e3366fa-18ed-4bd7-ac7c-c12f697a92df","resolution":{"observed_at":"2026-08-15T14:28:11.194287Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.10518","last_updated":"2026-08-11T05:46:12Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-15T14:16:39.817180Z","submitted_at":"2026-08-11T05:46:12Z","title":"Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\\\"odinger Operators of Finite Index"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":21},"total_outbound_references":26},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2608.10518."}