{"as_of":"2026-08-14T23:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0e2f8f5bc519c7b5691c85198f7dfe2c8977365974dec67c7484263d55765de0","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T19:41:12.660610Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2607.16949/citation-record","integrity":"/paper/2607.16949/integrity","json":"/paper/2607.16949/citation-record.json","paper":"/paper/2607.16949"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-022-01140-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Inventiones mathematicae","work_id":"a0e851a8-3474-4b0c-a810-7b40bc64eed4","year":2022},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:09.912627Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:f53df470dc0d8ddd28b8be456a55d7b401c5f45ae17eb9ee3646645ebc1ebec0","observation_id":"39e3c2b8-1ec8-46c9-ad67-7144c58bcb5c","resolution":{"observed_at":"2026-08-01T19:43:24.276849Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-01T19:41:10.024324Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.024324Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:8ee3897e49721e0913e8d755f7469d321880bc42950f87d06e97f8f374776753","observation_id":"c1a39659-de5d-4e4d-95e0-db626d90daed","resolution":{"observed_at":"2026-08-01T19:41:10.024324Z","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":"10.4153/s2976859425100003","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Canadian Mathematical Communications","work_id":"c6f236d9-46d2-4cd0-becd-1a2fb087bf66","year":2026},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.108685Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:803f9b0b0a1d658cca51c9f88ab4cde7c72b965a831dec56c442ee7cd0732434","observation_id":"1f5a0d69-b93e-4ed0-a6b2-260e5daf7159","resolution":{"observed_at":"2026-08-01T19:43:23.920919Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/tran/8180","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Transactions of the American Mathematical Society","work_id":"afc93cf4-279d-4042-b4ce-713e8916ea76","year":2021},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.175614Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:385872846691e956b9a7b8c8ffbce4bd25b22c62ae8e603a8be0108196b50140","observation_id":"b0fa3e22-f609-43be-8b05-9932873df926","resolution":{"observed_at":"2026-08-01T19:43:23.837534Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-019-03539-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Communications in Mathematical Physics","work_id":"70693891-645c-4720-8687-ff9a408ba2f7","year":2020},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.292681Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:300a66007c4dee7da3b9e4d202bef3b9e1dd98572165acc156bf0030abc18c8c","observation_id":"68b2aaea-89f8-4fab-9c02-cd2f37e0b8f2","resolution":{"observed_at":"2026-08-01T19:43:23.659290Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/aif.3461","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Annales de l’institut Fourier","work_id":"f04906d5-b856-48d2-afcc-20677f41639a","year":2022},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.414323Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:6bd2eb649a06fe01c0ee9646d50e915dd6bb5027c6566e3f85387141150ecf56","observation_id":"fe46fa4b-43b2-4e71-b746-f2b68ae6827a","resolution":{"observed_at":"2026-08-01T19:43:23.523009Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jncg/555","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Noncommutative Geometry","work_id":"cacd54cd-af33-4835-988f-f34a5480ef5a","year":2024},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.490965Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:25fd2ed12a9d8cc779f96caae7b94f725cdc92e18349d7c9cbfc0ad42d6e4d0b","observation_id":"07f44f5f-c1ba-4973-ba38-7b8373085bcf","resolution":{"observed_at":"2026-08-01T19:43:23.319294Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-01T19:41:10.538461Z","title":"Friedman, A proof of Alon's second eigenvalue conjecture and related problems, Mem","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.538461Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:aff4362b574f4210b8b23026dc2b3700e4648a510ba101c869d347c83be08e07","observation_id":"fa48a922-4e8a-4500-8e19-831d037235bf","resolution":{"observed_at":"2026-08-01T19:41:10.538461Z","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":"10.1017/cbo9780511629365.008","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Higson and J","venue":"Cambridge University Press eBooks","work_id":"aaba360a-f8f0-4d34-986d-a7c1e59feaa5","year":1995},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.631871Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:5c6d1a5d419453a7a26b8d1d705dd7cb5432052f5b2f4dc494f6a9e2926b626c","observation_id":"3a7b2f2e-f966-4c8a-bf0d-6d61573a8399","resolution":{"observed_at":"2026-08-01T19:43:23.182389Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01456961","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"K o nig, \\\"Uber Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre, Math","venue":"Mathematische Annalen","work_id":"d9133cbd-247e-4d62-bdb7-6a5d0a8ae878","year":1916},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.796159Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:f3274e7baa9cb1bc15620107d303805768c2449c698b15ff0fa4fb794def3943","observation_id":"a96043e7-9777-4763-8d8a-f07194bffe1d","resolution":{"observed_at":"2026-08-01T19:43:23.009786Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.06720","doi":"10.48550/arxiv.2602.06720","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Krutoy, Bijective rigidity of uniform Roe algebras and injectivity of the comparison map, preprint, arXiv:2602.06720v2 (2026)","venue":"Open MIND","work_id":"604ff1b9-075d-4feb-b2a2-26dc6f624b03","year":2026},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:10.918671Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:2075ee453aaf7ee8c4c104ceca978844b5d00b2acfe52c1909dd2863980b521c","observation_id":"7942acff-d845-4336-880a-eb8fad5d0c01","resolution":{"observed_at":"2026-08-01T19:43:22.959024Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-016-2699-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kubota, Controlled topological phases and bulk-edge correspondence, Comm","venue":"Communications in Mathematical Physics","work_id":"c7a190b7-59cd-44ee-b72b-7f573ebc845a","year":2017},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.029105Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:a843edabd469aac7e06c19c50b7c5091b4f1dde73a66c618b17857acb232f37f","observation_id":"eb279462-2e9f-45b7-9a53-31b5f2f1e084","resolution":{"observed_at":"2026-08-01T19:43:22.877472Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/981","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Lu and L","venue":"The Electronic Journal of Combinatorics","work_id":"33f42d95-d02e-4fe3-ad6e-ee3141da7061","year":2007},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.148598Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:ea7cf226391dfbcd67ef56b6f4aac54daddf76e64843aa93b330affa9c0c3d8e","observation_id":"6d9669cf-e41e-4c5f-8aea-7ac60c42158d","resolution":{"observed_at":"2026-08-01T19:43:22.646124Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10240-025-00155-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Mart\\'inez and F","venue":"Publications mathématiques de l IHÉS","work_id":"13775224-febc-453a-923a-4386019022af","year":2025},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.327207Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:bab89957557846945b91bae146f09e4ea098fde0f8c6f62c8be314fcefc30d50","observation_id":"8c33f41b-1d80-4910-8e4d-914c58bc2443","resolution":{"observed_at":"2026-08-01T19:43:22.523128Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/1819","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"The Electronic Journal of Combinatorics","work_id":"68219392-f725-42df-b6f9-4eed00d5947b","year":2004},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.434636Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:9d1e0bd3ac66769351480b58dd235a07e1c78dc57747b9fa715b535a0ec9da71","observation_id":"4a889535-ec13-41c2-9ad3-81b51d2dec0f","resolution":{"observed_at":"2026-08-01T19:43:22.466058Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-01T19:41:11.598612Z","title":"Roe, An index theorem on open manifolds","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.598612Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:573c1f19048b88fe14b8f9aae0233c9b2676d8e36738c011216b64c6d5058bb2","observation_id":"a2bea19a-24ac-47e7-a3c6-18e70e9618f1","resolution":{"observed_at":"2026-08-01T19:41:11.598612Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T19:41:11.706755Z","title":"Roe, Coarse cohomology and index theory on complete Riemannian manifolds, Mem","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.706755Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:f54f655013cc3e5581aa0915752b1b2d1b7e9296db7403a03e31cea284a9df5b","observation_id":"97b52ef4-9a8b-4499-9d8e-ea7e3002697c","resolution":{"observed_at":"2026-08-01T19:41:11.706755Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T19:41:11.812866Z","title":"Roe, Index theory, coarse geometry, and topology of manifolds, CBMS Regional Conference Series in Mathematics, vol","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.812866Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:97aeaea12f7e8f1ec3fdec0c69ad41b671c7776cd8a598e9d1add8101268c730","observation_id":"74a7eb32-27d1-4fe2-9282-cc990ba3dfd7","resolution":{"observed_at":"2026-08-01T19:41:11.812866Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T19:41:11.950158Z","title":"Roe, Lectures on coarse geometry, University Lecture Series, vol","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:11.950158Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:5a9e11940198729545cdd8d74035b8d4c829ff975a1da7cdd6b48473de1c207b","observation_id":"15f2b931-65a0-4c95-93b8-b7418aa186f4","resolution":{"observed_at":"2026-08-01T19:41:11.950158Z","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":"10.1016/j.jfa.2013.07.004","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Roe and R","venue":"Journal of Functional Analysis","work_id":"a893a173-cfcb-4e3e-b636-e0cb9ecfadc8","year":2014},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:12.087583Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:acc62c500641f901c35b2c23f89c94c418a787a5a1e15dbb46499f9084d31ebf","observation_id":"0db4490f-cd16-46a3-9c41-47a009c1fe3c","resolution":{"observed_at":"2026-08-01T19:43:22.164253Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.aim.2013.09.006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"S pakula and R","venue":"Advances in Mathematics","work_id":"0b6f6c90-2cdb-4aee-834a-794c5bfb6c83","year":2013},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:12.263048Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:f0c9221aac6104d1728ceaa4088e2ff6c568c10894f6e5c9da3c4910d3289017","observation_id":"d2070e72-730a-4931-a897-90d531eacbfd","resolution":{"observed_at":"2026-08-01T19:43:21.911992Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.01998","doi":"10.48550/arxiv.2602.01998","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Vignati, The rigidity problem for uniform Roe algebras, preprint, arXiv:2602.01998v1 (2026)","venue":"Open MIND","work_id":"07ebcaea-ee34-44c0-805f-8d03e37f7692","year":2026},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:12.392594Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:401d34b405e0f882d1d180c11f92fa811b5f6b1699a87f776665fb9e0034ef0d","observation_id":"76b7c774-aa7b-469b-92d2-1a27fd3d883c","resolution":{"observed_at":"2026-08-01T19:43:21.770939Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/ggd/570","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"White and R","venue":"Groups Geometry and Dynamics","work_id":"2b12332b-f79b-4964-8795-b870d05858e2","year":2020},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:12.542267Z"},"links":{"citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:2033d01a16968d3ec1d06bf0aa85fa416310d50260e91e88e9b214e088f4f828","observation_id":"f4e4efa3-784a-4e69-923a-246d94590eb7","resolution":{"observed_at":"2026-08-01T19:43:21.492625Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.15096","last_updated":"2026-07-16T15:08:34Z","snapshot_observed_at":"2026-08-07T09:45:51.210694Z","submitted_at":"2026-07-16T15:08:34Z","title":"Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces","version":1},"cited_work":{"arxiv_id":"2607.15096","doi":"10.48550/arxiv.2607.15096","metadata_source":"pith","pith_arxiv_id":"2607.15096","snapshot_observed_at":"2026-08-02T00:16:10.520619Z","title":"Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces","venue":"math.OA","work_id":"d3ff79ae-458c-48e4-a1ad-102390bce5bb","year":2026},"citing_paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-01T19:41:12.660610Z"},"links":{"cited_paper":"/paper/2607.15096","citing_paper":"/paper/2607.16949"},"observation_digest":"sha256:8c72760ad18f4c9194cd549c4e1de2e284e954c9696c116281ff3c4cb7c21180","observation_id":"392b2e3e-4716-4632-9538-c936bef5c338","resolution":{"observed_at":"2026-08-01T19:43:21.287557Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.16949","last_updated":"2026-07-18T20:04:54Z","latest_version":1,"primary_category":"math.OA","snapshot_observed_at":"2026-08-14T22:31:45.588849Z","submitted_at":"2026-07-18T20:04:54Z","title":"On the embedding rigidity problem for uniformly locally finite coarse spaces"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":16,"verified_fuzzy":0},"total_outbound_references":24},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.16949."}