{"as_of":"2026-08-21T00:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:26ef31ad50b81ec09cfe987eceb307e57f5f8e54829673be3c0c4e77103fa51b","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T08:54:40.071646Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T17:30:22.229926Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-05T17:30:24.520664Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"cited_work":{"arxiv_id":"2607.29354","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.29354","snapshot_observed_at":"2026-08-05T17:30:24.520664Z","title":"Localisation of pseudospectra on discrete groups","venue":"math.SP","work_id":"b1c8f33a-2da5-4cf5-88a0-c3b8ebaeb84d","year":2026},"citing_paper":{"arxiv_id":"2608.03526","last_updated":"2026-08-04T12:10:28Z","snapshot_observed_at":"2026-08-20T23:54:49.665389Z","submitted_at":"2026-08-04T12:10:28Z","title":"Spectral and Pseudospectral Approximation of Finite-Interaction-Range Operators in Doubling Metric Measure Spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T17:30:22.229926Z"},"links":{"cited_paper":"/paper/2607.29354","citing_paper":"/paper/2608.03526"},"observation_digest":"sha256:9e1d9ce3fbda61517e73d2adacaf61bf3dbd2072e8f7a518b86513cbf604ed52","observation_id":"25b3ed90-072e-4327-a8d0-76d67f06587f","resolution":{"observed_at":"2026-08-05T17:30:24.631531Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.29354/citation-record","integrity":"/paper/2607.29354/integrity","json":"/paper/2607.29354/citation-record.json","paper":"/paper/2607.29354"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T08:54:36.689829Z","title":"Avron, P.H.M","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:36.689829Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:a01d2125352f05cc132b4a40bccf51df8580ff6979ccd19aabd5df115a50ee42","observation_id":"d7e4ae19-e7c2-4dc0-bdea-ad004444f96b","resolution":{"observed_at":"2026-08-03T08:54:36.689829Z","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":"2026-08-03T08:54:36.782366Z","title":"Ben-Artzi, A","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:36.782366Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:8bd308f5c16d5df5af7f72e5fc4f0b8b4b3cf44ff6181c9eb7af5c7a9eb82f24","observation_id":"543072bc-eecd-4f44-8923-a4292ee09be6","resolution":{"observed_at":"2026-08-03T08:54:36.782366Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1508.03280","last_updated":"2020-06-15T17:50:03Z","snapshot_observed_at":"2026-08-14T22:36:36.994335Z","submitted_at":"2015-08-13T17:42:14Z","title":"Computing Spectra -- On the Solvability Complexity Index Hierarchy and Towers of Algorithms","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1508.03280","snapshot_observed_at":"2026-08-03T08:54:36.944314Z","title":"Ben-Artzi, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:36.944314Z"},"links":{"cited_paper":"/paper/1508.03280","citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:6701c3e2c637eac9cefe7a444eac6b96b9428d48c93ea02349974a5dd52c39f0","observation_id":"dd49f581-6292-4bb5-b04c-7f2b76b5cf20","resolution":{"observed_at":"2026-08-03T08:54:36.944314Z","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":"2026-08-03T08:54:37.112756Z","title":"Boyko and V","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.112756Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:ebf6df1421ed434d53378ff771ba8f20c26d6e135ec29a847f20c8ca3b637587","observation_id":"d8cba5df-d0c2-4563-9ec7-9d5b6d193398","resolution":{"observed_at":"2026-08-03T08:54:37.112756Z","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":"2026-08-03T08:54:37.217597Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.217597Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:e82dff3415a2f9c9b0d766c83f8359b5f8868fef38b2aeb9afdc55ab02a3df48","observation_id":"9b294bb3-8fa1-4b70-89a3-ebdfd1015e4c","resolution":{"observed_at":"2026-08-03T08:54:37.217597Z","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":"10.1002/pamm.202300016","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"PAMM","work_id":"86b15be0-d265-4523-ad07-ca606513f065","year":2023},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.335893Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:4adf3d3afdd72558cb1576feb108270a3326afa64837aee43f89a4c593c7faab","observation_id":"2f06e305-d681-4bd3-a8bc-571b3460cc98","resolution":{"observed_at":"2026-08-03T08:59:36.673432Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-03T08:54:37.459069Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.459069Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:10ec575f6ff3a02ca17e213af4d2889fdebe205054bccfa4a9429f89f353d35b","observation_id":"d28bf8ef-3549-484a-98c1-6bde47401a3d","resolution":{"observed_at":"2026-08-03T08:54:37.459069Z","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":"2026-08-03T08:54:37.558781Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.558781Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:8b152b0ea88ff67a43b1483ac3dae0847dc927d03f795b75dfb605f8d1881623","observation_id":"c8038bc2-6764-410a-8959-cbf437b4e786","resolution":{"observed_at":"2026-08-03T08:54:37.558781Z","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":"2026-08-03T08:54:37.687795Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.687795Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:9e689435c9034a20a51ada9020cee5290cfadb30284f30d11dbee854ffa00f6b","observation_id":"40e84169-1745-478f-9b9c-ea854eb356a1","resolution":{"observed_at":"2026-08-03T08:54:37.687795Z","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":"2026-08-03T08:54:37.800261Z","title":"Choi, G.A","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.800261Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:4e23e9d8689017f2dd57f6a9c24839196d51972858e848f17c9a98ea9e0892f1","observation_id":"c6ad8925-9ad4-47da-82a1-97755a2021be","resolution":{"observed_at":"2026-08-03T08:54:37.800261Z","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":"2026-08-03T08:54:37.912310Z","title":"Chonchaiya : Computing the Spectra and Pseudospectra of Non-Self-Adjoint Random Operators Arising in Mathematical Physics, PhD thesis , University of Reading, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:37.912310Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:ba5a42dafd8c28b7aa99686493804f1f468192bd92b3ed908277268788b647be","observation_id":"405758dc-018c-4ef2-986a-ca98d61f8aa9","resolution":{"observed_at":"2026-08-03T08:54:37.912310Z","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":"2026-08-03T08:54:38.021236Z","title":"Cohn : Algebra , vol","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.021236Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:369fda989aeff909969a8a4c441bc4343b95e2d21f37e8c8d218b2e9ed8bce34","observation_id":"e1b3b63a-ee35-4bb7-9b51-d11cd7b970d6","resolution":{"observed_at":"2026-08-03T08:54:38.021236Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.20353","last_updated":"2026-06-23T08:24:22Z","snapshot_observed_at":"2026-08-20T17:43:31.821858Z","submitted_at":"2024-07-29T18:06:42Z","title":"Computing Spectral Size: Rigorous Algorithms and the Limits of Computation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.20353","snapshot_observed_at":"2026-08-03T08:54:38.132921Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.132921Z"},"links":{"cited_paper":"/paper/2407.20353","citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:83c19ae0701d2044d114762fe0bbb579f939134d3be735e7d2fff4821e103270","observation_id":"6a9eb06e-8343-4aa6-89c1-c40e400a8063","resolution":{"observed_at":"2026-08-03T08:54:38.132921Z","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":"2026-08-03T08:54:38.209892Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.209892Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:066fb9d357418d595e14b9d0ed486efbe8a342673e26aa5350f186a45b7055cb","observation_id":"35b7252c-8553-4a81-a1e0-ffb8a0a48d1e","resolution":{"observed_at":"2026-08-03T08:54:38.209892Z","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":"2026-08-03T08:54:38.283170Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.283170Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:e501606fb9b9259b27d49eb2c4fe1313e0145c6db2ac7629b42b32af5b98de9f","observation_id":"73f9cd75-ceca-424b-8a6f-1f25c2e3122f","resolution":{"observed_at":"2026-08-03T08:54:38.283170Z","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":"2026-08-03T08:54:38.356909Z","title":"Globevnik and I","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.356909Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:bc3d24b832942e7c2f8b1bf91f7320e6633bde375209842af0fcbd685cd249b6","observation_id":"c9f71b23-1484-498a-bec5-d29e08c1ec0b","resolution":{"observed_at":"2026-08-03T08:54:38.356909Z","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":"2026-08-03T08:54:38.466911Z","title":"Globevnik : Norm-constant analytic functions and equivalent norms, Illinois J","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.466911Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:aabc5ebc94dfa5c78498a57ec295b99dea04b262a28ab50b7108657625e48e05","observation_id":"c07615e5-60dc-4a04-b61e-5ba813b50c72","resolution":{"observed_at":"2026-08-03T08:54:38.466911Z","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":"2026-08-03T08:54:38.578512Z","title":"Hagen, S","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.578512Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:b243c4ad79a4b4c9f16a940048ab54fab630154e7435400aca274f4793011425","observation_id":"05bdf9db-db28-4911-bb7d-e3618f375d19","resolution":{"observed_at":"2026-08-03T08:54:38.578512Z","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":"2026-08-03T08:54:38.654802Z","title":"Hagger, M","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.654802Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:3df28a6093830c8d2fc93f12aec97da6fb33c6cf124c216ad1c3d467687fc7d7","observation_id":"03348205-4ab6-4783-b083-755512e5f3f4","resolution":{"observed_at":"2026-08-03T08:54:38.654802Z","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":"2026-08-03T08:54:38.770154Z","title":"Hege : Spectral gaps in systems of finite local complexity , PhD thesis , University of T\\\"ubingen, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.770154Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:72977f2d439cb1843e4c6800912b9e9a5ec59529c95bd7b30641e1daa90afa4c","observation_id":"78ba7f68-694b-478d-b8c1-ad7d6843b657","resolution":{"observed_at":"2026-08-03T08:54:38.770154Z","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":"2026-08-03T08:54:38.881945Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.881945Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:bf3018466907fe7383841d2a57aace9d3d4c3e80989af26a74dc603c36be45bb","observation_id":"c21ce0a8-37da-430b-8b65-7b8ad5370176","resolution":{"observed_at":"2026-08-03T08:54:38.881945Z","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":"2026-08-03T08:54:38.963099Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:38.963099Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:5df7219cc528a0bcc075ffd9de175f6d87dd31bbb2b3434cf026875ffbfe7112","observation_id":"9616d2e0-a45c-4917-af1d-d32c31093c82","resolution":{"observed_at":"2026-08-03T08:54:38.963099Z","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":"2026-08-03T08:54:39.062447Z","title":"Keller, D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.062447Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:18a4baca448dee6dbc3af38b64c8e68f68bcc1e3f3442524bcd3b071c1153dab","observation_id":"8af49969-4b0e-4dc2-89f7-1187873abf76","resolution":{"observed_at":"2026-08-03T08:54:39.062447Z","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":"2026-08-03T08:54:39.125357Z","title":"Lindner : Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method , Frontiers in Mathematics, Birkh\\\"auser 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.125357Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:d6f1e10d76cf72e03f3ba5a47d99864029347ff94dde05e6dd3f0cba1cfcece6","observation_id":"90145afe-0bfc-4f11-8eab-cfd1887ca05e","resolution":{"observed_at":"2026-08-03T08:54:39.125357Z","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":"2026-08-03T08:54:39.216546Z","title":"Lindner and M","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.216546Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:a539402dd7c810d4704dbc812a533bbc3f71aab48bc5e52b72768d36c9d5ff82","observation_id":"071e7c8f-1ef7-420c-a857-09e5acdcc8af","resolution":{"observed_at":"2026-08-03T08:54:39.216546Z","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":"2026-08-03T08:54:39.317486Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.317486Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:13895d79b1389bc38e459097e459d7cbe7e3c5978cbb541e739e3d6c88279fc3","observation_id":"6b75e0df-60a1-4939-8c18-5bc21ef48460","resolution":{"observed_at":"2026-08-03T08:54:39.317486Z","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":"2026-08-03T08:54:39.444970Z","title":"Reed and B","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.444970Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:70861a0d8c11d45f3571f2bba4d313eb555c3d698a039a1e4100a4e7a946e94e","observation_id":"c4d44c4f-156d-463e-9a3c-23585786f499","resolution":{"observed_at":"2026-08-03T08:54:39.444970Z","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":"2026-08-03T08:54:39.577875Z","title":"Shargorodsky : On the level sets of the resolvent norm of a linear operator, Bulletin of the LMS 40 (2008), 493--504","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.577875Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:9761f858b0f8b016fa1aa044d9f83f7d2ed5049db12e55cdc12d66995c067e2a","observation_id":"ceee39b4-9d28-4e5c-a251-46098914c1cd","resolution":{"observed_at":"2026-08-03T08:54:39.577875Z","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":"2026-08-03T08:54:39.731352Z","title":"Shargorodsky: On the definition of pseudospectra, Bull","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.731352Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:89579e1a9c32c8d3fbd28ea70e21bc758507fd977935a98f793b21aa5b1e693a","observation_id":"197bdd8d-417d-4086-b124-b47444983533","resolution":{"observed_at":"2026-08-03T08:54:39.731352Z","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":"2026-08-03T08:54:39.814043Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.814043Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:db2b1f080b2316f19e83aa0722d615d6d3ae5d414fd243855a85566785b406ed","observation_id":"211f2c35-6820-43b8-ad79-b595b6746d27","resolution":{"observed_at":"2026-08-03T08:54:39.814043Z","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":"2026-08-03T08:54:39.914632Z","title":"Wittig : Spectral Enclosures for Non-Self-Adjoint Operators , Master Thesis, Uni Hamburg & TU Hamburg, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:39.914632Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:9b8b3c0f971533d2b757ed9e5364171b0ba9979c96f95af7703c746c037a9ab0","observation_id":"ace2b508-9448-4b21-9172-776de9f3c1ec","resolution":{"observed_at":"2026-08-03T08:54:39.914632Z","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":"2026-08-03T08:54:40.006243Z","title":"Wittig : Spectral and Pseudospectral Approximation of Finite-Interaction-Range Operators in Doubling Metric Measure Spaces, in preparation","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:40.006243Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:56d0139effa632ace288b14e7038669ef93f02bf65fae88eb47bb62bd287820f","observation_id":"c0ad5fc5-437a-4543-92f6-17dc8f3c3c45","resolution":{"observed_at":"2026-08-03T08:54:40.006243Z","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":"2026-08-03T08:54:40.071646Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-03T08:54:40.071646Z"},"links":{"citing_paper":"/paper/2607.29354"},"observation_digest":"sha256:321cebce1f4e244450c42866646b6fcf475f910f92212d588098ef06097b2433","observation_id":"0b379b38-d397-4c9c-8f5c-4d983e5ee849","resolution":{"observed_at":"2026-08-03T08:54:40.071646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.29354","last_updated":"2026-07-31T12:38:17Z","latest_version":1,"primary_category":"math.SP","snapshot_observed_at":"2026-08-17T12:57:45.251943Z","submitted_at":"2026-07-31T12:38:17Z","title":"Localisation of pseudospectra on discrete groups"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":33},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2607.29354."}