{"as_of":"2026-08-13T05:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:256cbe3fda554b555779637eb04f5f5b9109d8740afc41526d81b1a3cfbd91ef","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T13:32:53.734897Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2411.16309/citation-record","integrity":"/paper/2411.16309/integrity","json":"/paper/2411.16309/citation-record.json","paper":"/paper/2411.16309"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T13:32:54.076688Z","title":"Balmer, The spectrum of prime ideals in tensor triangulated categor ies, J","venue":null,"work_id":"04949406-c43d-4694-9eec-366c57e2aef6","year":2005},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.622042Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:c0c0ecee11135c470f3dc9be51d4c76398d1e894afa85d0bb64299603829c540","observation_id":"66636487-070d-4f5b-9b70-ffc1e5737db2","resolution":{"observed_at":"2026-08-12T13:32:54.079557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.068919Z","title":"Borceux and G","venue":null,"work_id":"b4b11e98-f447-4e0c-ad51-b8f0a9b93df7","year":1987},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.625760Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:3a2f951963a2691f270a36a1b19d98207b53389882f40e224e6eeb5166d21324","observation_id":"93771135-2b52-43f5-a357-0c76bd7a9826","resolution":{"observed_at":"2026-08-12T13:32:54.071767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.061030Z","title":"Brandenburg, Rosenberg’s reconstruction theorem, E xpo","venue":null,"work_id":"e8632124-8f0f-4aaf-8039-96ebde3ef57f","year":2018},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.628811Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:9343a4f2b225c6183f81c9be81cf221d2369080657e246c520769feaca32a3af","observation_id":"bb68b5fc-c6c1-4601-9095-e3b4f732b167","resolution":{"observed_at":"2026-08-12T13:32:54.063949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.052818Z","title":"Brenner, Decomposition properties of some small diag rams of modules, in Symposia Math- ematica, Vol","venue":null,"work_id":"1c80ad5d-23b0-4cb4-8919-9f995ec31f6c","year":1972},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.631834Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:9d3a2844488a00d6bd6002f6e2963d02368d508d4f6ec7f106bb240878f136e0","observation_id":"ec3312dd-1a7e-48c9-ab6a-d8f3e8677a33","resolution":{"observed_at":"2026-08-12T13:32:54.055748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.045034Z","title":null,"venue":null,"work_id":"2c667ad7-40ac-4d1d-8414-896a425b0d7f","year":1959},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.634919Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:0ec3884ca7afd0c33915715053e93c39529c37ac47140fa3d9aa063db0f93f5b","observation_id":"956ee76e-5cfe-41a3-99f7-2115cb00256a","resolution":{"observed_at":"2026-08-12T13:32:54.047834Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.037012Z","title":"Crawley-Boevey, Locally ﬁnitely presented additive categories, Comm","venue":null,"work_id":"251e8486-e53f-4e47-b051-54880a2834bb","year":1994},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.638189Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:90bca2b225540c9ab2dc83ad14c8bf0f397537b35db197fde81a254ff05c272e","observation_id":"20bc3671-0a4e-49ba-bb8d-c1101bb20757","resolution":{"observed_at":"2026-08-12T13:32:54.039891Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.028287Z","title":"Crawley-Boevey, Inﬁnite-dimensional modules in the representation theory of ﬁnite- dimensional algebras, in Algebras and modules, I (Trondheim, 1996) , 29–54, CMS Conf","venue":null,"work_id":"10dea106-7add-4a18-b48d-5e13601ae314","year":1996},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.641422Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:e065aa2e9b40c36cb33202e11e165d8bdd772fb2bfaf27a6ae300b3c980badb5","observation_id":"1bc3b2a2-b50c-454e-8f9c-0aeb06d872f4","resolution":{"observed_at":"2026-08-12T13:32:54.031890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.020309Z","title":"Dauns, Module types, Rocky Mountain J","venue":null,"work_id":"42f05b68-53a9-4a87-9f8f-2dc95f229da5","year":1997},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.644311Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:84230ac2fee34aeecae7df95c45a9235718153855a858e56a84703666821baec","observation_id":"497bfde5-4c66-46b2-b3e3-27890982bd93","resolution":{"observed_at":"2026-08-12T13:32:54.023129Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.012232Z","title":null,"venue":null,"work_id":"9cdb3be5-b9c6-403d-bb6a-9dd37c379512","year":2019},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.647282Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:122d35fe258a6102a84e36199ac56a2d08bd8a9bcdd5fcf42343c3943a62afd5","observation_id":"03261a74-e0e4-4ee6-be62-16183e377391","resolution":{"observed_at":"2026-08-12T13:32:54.015148Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:54.004203Z","title":"Facchini, Spectral categories and varieties of prea dditive categories, J","venue":null,"work_id":"d6b86b03-0e4d-46c2-b61c-b5238eca5260","year":1983},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.650163Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:1370dfc72a4eff7f1b714130bba9b37abcb85a46766f3cf19ecfdb4fb805cc51","observation_id":"0cc670b8-57bc-4c41-9627-4ca3932fc249","resolution":{"observed_at":"2026-08-12T13:32:54.007210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.995973Z","title":"Facchini, Decompositions of algebraically compact modules, Paciﬁc J","venue":null,"work_id":"058bf4b6-722d-47ff-9ba4-870ac4b6603b","year":1985},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.653115Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:54ea4e161d3b278a20f46e8ac6103f65802b51345e5d82074bb1c8aad3b9e6d7","observation_id":"f5153ce3-8040-4534-9038-078ff586128b","resolution":{"observed_at":"2026-08-12T13:32:53.999003Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.988037Z","title":"Gabriel, Des cat´ egories ab´ eliennes, Bull","venue":null,"work_id":"429d077e-6144-455f-8bf9-3c94d0e53b78","year":1962},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.655879Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:cb4386d315ffde330d97e97782d6fc275c9459fd2267274b91a6c6e104597f12","observation_id":"3714cfad-7dab-481e-a2a7-a2b1e2a5372e","resolution":{"observed_at":"2026-08-12T13:32:53.990869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.980059Z","title":"Gabriel and U","venue":null,"work_id":"ff02060e-1794-4005-bfe8-bff513ef0bb5","year":1966},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.658643Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:5c717dc3d5a508efafc0deffb8d415bff790055a31a3c4cdcee280289f87c4e9","observation_id":"ac2848c8-f335-437a-accd-0e02d66d4995","resolution":{"observed_at":"2026-08-12T13:32:53.982845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.971624Z","title":null,"venue":null,"work_id":"6e4caff3-2169-42cf-82b7-e5e141c3b18d","year":1986},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.661538Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:cd4d434dc6d64c257d3915833d329518e667ee2e3d2beea4a6effa4ee2345d71","observation_id":"299b865b-80ee-417e-8ba3-2a1c852136c2","resolution":{"observed_at":"2026-08-12T13:32:53.974445Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.963793Z","title":null,"venue":null,"work_id":"2662f552-7895-4511-9cec-4b492d7f60f4","year":1979},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.664315Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:94f06344577c98e52b281047277be55b7a318aeab2916f375bdd4c9094025f42","observation_id":"5170b3e2-426b-4815-ae17-3dd6ec92aa9d","resolution":{"observed_at":"2026-08-12T13:32:53.966507Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.955662Z","title":null,"venue":null,"work_id":"af711798-06a9-49d7-aebf-a049160ad004","year":1976},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.667221Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:74f1a4564a8a4a87c682d9222829309f1bbe1a1c8499da9ad3dcf63ccfa797d1","observation_id":"335d97d8-6b93-4f6f-8613-b46cc699a67f","resolution":{"observed_at":"2026-08-12T13:32:53.958603Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.947553Z","title":null,"venue":null,"work_id":"1f665ad1-12a5-4466-b80b-42b0393c3911","year":2005},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.669946Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:1059734106b60fd085d41d94abbea48a9b6ef80c9271254ee3b945802f15a3ef","observation_id":"874852a4-0233-4beb-a2df-a0a122bacf8e","resolution":{"observed_at":"2026-08-12T13:32:53.950478Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.939604Z","title":"Gruson and C","venue":null,"work_id":"0444a032-4034-49be-849b-e6c4550b37ff","year":1980},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.672794Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:fb5d5da60335d37444a02c24ba952b8a1ccab1a2ff83571e8a07c2151cc126a0","observation_id":"67b64a33-a4b0-4cfe-b198-d808a681ab19","resolution":{"observed_at":"2026-08-12T13:32:53.942386Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.931686Z","title":"Herzog, The Ziegler spectrum of a locally coherent Gr othendieck category, Proc","venue":null,"work_id":"d4d09f16-8cfe-488e-a5f4-42217919c09e","year":1997},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.675589Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:145a2368d4e7a5ae94a87f50dc2e052ce9de145dba9ebac1d8f2a9b0d5115b8d","observation_id":"3768277d-d102-4b26-878a-ea156dc7a896","resolution":{"observed_at":"2026-08-12T13:32:53.934594Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.923795Z","title":null,"venue":null,"work_id":"3389d4c3-38ff-4ee1-93e9-dd6256d9c0cb","year":1989},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.678504Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:3595bf076bb3fca6aad18f8df46d72ec6b520e964d8bd64425a005d62f1c4688","observation_id":"bf0cdcac-dc7d-47ed-9d92-8c25e0f5c546","resolution":{"observed_at":"2026-08-12T13:32:53.926613Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.915896Z","title":null,"venue":null,"work_id":"2124d7d5-4763-4f1d-bd60-5c9c80a68a38","year":1982},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.681559Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:6b96bd3d51b39223698bf7e75becd612d0217887ac4d253d36a3fad340e157ee","observation_id":"41809cbd-33c7-4aae-8a6f-311a7fd6d266","resolution":{"observed_at":"2026-08-12T13:32:53.918641Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.907852Z","title":"Kanda, Classiﬁcation of categorical subspaces of lo cally Noetherian schemes, Doc","venue":null,"work_id":"8004d0d9-46d2-47cd-8287-6bb26d533d9a","year":2015},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.684373Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:4947da971960121ee2e6ddd8a17ca9d99e4d3fcbd6d6bd4c411ebda25e3c1e56","observation_id":"18d83eac-3f1a-425e-8fb6-cf56bb94bf3c","resolution":{"observed_at":"2026-08-12T13:32:53.910713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.899741Z","title":"Kaplansky, Projections in Banach algebras, Ann","venue":null,"work_id":"703103d0-5226-42af-8f7e-67d4cc7445d6","year":1951},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.687358Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:6f377b40ab25c0508ee5b5279380659184af1c06ded3bdb5f90cb51b94f3f9d7","observation_id":"a34b7bed-db76-4da8-ae88-e0a651d3078c","resolution":{"observed_at":"2026-08-12T13:32:53.902627Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.891815Z","title":"Krause, The spectrum of a locally coherent category, J","venue":null,"work_id":"230dcf17-8823-4995-9ba9-0dfbbceaa806","year":1997},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.690189Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:09d63acfc048a85ed46cd2ffe13f5a63c333315c31544f145dd80c7fc49b78df","observation_id":"f46e8db3-361c-4232-8e92-476f6f2493b5","resolution":{"observed_at":"2026-08-12T13:32:53.894737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.883618Z","title":"Krause, Exactly deﬁnable categories, J","venue":null,"work_id":"c766d04e-83ff-4249-8bbe-d7238796f5c7","year":1998},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.692943Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:4e3d27d6d577173b8941cb967c361db354d09255c9eaa9a5cdccf541c8e84f25","observation_id":"47e44b1e-3179-4ab3-92ed-8a389b158e12","resolution":{"observed_at":"2026-08-12T13:32:53.886471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.875336Z","title":"Krause, The stable derived category of a Noetherian s cheme, Compos","venue":null,"work_id":"f659b724-46c0-4441-945a-873f810df2fb","year":2005},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.695714Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:86ffe03bf773c727c7305a749ed20bd1d042ca3b104a9dd7971641348187d63e","observation_id":"e5198b82-f506-4855-8747-a5a987151f56","resolution":{"observed_at":"2026-08-12T13:32:53.878473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.867024Z","title":"Krause, Homological theory of representations , Cambridge Studies in Advanced Mathe- matics, Cambridge University Press, 195, Cambridge, 2022","venue":null,"work_id":"dd7aa8cb-8b2e-4e83-b187-c320c161f89a","year":2022},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.698291Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:69fcdcf636a90696b876f20bd87a87bf328eddb215e904b5eb472d8188d92e5b","observation_id":"d2610686-7dbe-4d52-920e-454f762f7c84","resolution":{"observed_at":"2026-08-12T13:32:53.870092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.858749Z","title":"Matsui and R","venue":null,"work_id":"e5ac43fa-ea5b-471c-9e0b-e7e34734dbf0","year":2022},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.701121Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:d5076b70f29496676a01659e6c561e66dbabdba73da93f64fa97ba162d36dafb","observation_id":"190b8aad-fcec-4b86-b131-b80413ad9b2c","resolution":{"observed_at":"2026-08-12T13:32:53.861644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.850843Z","title":null,"venue":null,"work_id":"2495f771-4d59-4476-8561-9bb9040fc011","year":1936},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.703995Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:97eea1cb893c180c75eb033fc5e677e031518fb49d50afb68c00c339c081c8cc","observation_id":"aa74a0b7-631e-405c-a831-cb0f2b807895","resolution":{"observed_at":"2026-08-12T13:32:53.853617Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.842550Z","title":"Neeman, The chromatic tower for D(R), Topology 31 (1992), no","venue":null,"work_id":"beb128ef-9d2c-4889-b8f4-a741145b0530","year":1992},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.706895Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:67dee112a507bb0298e8725103ecaec4f7eb748fea87131f52d0dc2b299c9f2d","observation_id":"7a270dbd-2530-491f-a11c-bbd554f4c375","resolution":{"observed_at":"2026-08-12T13:32:53.845665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.834463Z","title":"Prest, Model theory and modules , London Mathematical Society Lecture Note Series, 130, Cambridge Univ","venue":null,"work_id":"e9af0716-55e1-4812-a4ef-92f9aeed8e71","year":1988},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.709507Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:75e480d0717736286cb723936bcebadbae062eacfe4897a3f5c9af6d699f7269","observation_id":"7f17f478-1fef-4149-b3d1-e63fca3d571e","resolution":{"observed_at":"2026-08-12T13:32:53.837462Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.826146Z","title":"Prest, Purity, spectra and localisation, Encyclopedia of Mathematics and its Applications, 121, Cambridge Univ","venue":null,"work_id":"737b300e-929f-49df-a959-74680553d82b","year":2009},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.712137Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:a7129f47fa97a6e3f771c109d17beab1d507610a4123d3eb79ed9cdb725ce859","observation_id":"49be17c6-43ca-498b-807f-3651fff547ea","resolution":{"observed_at":"2026-08-12T13:32:53.829303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.816889Z","title":"Roos, Locally distributive spectral categories and strongly regular rings, in Reports of the Midwest Category Seminar , 156–181, Lecture Notes in Math., No","venue":null,"work_id":"69efd061-31e6-44a9-ba62-4b0da5fac59b","year":1967},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.714760Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:c5336b9480343249a6e1bddaa50bee4523c48c30be1c5821e4054b7345ee3b97","observation_id":"9818270d-f7c1-440a-8a20-0e34d19e4df2","resolution":{"observed_at":"2026-08-12T13:32:53.820328Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.808145Z","title":null,"venue":null,"work_id":"69d7c73b-a37b-4728-b4ab-f806bf94d668","year":1998},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.717702Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:fc32310752e1be4e08a79e3a143b12ef8e12cba655b554ee4cbee21970b8feee","observation_id":"ad4cbcf9-3699-45e6-81b2-c8102008bc8e","resolution":{"observed_at":"2026-08-12T13:32:53.811083Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.798719Z","title":null,"venue":null,"work_id":"ac6bb35a-ed65-4357-a284-b71063c9d78c","year":1995},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.720501Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:a5b80b436a7d8f3430325f1b0ea550408de769beeb3b93adfea62490f0efd501","observation_id":"1f9e25e6-c4fa-432b-9266-0bc6d89ffc1a","resolution":{"observed_at":"2026-08-12T13:32:53.802169Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.789576Z","title":null,"venue":null,"work_id":"d6141a88-beef-4265-94e4-61fca67abcb0","year":1975},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.723437Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:e9013b997968c96886b56b928889cf3bbff7dff66bf70dae2b40e0df0f53d89a","observation_id":"e79596ce-0e17-4b0f-a485-fd17c18400f6","resolution":{"observed_at":"2026-08-12T13:32:53.792663Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.781154Z","title":"Stevenson, Localizing subcategories of Grothendie ck categories, Preprint, 2024","venue":null,"work_id":"eff2894c-daeb-4a7a-aec2-22a0cb562264","year":2024},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.726610Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:4db89544fcab48779cb8f3945ef4eb2ae5e78c01b6a6d03db2d45619048cc161","observation_id":"c337a072-f7c7-477d-85d6-e0463b816f8e","resolution":{"observed_at":"2026-08-12T13:32:53.784021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.772569Z","title":"Takahashi, On localizing subcategories of derived c ategories, J","venue":null,"work_id":"63028ef6-bc33-4b20-8fc3-68992936574c","year":2009},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.729554Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:0e79b8773b3804e6d75088fd14d125266e12a028df4144dd3cb2445b8c8f2fd6","observation_id":"698dfb3b-b8de-4393-88a8-40caebfc018a","resolution":{"observed_at":"2026-08-12T13:32:53.775401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.764035Z","title":"W u and X","venue":null,"work_id":"b39579ff-f6e8-4d88-a7a8-d3eec99fb98f","year":2024},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.732187Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:d461da73420c5f5ecb0025d58d19fdb5faf5f2664b5b7e4d2e8b6f61344d407b","observation_id":"7bd17eab-be9b-4ee7-ab63-bbd728c5e135","resolution":{"observed_at":"2026-08-12T13:32:53.766950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:32:53.753839Z","title":"Ziegler, Model theory of modules, Ann","venue":null,"work_id":"8825a2ff-cb6a-47f0-9b40-20227b261033","year":1984},"citing_paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-12T13:32:53.734897Z"},"links":{"citing_paper":"/paper/2411.16309"},"observation_digest":"sha256:108756acc8d8e84b3aa5dd0a78690b49c6df3a8a014e39bb4fefd1d5d897912f","observation_id":"d767b580-1926-461b-b688-52484af1a840","resolution":{"observed_at":"2026-08-12T13:32:53.758291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.16309","last_updated":"2024-12-10T18:22:47Z","latest_version":2,"primary_category":"math.CT","snapshot_observed_at":"2026-08-12T23:06:55.561128Z","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":0,"verified_fuzzy":28},"total_outbound_references":40},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2411.16309."}