{"as_of":"2026-08-22T06:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4a49728ad02d2e5fc5871d17c6db6056714b3b88d8bca3594b01917a50a13939","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:11:59.287264Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2508.17603/citation-record","integrity":"/paper/2508.17603/integrity","json":"/paper/2508.17603/citation-record.json","paper":"/paper/2508.17603"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.141628Z","title":"The spectrum of prime ideals in tensor triangulated categories","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.141628Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:8e826d5760129cf4b521ab55cdfb9340e13377b3bd58632d63205a5b050f3dca","observation_id":"8f0012b3-4836-4cca-b320-6f7ad8a13c93","resolution":{"observed_at":"2026-08-15T17:11:59.141628Z","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":"2026-08-15T17:11:59.147381Z","title":"Spectra, spectra, spectra -- tensor triangular spectra versus Z ariski spectra of endomorphism rings","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.147381Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:a60adc1418f22da49686ecb833d3df66587a26e7457a4ad9d35bbae78220cf04","observation_id":"4f48ac99-d794-4747-b842-b861f180c329","resolution":{"observed_at":"2026-08-15T17:11:59.147381Z","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":"2026-08-15T17:11:59.152634Z","title":"On the surjectivity of the map of spectra associated to a tensor-triangulated functor","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.152634Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:ce02a3fc254153b6ad72409da928ca1e1ed613a3313342441fe12c15c3528eed","observation_id":"edd0d7dc-2391-4269-a8fc-87b21ab7e7a2","resolution":{"observed_at":"2026-08-15T17:11:59.152634Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.728206Z","title":"Descent in tensor triangular geometry","venue":null,"work_id":"9543b3ac-fbe4-4f9e-9f62-ad605321d2f9","year":2024},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.157815Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:3b83842b2361e8c41e8f5f62d6602c48de1e90c49b889d5365490cecd6ad77f2","observation_id":"4c00eb66-9ad0-4ed1-a854-70b255c2fa12","resolution":{"observed_at":"2026-08-15T17:11:59.732692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.02308","last_updated":"2023-05-03T17:54:53Z","snapshot_observed_at":"2026-08-16T15:35:53.637606Z","submitted_at":"2023-05-03T17:54:53Z","title":"Descent in tensor triangular geometry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.02308","snapshot_observed_at":"2026-08-15T17:11:59.163377Z","title":"Cosupport in tensor triangular geometry","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.163377Z"},"links":{"cited_paper":"/paper/2305.02308","citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:1b9911c40d10958739bd39acdceaf4f2596b95f3d90a26cf1fbaa239cf09a9e4","observation_id":"06269341-1104-467d-b43b-3f3dd4f35818","resolution":{"observed_at":"2026-08-15T17:11:59.163377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.712750Z","title":"On surjectivity in tensor triangular geometry","venue":null,"work_id":"8c9a67f5-5bf3-407b-b505-b7190f1d3904","year":2024},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.169278Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:ecf183c73d18419d64507196549352108ebefa2504037ad425539a93c7d825c7","observation_id":"c4e199b5-9af8-40b1-88b4-3842bf9d5c2a","resolution":{"observed_at":"2026-08-15T17:11:59.717690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.175171Z","title":"Grothendieck-- N eeman duality and the W irthm\\\"uller isomorphism","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.175171Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:e544b53664ca2e45f62047def95d7c8f5da3f9e7c9b8c1ab2e23821dab15beb6","observation_id":"519c5201-6930-422c-a059-0f8d29da5217","resolution":{"observed_at":"2026-08-15T17:11:59.175171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.684240Z","title":"Stratification and the comparison between homological and tensor triangular support","venue":null,"work_id":"48b23683-e5d7-443d-bffc-e4124c6cab58","year":2023},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.180723Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:48316824448b2fb6288d83c8ea0998cb00a8c4dcb111d3d9c013f94ee3a7c78d","observation_id":"0a6686d8-0245-4a29-ac07-b5ec1c2425f5","resolution":{"observed_at":"2026-08-15T17:11:59.690598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.185457Z","title":"Stratification in tensor triangular geometry with applications to spectral M ackey functors","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.185457Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:4e80e7d0fe02e262ff3b4d208becb71b0fe39b07839bdef9d9a480598dd7bc84","observation_id":"5fc2f975-713d-4046-b0af-c13e7c80bdc5","resolution":{"observed_at":"2026-08-15T17:11:59.185457Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.14761","last_updated":"2024-11-22T06:48:41Z","snapshot_observed_at":"2026-08-17T21:00:59.598085Z","submitted_at":"2024-11-22T06:48:41Z","title":"Perfect complexes and completion","version":1},"cited_work":{"arxiv_id":"2411.14761","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.14761","snapshot_observed_at":"2026-08-15T17:11:59.361086Z","title":"Perfect complexes and completion","venue":"math.AC","work_id":"8c866071-3851-42d6-934b-d819c334094f","year":2024},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.189816Z"},"links":{"cited_paper":"/paper/2411.14761","citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:95d04c0c800a0ea5ad5769c3d35c52c7cf37cc28670d989097eba1154f260677","observation_id":"9f33582d-73bc-419a-91f5-e320a9cab0c4","resolution":{"observed_at":"2026-08-15T17:11:59.366656Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.654177Z","title":"Does full imply faithful? J","venue":null,"work_id":"17642082-6e81-40ea-9a10-711a825424bc","year":2013},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.194857Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:544833d3eeaca0461f9f22a942ebf0ece288893ba7218d6ec71f253d9cf47c93","observation_id":"e5ce0715-ec4f-4518-9895-d532efa4f13d","resolution":{"observed_at":"2026-08-15T17:11:59.659533Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.199969Z","title":"Spectral spaces , volume 35 of New Mathematical Monographs","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.199969Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:b3d103129c8a3df33d95e8d326d502437436a26bc4a5d62a08e0a7ff8bed16e8","observation_id":"a0ada757-017d-405c-8369-e84b9474f5e3","resolution":{"observed_at":"2026-08-15T17:11:59.199969Z","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":"2026-08-15T17:11:59.207592Z","title":"Commutative algebra , volume 150 of Graduate Texts in Mathematics","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.207592Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:52775017a1ad542273632ece1cc8f58d4baa03706371814cc47659ed3d2d6a11","observation_id":"a4490cbd-3ab4-4337-97a8-84edde0b08f3","resolution":{"observed_at":"2026-08-15T17:11:59.207592Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.612566Z","title":"Isomorphisms between complexes with applications to the homological theory of modules","venue":null,"work_id":"a20acc4d-ea30-425d-aa82-1f65cd4aa026","year":1977},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.212691Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:3cbeebcbba41dc74896060d1cdf7986c3cd06fdd9f6cd0e7a00927b1d7609425","observation_id":"456a6545-4aff-41ac-8c2c-23ab95bd6a72","resolution":{"observed_at":"2026-08-15T17:11:59.617783Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.594763Z","title":"General lattice theory , volume 75 of Pure and Applied Mathematics","venue":null,"work_id":"b5ebed93-c11c-46c7-8d96-85e754d2d1cf","year":1978},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.217614Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:236e33fe252a6ba23003a6a59f3bd5907729faeaabc708d7eaa03f1d60e0e18e","observation_id":"a6f67da5-1ec3-4322-9fa0-c3bc4255849d","resolution":{"observed_at":"2026-08-15T17:11:59.600395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.578496Z","title":null,"venue":null,"work_id":"18dfcf98-74a7-42fc-ae48-eb8bc313819f","year":1952},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.222515Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:6f4090fc485f88e1b6bad30180b301cb68f79768cb13c3faf26a1ead9b8b776a","observation_id":"21c2d795-b0aa-4573-b3be-7139ebbfcd4c","resolution":{"observed_at":"2026-08-15T17:11:59.583287Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.227363Z","title":"Hochster","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.227363Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:8cabb3aa372df08631c0ac5e3614c9f8b3cebc1930571c88af3f413d1c50030a","observation_id":"957da6b0-3103-4d0d-a591-25b7616230d7","resolution":{"observed_at":"2026-08-15T17:11:59.227363Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.551512Z","title":"Johnstone","venue":null,"work_id":"37ce366f-ec8c-43ac-b596-ca1f6b3b7649","year":1982},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.232267Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:40997956996f0f313f9748df74eaf443607f81062e74d29c5c330e5183dfb045","observation_id":"2d23bea7-5433-4727-ad08-1b8061b7a27c","resolution":{"observed_at":"2026-08-15T17:11:59.556689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.237170Z","title":"Hochster duality in derived categories and point-free reconstruction of schemes","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.237170Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:1c271c319199424020fd04bfed92ca79e279693b851afb45bdb51e543278aa85","observation_id":"05d860aa-428a-4aba-b78f-b350343faee8","resolution":{"observed_at":"2026-08-15T17:11:59.237170Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.523802Z","title":"Derived categories, resolutions, and B rown representability","venue":null,"work_id":"b37496ff-cb59-4a03-bd65-8195d4009f48","year":2007},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.241921Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:27468ac5d7722d4df39ffbecbd2113660de934f9d8218c1be33067a996c38e90","observation_id":"d194c1d8-f647-4600-92eb-043e1a827b08","resolution":{"observed_at":"2026-08-15T17:11:59.528986Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.247189Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.247189Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:8d6f1da149c69bf773e667fec0fefe1ae36a90a06825f450e0f22eaa303e7fe5","observation_id":"8b1671e0-5121-4908-809b-b7b74f4aaa30","resolution":{"observed_at":"2026-08-15T17:11:59.247189Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:11:59.492173Z","title":null,"venue":null,"work_id":"de33dbf0-a7c5-4358-9b62-e932845458fd","year":2021},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.251884Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:05b4523022deeff695a4f3979894ab8f6d33c01a21934a7356a4b26c755cdec8","observation_id":"7790eeff-a095-42f7-aa66-237f8a0a018a","resolution":{"observed_at":"2026-08-15T17:11:59.498072Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.468856Z","title":"Connectedness of the B almer spectrum of the right bounded derived category of a commutative N oetherian ring","venue":null,"work_id":"40475efb-bfa3-47af-98ed-92ad4ee926fe","year":2019},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.256574Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:662003e1771ea3a8cfd6ac970474da3a8506b88b94256e056c3544886ac0a477","observation_id":"277916a4-4ff3-48d6-8c46-65bb4ddd89b5","resolution":{"observed_at":"2026-08-15T17:11:59.474674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.452666Z","title":"Thick tensor ideals of right bounded derived categories","venue":null,"work_id":"a99aabe6-c646-48cf-988e-2a1b6b74d0c0","year":2017},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.261827Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:dbb4b0ca41ef4b38854c096466e91a05a0f4fc4ceadb982afd6fb6be8166c19c","observation_id":"f975e776-1d8c-4459-8690-bcf3ce3f470a","resolution":{"observed_at":"2026-08-15T17:11:59.457412Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.266766Z","title":"The connection between the K -theory localization theorem of T homason, T robaugh and Y ao and the smashing subcategories of B ousfield and R avenel","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.266766Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:60717bc843f26e6c6bee09400087c6d50146773a27942b6cf1d0528b4662042c","observation_id":"1b0bfe04-5aee-462f-9524-57090eb86ff9","resolution":{"observed_at":"2026-08-15T17:11:59.266766Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.09361","last_updated":"2024-12-12T15:28:16Z","snapshot_observed_at":"2026-08-16T13:00:09.464806Z","submitted_at":"2024-12-12T15:28:16Z","title":"Arithmetic localisation and completion of spectra","version":1},"cited_work":{"arxiv_id":"2412.09361","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.09361","snapshot_observed_at":"2026-08-15T17:11:59.330928Z","title":"Arithmetic localisation and completion of spectra","venue":"math.AT","work_id":"28ab9317-ef65-4767-bbbf-836bd90fd4ea","year":2024},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.271723Z"},"links":{"cited_paper":"/paper/2412.09361","citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:a4d0626b7154d4651457c3bac1608fe4dbcd8cc7004fd884b244436c69134606","observation_id":"fec74cef-316a-4c3b-a4f6-d903d28af6cb","resolution":{"observed_at":"2026-08-15T17:11:59.339765Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.423435Z","title":"SGA 6\\,: Th\\'eorie des intersections et th\\'eor\\`eme de R iemann- R och , volume 225 of Lecture Notes in Mathematics","venue":null,"work_id":"671e7e22-09a9-4c95-877c-172a8e01ece6","year":1971},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.276682Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:9b6de5713efa2fb05be36795dd26155257eb62f5a54f3d3929f908dd777a505d","observation_id":"242db874-8716-4dea-b70a-c6f164cb5f78","resolution":{"observed_at":"2026-08-15T17:11:59.429521Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-15T17:11:59.281901Z","title":"S tacks P roject","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.281901Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:ee7e0851ad3d6059506ddf3c4cc9c2505edddb293dafa69bc51c820c16ba1560","observation_id":"99d540c5-099a-469c-afa2-458b3adfa459","resolution":{"observed_at":"2026-08-15T17:11:59.281901Z","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":"2026-08-15T17:11:59.287264Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T17:11:59.287264Z"},"links":{"citing_paper":"/paper/2508.17603"},"observation_digest":"sha256:9a080699f7dae1e8783545bb2760d4b612b0c9677489a18b51ef8d5d4d5b45b1","observation_id":"217f300f-1780-4617-a8bb-76ee3e123821","resolution":{"observed_at":"2026-08-15T17:11:59.287264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2508.17603","last_updated":"2025-08-25T02:06:46Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-17T18:33:55.192789Z","submitted_at":"2025-08-25T02:06:46Z","title":"The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":16,"verified_exact":1,"verified_fuzzy":11},"total_outbound_references":29},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2508.17603."}