{"as_of":"2026-08-12T13:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1a00463e85271bbc6e0f1fdd869242ae3019a3337cbb9360453a0d2fbbd95e5c","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T22:50:28.277032Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"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/2501.01609/citation-record","integrity":"/paper/2501.01609/integrity","json":"/paper/2501.01609/citation-record.json","paper":"/paper/2501.01609"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T22:50:28.529970Z","title":"On (enriched) left B ousfield localization of model categories, 2007","venue":null,"work_id":"9ab4cef0-6e3d-4d5b-8636-1d4648f7a312","year":2007},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.193237Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:35d9cfbfe03994e138d25bf1d1ec905b3e8d45c54e54cdf9dbb0ef3ff79807aa","observation_id":"21d6c1dc-6651-4874-a564-952a02bc90ba","resolution":{"observed_at":"2026-08-10T22:50:28.534451Z","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":"2026-08-10T22:50:28.520784Z","title":"Handbook of Categorical Algebra","venue":null,"work_id":"b6bf7b5d-9357-4fc0-ba7b-7838e95a4d85","year":1994},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.197119Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:c2470a29a6557452815b208cd9a16bcd663d8a90316169798660460d9e9c6b30","observation_id":"fc67a322-3d65-48d9-b9df-c8edccb7c587","resolution":{"observed_at":"2026-08-10T22:50:28.523634Z","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":"2026-08-10T22:50:28.511941Z","title":"On the homology of non-connected monoids and their associated groups","venue":null,"work_id":"91fb0ec7-d145-4e57-82e7-0b4f707ec109","year":1972},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.200674Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:ba0d48c45101fd2ab31b37f0f9a21d95361e3b0bae3f4b4b0a367c6cfc5c7b53","observation_id":"98b6ed66-7b1b-4034-9a6e-5a9944ee96fa","resolution":{"observed_at":"2026-08-10T22:50:28.515399Z","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":"2026-08-10T22:50:28.503023Z","title":null,"venue":null,"work_id":"2fd441d9-19f8-4281-9ad6-58e995f4556c","year":1980},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.204300Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:1ffc9687efb7aa11548450d28fa2ffdc0672d2701706fc8c03a650b1f038df1a","observation_id":"6746094b-ef15-40a3-acc2-13228ca913e6","resolution":{"observed_at":"2026-08-10T22:50:28.506304Z","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":"2026-08-10T22:50:28.493281Z","title":"Cohomology of braid spaces","venue":null,"work_id":"eab4fe5f-d5af-410b-a0bd-4f5eef128e5b","year":1973},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.209015Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:55e065a84ae1b1b2ab5fa1b1605c27772e56a7bdc3a5afff5ec713862acae7b3","observation_id":"ca9088f8-3532-4110-a7e8-1c29378ee56f","resolution":{"observed_at":"2026-08-10T22:50:28.496625Z","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":"2026-08-10T22:50:28.484228Z","title":null,"venue":null,"work_id":"88e846d4-4214-4873-9d88-4177683bfbf0","year":2022},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.212439Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:1db6cd36b8ba7c0fa6389e70ad61e5162b29ef3b37ac63725bc77700e7834ca9","observation_id":"e6412072-d9b3-4864-a752-7f65990037f8","resolution":{"observed_at":"2026-08-10T22:50:28.487423Z","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":"2026-08-10T22:50:28.476396Z","title":null,"venue":null,"work_id":"4ecac5ed-1045-400a-8c76-0dd862a8b44f","year":2006},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.216176Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:f345e511636fd14c0517b737f9f2c434835596cfad3551e6fcb8c846b02d6443","observation_id":"e047e1d0-2734-4691-b801-7ddb2ffb200c","resolution":{"observed_at":"2026-08-10T22:50:28.478989Z","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":"2026-08-10T22:50:28.468600Z","title":"Cellular spaces, null spaces and homotopy localization , volume 1622 of Lecture Notes in Mathematics","venue":null,"work_id":"d24e5d3e-7465-4711-ad1b-7f8f20fe96ca","year":1996},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.219723Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:5b839a85260b4a8374a4edaf102454e6d7b4346fee22794b61f5d9f994de8591","observation_id":"759f4cf9-d437-42f3-bb06-823eae3c52d9","resolution":{"observed_at":"2026-08-10T22:50:28.471426Z","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":"2026-08-10T22:50:28.460655Z","title":"Iterated bar complexes of E –infinity algebras and homology theories","venue":null,"work_id":"3e4ab78c-1ee6-4c22-b443-c0dde25cfd71","year":2011},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.223231Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:63c897eb51ca47b3832e0c660c03ea70f2624b3cea0d5fe7dbfca46eae54fdbf","observation_id":"80b44968-23c8-4a64-8d95-bfb4bc80441b","resolution":{"observed_at":"2026-08-10T22:50:28.463423Z","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":{"arxiv_id":"1805.07184","last_updated":"2023-12-28T19:50:13Z","snapshot_observed_at":"2026-08-02T04:03:00.932894Z","submitted_at":"2018-05-18T13:01:55Z","title":"Cellular $E_k$-algebras","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.07184","snapshot_observed_at":"2026-08-10T22:50:28.226645Z","title":"Galatius, A","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.226645Z"},"links":{"cited_paper":"/paper/1805.07184","citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:5a4b2f7cf3cca34bb9f7f943c8c61a1a96de04c775a68415cc8de23f15f41d10","observation_id":"9001de15-b3ab-42e2-891a-3bf13598a79e","resolution":{"observed_at":"2026-08-10T22:50:28.226645Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.05620","last_updated":"2025-01-18T21:56:00Z","snapshot_observed_at":"2026-08-12T09:31:29.469052Z","submitted_at":"2020-05-12T08:54:07Z","title":"$E_\\infty$-cells and general linear groups of infinite fields","version":3},"cited_work":{"arxiv_id":"2005.05620","doi":null,"metadata_source":"pith","pith_arxiv_id":"2005.05620","snapshot_observed_at":"2026-08-10T22:50:28.324037Z","title":"$E_\\infty$-cells and general linear groups of infinite fields","venue":"math.AT","work_id":"bcdf65b0-9999-458c-ae71-4bdc002e373d","year":2020},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.230481Z"},"links":{"cited_paper":"/paper/2005.05620","citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:e8fb702fc3ebdecb97fea227eaa91c636b0df96b26bc74897b6a35dd018e25b4","observation_id":"4c7ca3ba-2d2c-4690-9310-2d5fe3e3564c","resolution":{"observed_at":"2026-08-10T22:50:28.329740Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":{"arxiv_id":"1803.11165","last_updated":"2018-03-29T17:18:58Z","snapshot_observed_at":"2026-07-06T06:30:55.970076Z","submitted_at":"2018-03-29T17:18:58Z","title":"Configuration spaces in algebraic topology","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1803.11165","snapshot_observed_at":"2026-08-10T22:50:28.234138Z","title":"Configuration spaces in algebraic topology, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.234138Z"},"links":{"cited_paper":"/paper/1803.11165","citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:e1b6cedf8c0df34d5b27b01a238f1c1ec325f6f4c43071cc80eb3889a7431d8f","observation_id":"8f430fba-b590-4856-890a-6884a1c1f47b","resolution":{"observed_at":"2026-08-10T22:50:28.234138Z","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":"2026-08-10T22:50:28.451791Z","title":"Kadeishvili and S","venue":null,"work_id":"93eb0e3d-2158-4515-bdb3-32cb38469345","year":1998},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.237870Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:58e1bccf0f9f673c7b4d6d337c27b920b9af25087a35a5efabaabe984f6c32fa","observation_id":"0f4bdcd7-d2cb-42f3-865d-cc75102d15e5","resolution":{"observed_at":"2026-08-10T22:50:28.455247Z","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":"2026-08-10T22:50:28.442394Z","title":null,"venue":null,"work_id":"b0879bdc-f671-42f8-8de0-d5995e3c80d7","year":2023},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.241082Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:47ee9cdfbcd31b4b3542c642d85eeff6af5feb0b82d0050e0b5822edc30e001c","observation_id":"67719340-d625-4945-b1e0-75d413a37968","resolution":{"observed_at":"2026-08-10T22:50:28.446020Z","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":"2026-08-10T22:50:28.432705Z","title":"Mirzaii and W","venue":null,"work_id":"597cd9e6-f121-466e-a0fb-ebd6f2bd4b86","year":2002},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.244308Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:ddff0bdd5a816e266a5f078533926a0e930cf1c5715b19a50c3030d73585a687","observation_id":"5c35cdbd-631c-4fd3-85c4-c56aad827e7f","resolution":{"observed_at":"2026-08-10T22:50:28.436200Z","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":"2026-08-10T22:50:28.422629Z","title":"Finite generation of the groups ki of rings of algebraic integers","venue":null,"work_id":"aae68f20-af26-4b9c-a3a2-1911e15c1c27","year":1973},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.247515Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:b36b9f399589ef92702308ceaca93767f6a069fea1baf188bcb4b84ad84a5217","observation_id":"0fd72ff2-6cbf-4dba-b457-0be60d7610fa","resolution":{"observed_at":"2026-08-10T22:50:28.426136Z","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":"2026-08-10T22:50:28.413618Z","title":null,"venue":null,"work_id":"1721e800-4b02-4c3d-9809-bc879668bfeb","year":1992},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.250805Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:e878b83501a5c4c9d92c983d88967ed8636ad07beaa9be8bfc91cd63ee5817fe","observation_id":"e3d8ce93-8e19-4f91-bed9-44ee5047394c","resolution":{"observed_at":"2026-08-10T22:50:28.416752Z","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":{"arxiv_id":"2110.12264","last_updated":"2021-10-23T17:19:47Z","snapshot_observed_at":"2026-08-03T18:08:25.971971Z","submitted_at":"2021-10-23T17:19:47Z","title":"The weight and rank filtrations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.12264","snapshot_observed_at":"2026-08-10T22:50:28.253851Z","title":"The weight and rank filtrations","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.253851Z"},"links":{"cited_paper":"/paper/2110.12264","citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:df2204446761b58950976c29db9fbf4522aeb7553cf668b9f201b5984a24652c","observation_id":"d0b1c4d1-d963-45f9-9b80-451973b9b80c","resolution":{"observed_at":"2026-08-10T22:50:28.253851Z","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":"2026-08-10T22:50:28.403786Z","title":"Randal-Williams","venue":null,"work_id":"4a62918b-0fd4-4beb-b8ca-dd784f47e948","year":2022},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.257471Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:5668d859d7960bcb1524dfabd5c023cd129be7bb885e5be1fb2afad995046c31","observation_id":"0b0c678d-1078-4894-a426-047d91468982","resolution":{"observed_at":"2026-08-10T22:50:28.407429Z","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":"2026-08-10T22:50:28.394335Z","title":"Symmetric spectra","venue":null,"work_id":"6085b673-fa5a-4c5d-8b3b-6f78ecf8c111","year":null},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.260693Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:06e3e407a143c6cc3bd669b4975fe8804a9cc624bab4a86317dfac92ea50c9f7","observation_id":"adaf2b70-a732-4252-86d2-774bc7a9be8c","resolution":{"observed_at":"2026-08-10T22:50:28.397508Z","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":"2026-08-10T22:50:28.384429Z","title":"Categories and cohomology theories","venue":null,"work_id":"847f2157-bc79-4fe5-a3ed-b9b7a6d86a28","year":1974},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.264248Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:f7ce6b85d6b67aea595f0a74eb3398d213ea7a5980139ab92d28d2aa84575c3d","observation_id":"1b5859e6-bb73-446a-838c-b880e3ebbd72","resolution":{"observed_at":"2026-08-10T22:50:28.387751Z","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":"2026-08-10T22:50:28.374015Z","title":"Spherical complexes attached to symplectic lattices","venue":null,"work_id":"6192b225-3073-4a39-a707-df0f6f43026c","year":2011},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.267521Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:e72cf572ee68330a639a2f8d0fb97c9d06ce959666232e4f5b18f0ff8174336f","observation_id":"18be0018-0ce6-4318-a019-a0c28742960d","resolution":{"observed_at":"2026-08-10T22:50:28.377922Z","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":"2026-08-10T22:50:28.363856Z","title":"Waldhausen","venue":null,"work_id":"ae02d168-3a90-40bd-9b42-49ffc4505771","year":1983},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.270702Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:55321ee900942233a643ef6b24dfa50f15f2d90c8fdd54bd1bfa0a5cf25c3817","observation_id":"f00673dd-d4ff-47ad-9f06-022ea651125d","resolution":{"observed_at":"2026-08-10T22:50:28.367308Z","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":"2026-08-10T22:50:28.354877Z","title":null,"venue":null,"work_id":"5d59a224-450c-401f-8938-5b2c4ad14a37","year":2013},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.273995Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:e0f3a5dc33a3a46aa48d546b2ec66b99a1977ffb3a06bd60ce9fd98e01f35c3a","observation_id":"d22c007e-d6d7-4a71-8d62-aca64a53f254","resolution":{"observed_at":"2026-08-10T22:50:28.357846Z","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":"2026-08-10T22:50:28.345729Z","title":null,"venue":null,"work_id":"2ceee899-7a91-4133-b8f0-c6a740a606a4","year":1995},"citing_paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-10T22:50:28.277032Z"},"links":{"citing_paper":"/paper/2501.01609"},"observation_digest":"sha256:5acab3edcc77457fa52ec731e3e04acc66ae3ee3e3d055ba8d44f08b852a6df8","observation_id":"6fa9504e-264c-45a2-a968-b854101e63ec","resolution":{"observed_at":"2026-08-10T22:50:28.348693Z","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"}}],"paper":{"arxiv_id":"2501.01609","last_updated":"2025-01-03T03:06:30Z","latest_version":1,"primary_category":"math.KT","snapshot_observed_at":"2026-08-11T02:13:20.891306Z","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":14},"total_outbound_references":25},"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 12 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2501.01609."}