{"as_of":"2026-08-13T03:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6f83cac712c99bdd03269a1a1f42b77de52d6ccfed2b2f9f1c26e9833e26d6b8","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T21:19:25.653001Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T16:32:20.499768Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-01T21:36:15.800308Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"cited_work":{"arxiv_id":"2509.08144","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.08144","snapshot_observed_at":"2026-07-01T21:36:15.800308Z","title":null,"venue":null,"work_id":"8045523e-1a9c-4fc7-aa31-da9c32e21a46","year":null},"citing_paper":{"arxiv_id":"2606.01093","last_updated":"2026-05-31T08:25:31Z","snapshot_observed_at":"2026-08-11T08:55:37.263227Z","submitted_at":"2026-05-31T08:25:31Z","title":"On the category of modules over bands: relative schemes, hyperring schemes and proto-exactness","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"cited_paper":"/paper/2509.08144","citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:5c69c98c42ee6458ada23053d08de9ff6167845e2a722b54a3d6949d3477bb2a","observation_id":"146a7d6b-318e-4f66-9c0e-0558193ae619","resolution":{"observed_at":"2026-07-01T21:36:15.802116Z","resolver_source":"arxiv_id","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"}}],"links":{"evidence":"/evidence","html":"/paper/2509.08144/citation-record","integrity":"/paper/2509.08144/integrity","json":"/paper/2509.08144/citation-record.json","paper":"/paper/2509.08144"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:19:26.258887Z","title":"Slope filtrations","venue":null,"work_id":"0c876e20-bf03-47e2-b015-c7cb6434268f","year":2009},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.099255Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:4f8b2fbc964d8ef9fad271b61eff7ec1a14b70d3fbccaf644e97f455eb431721","observation_id":"4ea5abc1-bd41-4db7-b09d-7ec5793dadd6","resolution":{"observed_at":"2026-08-04T21:19:26.263718Z","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":"2026-08-04T21:19:26.242671Z","title":"Vectors of matroids over tracts","venue":null,"work_id":"027dfb38-2534-4b38-a685-b560345fabe5","year":2019},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.216637Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:d6a1ea073e8b51e61c16d5680a2cfdef6a440423000f025f055862cd5d000931","observation_id":"9582665d-70a1-4715-9a17-4c5b78f781ff","resolution":{"observed_at":"2026-08-04T21:19:26.249855Z","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":"2026-08-04T21:19:26.225860Z","title":"Matroids over partial hyperstructures","venue":null,"work_id":"cb6757ba-30eb-441b-8ae9-5d93896d6b9c","year":2019},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.281278Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:c215c83aa802efb0ab1c7bac2393a2b3db006f67573ba4eb6c0c28e4065ae46e","observation_id":"c7dc4757-4d31-424f-88a9-5384487c6b90","resolution":{"observed_at":"2026-08-04T21:19:26.231350Z","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":"2026-08-04T21:19:26.211182Z","title":"Axioms for infinite matroids","venue":null,"work_id":"b778f84f-7683-4181-8f51-ecee8e3ee661","year":2013},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.327222Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:531b3326305bac13952f3475318d19cf6861c44ff8e42cd43639d96ae0a15653","observation_id":"895b691e-b9e9-46da-89f2-8682b481fd7e","resolution":{"observed_at":"2026-08-04T21:19:26.216361Z","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":"2026-08-04T21:19:26.198070Z","title":"New building blocks for F _1 -geometry: B ands and band schemes","venue":null,"work_id":"300824a5-4d83-4e85-8c11-c71d443c75c7","year":2025},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.426889Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:0f5cc00f350926fad6b6b89d757194e07ca19d1478ff080851e82fd0d1d5e4ac","observation_id":"879b8ed2-65dc-4ef6-8c2a-9b8f0920307e","resolution":{"observed_at":"2026-08-04T21:19:26.202232Z","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":"2026-08-04T21:19:26.180344Z","title":"The moduli space of matroids","venue":null,"work_id":"9cde8d29-0e9c-483e-8ca7-b59c990c1e74","year":2021},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.549781Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:a6ac695b0636723f017777c859cf03fc68273f37be299829eda5cbb695a596bc","observation_id":"4bb5c547-6598-4d9c-baa2-490784613652","resolution":{"observed_at":"2026-08-04T21:19:26.184945Z","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":"2026-08-04T21:19:26.157776Z","title":"Higher Segal Spaces , volume 2244","venue":null,"work_id":"66313f1f-b359-4305-92c7-7ad77a7c4736","year":2019},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.668152Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:885b90f4ff908ca8831dce1765d9c1be43a09ec51c5da6991739e0c89b01cabe","observation_id":"8101550c-3c42-4ce0-84e7-cf64a87dcd37","resolution":{"observed_at":"2026-08-04T21:19:26.165239Z","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":"2026-08-04T21:19:26.142055Z","title":"Grassmann- P l \\\"u cker relations and matroids with coefficients","venue":null,"work_id":"f1d72da2-2ecc-4bb5-a38e-e127a1966a0f","year":1991},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.737956Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:6b273c2649068991ce5af3a82e867e1b4292ff448f49d0ffea55f5706bf16c8d","observation_id":"c5dc0a67-5a2c-46d4-b315-876ba36e4ab5","resolution":{"observed_at":"2026-08-04T21:19:26.147502Z","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":"2026-08-04T21:19:26.127031Z","title":"On infinite matroids with strong maps: Proto-exactness and finiteness conditions","venue":null,"work_id":"534ed75c-226e-44b8-96ac-ee6725832b43","year":2022},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.867926Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:ba8f9abaabd31b08bf5b79e21c2e0325376f4215f1129b1268c1cc5729cafd2d","observation_id":"3943883c-9f97-49bb-b7ab-ef287e690434","resolution":{"observed_at":"2026-08-04T21:19:26.132905Z","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":"2026-08-04T21:19:26.114772Z","title":"Hopf algebras for matroids over hyperfields","venue":null,"work_id":"3677b56b-e55b-4dca-b5a7-1576dc241769","year":2020},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:23.946762Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:2bbc5593024047c30b7211dd5310d85ba496e048a581ee7bfae8d89d4a4e2ae8","observation_id":"cb0d7e1c-96c6-4aac-9575-135760b8b9cc","resolution":{"observed_at":"2026-08-04T21:19:26.118439Z","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":"2026-08-04T21:19:26.101509Z","title":"Proto-exact categories of matroids, H all algebras, and K -theory","venue":null,"work_id":"bec9177c-bf44-4c4e-a526-f600a13d06ba","year":2020},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.098626Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:855ae4d48c78ba4f521f29f07975eee14ebeb8643e6397c927519bcb543158d7","observation_id":"79bdd481-f96b-4645-b8c3-0bab16f2bd20","resolution":{"observed_at":"2026-08-04T21:19:26.106699Z","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":"2026-08-04T21:19:26.085277Z","title":"Group completion in the K -theory and G rothendieck-- W itt theory of proto-exact categories","venue":null,"work_id":"b5535d51-662c-453a-ae81-f29b84792ad7","year":2022},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.179843Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:3576ab5ba9cf5c4f2bd39ac531d53108fa60f6b9cb971b280cedd287d680902a","observation_id":"ecef440c-52aa-4b10-bc89-bb6f110e1a69","resolution":{"observed_at":"2026-08-04T21:19:26.090872Z","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":"2026-08-04T21:19:26.068800Z","title":"The category of matroids","venue":null,"work_id":"d5fe06ce-19f8-4482-a54f-ebdd862faae3","year":2017},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.235938Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:650585a01a2195c773c4855922991eed1463640b17db7f9e765538e9592c2a2a","observation_id":"541ca8c5-e9b8-4c99-bc9b-7064252ddd89","resolution":{"observed_at":"2026-08-04T21:19:26.075449Z","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":"2311.18648","last_updated":"2023-11-30T15:57:16Z","snapshot_observed_at":"2026-07-06T16:55:05.210009Z","submitted_at":"2023-11-30T15:57:16Z","title":"Tropical Quiver Grassmannians","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.18648","snapshot_observed_at":"2026-08-04T21:19:24.359216Z","title":"Tropical quiver G rassmannians","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.359216Z"},"links":{"cited_paper":"/paper/2311.18648","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:61fadb4b2d94c482d151328b19c9790b30bd83fd492f6f77f8a913d646c7fec5","observation_id":"1d08828f-423c-4210-9cdb-b5861bcbd32c","resolution":{"observed_at":"2026-08-04T21:19:24.359216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.09255","last_updated":"2026-04-13T11:41:19Z","snapshot_observed_at":"2026-07-06T17:59:55.100798Z","submitted_at":"2024-04-14T13:42:57Z","title":"Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\\mathbb{F}_1$-points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.09255","snapshot_observed_at":"2026-08-04T21:19:24.428409Z","title":"Quiver matroids--matroid morphisms, quiver G rassmannians, their E uler characteristics and F _1 -points","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.428409Z"},"links":{"cited_paper":"/paper/2404.09255","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:9037c4557237feccb570391963ae8d1c69ea53bf2499e133d2dc65793635faf5","observation_id":"02cc7f34-1621-413c-a5c3-5e29ac887180","resolution":{"observed_at":"2026-08-04T21:19:24.428409Z","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":"2026-08-04T21:19:26.054602Z","title":"On quiver representations over F _1","venue":null,"work_id":"7776843e-3c08-4e6c-9a31-a6a319fe627a","year":2023},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.590487Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:16df72d066296ab1d848d5723f46eccdb61ab79161dfbea0f0baec8afd86b66b","observation_id":"5c21f5f4-94dd-4253-bfee-0d523d660b5e","resolution":{"observed_at":"2026-08-04T21:19:26.058388Z","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":"2026-08-04T21:19:26.039147Z","title":"Coefficient quivers, F _1 -representations, and E uler characteristics of quiver G rassmannians","venue":null,"work_id":"03b13c33-5dea-400c-8e12-0499043948af","year":2024},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.638393Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:52ab51c05af8de52873f85893941cd3e307461194f6217b65c2bcea5600c6b84","observation_id":"ef781d8b-bb22-4092-9fef-6c9b9b360810","resolution":{"observed_at":"2026-08-04T21:19:26.043913Z","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":"2026-08-04T21:19:26.023063Z","title":"Hall L ie algebras of toric monoid schemes","venue":null,"work_id":"018d7a15-87f9-48ad-9ccf-3618c3854a90","year":2024},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.747433Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:e32861eeb21417bf918ddc96fda58c358e083e5d4304ded93fac679a11fe0d80","observation_id":"5ed7740d-e1dd-4637-95bd-2e46166b029d","resolution":{"observed_at":"2026-08-04T21:19:26.029665Z","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":"2026-08-04T21:19:26.004562Z","title":"Proto-exact categories of modules over semirings and hyperrings","venue":null,"work_id":"e8c97b2a-4bfd-4f89-a8b6-b80189aa026d","year":2023},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.797935Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:a94fcbc47c04417298c58e6196836252b1961fad0cba87a38477910ddea8687f","observation_id":"e661d2be-241f-42c1-bd53-34b9d9475e6e","resolution":{"observed_at":"2026-08-04T21:19:26.008239Z","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":"2026-08-04T21:19:25.989945Z","title":"Tropical toric geometry","venue":null,"work_id":"abb492ac-0eb5-453b-82df-86a4ffd603ac","year":2008},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.962513Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:4e98f2f5b52ee3dc623d894dc6af54a706e63070139010b7f2dffe7b89f8f44f","observation_id":"05278c31-1414-4fa1-9533-53c7565f1006","resolution":{"observed_at":"2026-08-04T21:19:25.994561Z","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":"2026-08-04T21:19:25.975277Z","title":"Eisenstein series and quantum affine algebras","venue":null,"work_id":"5f6ce16b-34c9-424c-bfc8-e3af56e4de93","year":1997},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:24.997154Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:8c8a28026320765fd057fe60a55473748109cb928979951b8929ade61c0a04d4","observation_id":"ad4e00f7-e297-483a-94a1-3a4a074a8c40","resolution":{"observed_at":"2026-08-04T21:19:25.979632Z","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":"2026-08-04T21:19:25.960635Z","title":"Equivariant vector bundles on toral varieties","venue":null,"work_id":"3d3bf810-18f9-4a0e-a3cd-27cc0097f040","year":1990},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.142153Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:4241dc637a581400fe3f19061cf76909037b583b79c246563425c7afa5580841","observation_id":"b8fbc351-1f09-4747-80a7-8f6d220e6968","resolution":{"observed_at":"2026-08-04T21:19:25.966058Z","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":"2405.03576","last_updated":"2024-08-14T01:42:57Z","snapshot_observed_at":"2026-08-13T00:13:52.085589Z","submitted_at":"2024-05-06T15:52:11Z","title":"Tropical vector bundles and matroids","version":2},"cited_work":{"arxiv_id":"2405.03576","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.03576","snapshot_observed_at":"2026-08-04T21:19:25.819417Z","title":"Tropical vector bundles and matroids","venue":"math.AG","work_id":"a9f9f2a8-541d-4c23-96be-e5687c764a35","year":2024},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.198450Z"},"links":{"cited_paper":"/paper/2405.03576","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:711accb65a6f9704bee4b80194ff4491795c04b80f18e5d48dd0fd352fc34a10","observation_id":"41d6fe0f-a80c-481b-bd8a-4ea39c8a89a9","resolution":{"observed_at":"2026-08-04T21:19:25.824808Z","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":"2405.03505","last_updated":"2024-05-06T14:19:45Z","snapshot_observed_at":"2026-08-13T00:13:56.142468Z","submitted_at":"2024-05-06T14:19:45Z","title":"Tropical Vector Bundles","version":1},"cited_work":{"arxiv_id":"2405.03505","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.03505","snapshot_observed_at":"2026-08-04T21:19:25.798583Z","title":"Tropical Vector Bundles","venue":"math.AG","work_id":"dabed9e9-4b3d-40de-9846-b76d46537cd2","year":2024},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.366598Z"},"links":{"cited_paper":"/paper/2405.03505","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:7be5f4c49ad927372ffe7ddfb420d16f9d4e706726a30f905ec70f3526784582","observation_id":"b7fe4e37-d628-41a6-8d2b-e5286d501aa6","resolution":{"observed_at":"2026-08-04T21:19:25.803046Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:19:25.944764Z","title":"Categorification of H arder-- N arasimhan theory via slope functions valued in totally ordered sets","venue":null,"work_id":"8b4307ba-7727-42c8-897b-b4147139cf3d","year":2023},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.461671Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:0a1252ccded3e09f144479cd9d32ffbd20caa9eff45fa16e15387dba9f35e9a3","observation_id":"70b6215b-b4f0-40ab-8e75-405c560ab54d","resolution":{"observed_at":"2026-08-04T21:19:25.948700Z","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":"2503.05940","last_updated":"2025-03-07T21:16:33Z","snapshot_observed_at":"2026-08-07T17:21:03.834080Z","submitted_at":"2025-03-07T21:16:33Z","title":"Proto-exact and parabelian categories","version":1},"cited_work":{"arxiv_id":"2503.05940","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.05940","snapshot_observed_at":"2026-08-04T21:19:25.769083Z","title":"Proto-exact and parabelian categories","venue":"math.RT","work_id":"924dfcb5-7dc9-4206-832d-c228f3e48842","year":2025},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.571605Z"},"links":{"cited_paper":"/paper/2503.05940","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:f45c53397c84559e369698d565becd13416c920c53151ceca0964e0d07ee8e15","observation_id":"3c6136ed-4464-4f03-bdbc-660617add288","resolution":{"observed_at":"2026-08-04T21:19:25.776785Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T21:19:25.931277Z","title":"Matroid theory , volume 3","venue":null,"work_id":"774516bc-a9fa-41a4-94b0-c65844a5e796","year":2006},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.630552Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:22cf23abc13f9b51b4c0a045ea08c5281f8baf60c303334aaac53baac911bdc5","observation_id":"15c3d687-1123-42b7-9d8a-a9b0644c8ead","resolution":{"observed_at":"2026-08-04T21:19:25.935176Z","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":"2026-08-04T21:19:25.913576Z","title":"Analytification is the limit of all tropicalizations","venue":null,"work_id":"6544d6e7-ca55-4423-b7db-3ea51f290da6","year":2009},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.636482Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:235407d34e0c1f7e7a8c3d9cee40c3a6cfcd919ff067cd0c3132ec4c495b6ec1","observation_id":"b6231cff-9107-4ab4-b9ce-9af4c7270aca","resolution":{"observed_at":"2026-08-04T21:19:25.919454Z","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":"2026-08-04T21:19:25.895300Z","title":"The H arder- N arasimhan system in quantum groups and cohomology of quiver moduli","venue":null,"work_id":"2dd589a1-f0de-465c-8d8b-402fe1fdf42c","year":2003},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.640560Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:925f87ef3088c61f0bb6adb50773a72babea8a26f219774512c824e6443ecf0d","observation_id":"1e41b553-298d-4e05-9171-b1e3a35b6215","resolution":{"observed_at":"2026-08-04T21:19:25.899314Z","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":"2026-08-04T21:19:25.874074Z","title":"Stability for an abelian category","venue":null,"work_id":"8e1f416d-138e-46e6-ab30-114d6fd0f82b","year":1997},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.644265Z"},"links":{"citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:90b20c62bad4e3af93ea7124d226ffa1e5afe2d51a47e633eb553585ae640af2","observation_id":"4ce2b967-4fea-4611-9aaa-22c0fe9e76f8","resolution":{"observed_at":"2026-08-04T21:19:25.881497Z","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":"math/0611617","last_updated":"2009-10-23T14:17:17Z","snapshot_observed_at":"2026-08-02T08:45:13.878936Z","submitted_at":"2006-11-20T20:28:14Z","title":"Lectures on Hall algebras","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0611617","snapshot_observed_at":"2026-08-04T21:19:25.648214Z","title":"Lectures on H all algebras","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.648214Z"},"links":{"cited_paper":"/paper/math/0611617","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:4f215d4dd7c2c80f3abcc36cb4e2538bfd2219a70e6f5409144774ed24bc2705","observation_id":"c245986d-12bc-4fb2-b0d4-1841babff599","resolution":{"observed_at":"2026-08-04T21:19:25.648214Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.03741","last_updated":"2025-07-24T00:18:11Z","snapshot_observed_at":"2026-08-07T17:26:49.020948Z","submitted_at":"2025-03-05T18:56:07Z","title":"On Semisimple Proto-Abelian Categories Associated to Inverse Monoids","version":3},"cited_work":{"arxiv_id":"2503.03741","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.03741","snapshot_observed_at":"2026-08-04T21:19:25.702508Z","title":"On Semisimple Proto-Abelian Categories Associated to Inverse Monoids","venue":"math.RT","work_id":"b4674966-ef65-4369-b6a3-be8cfefb431b","year":2025},"citing_paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-04T21:19:25.653001Z"},"links":{"cited_paper":"/paper/2503.03741","citing_paper":"/paper/2509.08144"},"observation_digest":"sha256:0b29acabf57e7f6daf49d5a91bf18789211633d4c711cb1aed2734ee93e62733","observation_id":"dfdfc589-dd6e-4002-a90b-dfcdd0d0252a","resolution":{"observed_at":"2026-08-04T21:19:25.713821Z","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"}}],"paper":{"arxiv_id":"2509.08144","last_updated":"2025-09-09T20:53:28Z","latest_version":1,"primary_category":"math.CT","snapshot_observed_at":"2026-08-10T14:46:45.589086Z","submitted_at":"2025-09-09T20:53:28Z","title":"Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":4,"verified_fuzzy":25},"total_outbound_references":32},"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 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2509.08144."}