{"as_of":"2026-08-11T19:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:750e7855f09c041643253d76f653c4585c755e82c9d6850264da3217cd5bf2f7","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T16:32:20.499768Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2606.01093/citation-record","integrity":"/paper/2606.01093/integrity","json":"/paper/2606.01093/citation-record.json","paper":"/paper/2606.01093"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T16:32:20.499768Z","title":"Baker and N","venue":null,"work_id":null,"year":2019},"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":1,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:398e230382973b1553020702028335b4ab0d04ee75474f429371b4d684fa8c68","observation_id":"1e06c08d-b26b-4695-86df-f17ca8cfc59b","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Baker and O","venue":null,"work_id":null,"year":2022},"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":2,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:25abd8b36177847a203d927b684cc9ef2d7b33ee35fcc8a011e0f0fe0832df38","observation_id":"d583e349-e34b-459c-bb4e-e0a54a0015c4","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Baker, T","venue":null,"work_id":null,"year":2025},"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":3,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:ae98535da813f7fb125f8001028b28d2b1ee790106afc9d2ceb9baa3c5c01a94","observation_id":"61b989f3-d5dd-43c0-a4a8-4ced1dea32d4","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Ben-Bassat and K","venue":null,"work_id":null,"year":2017},"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":4,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:cb61f37e46a2fee06c6cf3eea6ebe0cbc3aaed5a7586005e42ffd961cc24605e","observation_id":"90d5f4de-3b50-4b06-a6a9-96005c5ec6d5","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":null,"venue":null,"work_id":null,"year":2012},"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":5,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:1c0a3a98b3497dd8739e737de111b8d8a3c01b2a1435a645e52870d6e22cca4b","observation_id":"dc0f486a-3f0a-4c77-9df5-8d9baac4a47a","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Connes and C","venue":null,"work_id":null,"year":2011},"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":6,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:bd3fe801296713f7ad01ed4aef2f3d129db4114933a147c1ecff5d60a5a33e10","observation_id":"9306a4a8-6388-42c6-865c-45ca12fc3c57","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Connes and C","venue":null,"work_id":null,"year":2011},"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":7,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:dfcb2bcdfc529e0a1640d06ffb502ff555317baaad2a9d8c20a6577e8749db4c","observation_id":"889489ae-2432-4c46-a5a7-91bfa5982832","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Connes and C","venue":null,"work_id":null,"year":2010},"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":8,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:51e451a203bcd2764e9babc8834e7be6eb7aab3e69bd1219b1ade36e5cf0b657","observation_id":"04fddcff-3618-425a-966a-29a4d09702ab","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Davvaz and A","venue":null,"work_id":null,"year":2006},"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":9,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:cbaebed32fa04f17831a6192949fc1403522106e22923a3e6867f9335af09d6e","observation_id":"1486f867-d251-49c0-ba84-da5ebb8e6658","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Deitmar , Schemes over \\( _1\\), Number fields and function fields—two parallel worlds, Progr","venue":null,"work_id":null,"year":2005},"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":10,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:bba705407f89f0bd4c866297ee79adff2f394f04b8bd4d8129cf32d131307c8c","observation_id":"eb2f3a55-8c71-412c-9304-b938772211da","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Demazure and P","venue":null,"work_id":null,"year":1970},"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":11,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:9e63fa069f9ac73e8628df21228a959920f69172fbe03ea20029ae0032cda253","observation_id":"d4f27572-2e58-454f-b8d6-ef1c235e43c9","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Dyckerhoff and M","venue":null,"work_id":null,"year":2019},"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":12,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:498519a39e67633f3421d9958ffc9b84d5b119627bbfdee25469f0555042ca41","observation_id":"e9d6dbef-e2fa-4d42-9758-9714c3f716ee","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Eppolito, J","venue":null,"work_id":null,"year":2020},"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":13,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:b51ecb40b2a493318443ee89e4cbae31a0f6606e5d2372a1a4b3250a52dfb935","observation_id":"3a5b7b80-1df8-480d-936a-a3bb509eaad6","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Hosgood , Under Spec\\( Z \\): A reader's companion, Dissertation, Oxford University, 2016, https://thosgood.net/assets/files/under-spec-z.pdf","venue":null,"work_id":null,"year":2016},"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":14,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:e72de8d742666ca81657865e687fd14f646e284fd535d9a7be61560938cae727","observation_id":"1f5cfd2f-e2fe-494c-ab6f-9529671a5d6c","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Jun , Algebraic geometry of hyperrings, Adv","venue":null,"work_id":null,"year":2018},"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":15,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:eee99ed8e7745e30cb63526ed95fa9cadb42282c7e479292bc5a28781e4bf5ea","observation_id":"9609a9dc-f05b-48ca-bcd1-f7c7eb19bec4","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":null,"venue":null,"work_id":null,"year":2023},"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":16,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:2172caea78aabb52cf0445a5bbf249c9ff6282260485356383ce0a63ba51a36d","observation_id":"279e45eb-96e7-4bd6-abb0-86f26a1fb202","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":"sha256:922bc9ca8cd076628bdc835e34349d3814eef0044d088e3dacb15ff95b5c5216","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 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-28T16:32:20.499768Z","title":"Krasner , Quelques m\\'ethodes nouvelles dans la th\\'eorie des corps valu\\'es complets","venue":null,"work_id":null,"year":1949},"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":18,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:5d9a336042c3aff7a61fa72a2e927b889c2aa0e49d95ad64e789f31fecbcccdd","observation_id":"3210d213-fa75-45cb-9625-301abcfdc179","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Krasner , A class of hyperrings and hyperfields, Internat.\\ J.\\ Math.\\ Math.\\ Sci.\\ 6 (2) (1983), 307--311","venue":null,"work_id":null,"year":1983},"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":19,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:633ba37d6c880d083287dfaf0ebb6af93bf2394cf0f39182db5db446a98b0549","observation_id":"b9e662aa-b945-464e-bd46-5d51cf0d616e","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2404.09255","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.09255","snapshot_observed_at":"2026-07-01T21:36:15.803324Z","title":"Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\\mathbb{F}_1$-points","venue":"math.CO","work_id":"93ea0c00-0559-4e37-9504-8af3e35ed89c","year":2024},"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":20,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"cited_paper":"/paper/2404.09255","citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:04b2389f4ee7d78a79658c860deb592a8b2a407b70748dbb6bb4fad6019305f5","observation_id":"969ec7c8-83dd-4b13-bc4b-c6c48ce7685a","resolution":{"observed_at":"2026-07-01T21:36:15.804716Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-28T16:32:20.499768Z","title":"Lorscheid , Blue schemes, semiring schemes, and relative schemes after To\\\"en and Vaqui\\'e, J","venue":null,"work_id":null,"year":2017},"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":21,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:167b5d8ef7cace81c6653474d8772b96a8352d56b4959d17661affa222e53751","observation_id":"3c76be61-1baf-4495-98f9-d51731c0852f","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Manin , Lectures on zeta functions and motives (according to Deninger and Kurokawa), Ast\\'erisque, 228 (4), 121--163","venue":null,"work_id":null,"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":22,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:c4b908c45318eb4b0ff8250b8b6702f762493b2005d4d00589cac0f7b935e2a2","observation_id":"8714718f-ef18-4393-bed2-211d21291797","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":null,"venue":null,"work_id":null,"year":2011},"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":23,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:cc7fcd2468816f5e19e359fde0ff3830c84c558a4735e8415d27e47b03ecdc72","observation_id":"8c428af7-77bd-4c84-b0cd-abf35df62d4e","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Procesi Ciampi and R","venue":null,"work_id":null,"year":1987},"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":24,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:071b7f50569e64d7cf04b513965c2cdfe53f91f5e57338a4e26195e2a8d84a70","observation_id":"9a9573a7-feda-4054-870b-005570aa871c","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":null,"venue":null,"work_id":null,"year":1956},"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":25,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:7b098b81634f26b249a6ee7aeb45234460407529f6190149890c5e5c782428da","observation_id":"3dc1480e-7c86-442c-93a3-4f7d84e5f2be","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"To\\\"en and M","venue":null,"work_id":null,"year":2009},"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":26,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:fee1ee04a90d52a58b13bb8635d6dcc810ee5afaa5bf810501d1a884228fd2c5","observation_id":"9c0fb1f8-beb3-428a-bedc-e01e96c1d76e","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Tolliver , An equivalence between two approaches to limits of local fields, J","venue":null,"work_id":null,"year":2016},"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":27,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:77634f3f0851658b4325c3bcf48e36e644a761ae141b8079de4a87a73fffc6a9","observation_id":"25a20c7c-2618-43f8-9b24-d725154a9c0c","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Vezzani , Deitmar's versus To\\\"en-Vaqui\\'e's schemes over \\( F _1\\), Math","venue":null,"work_id":null,"year":2012},"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":28,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:c9c7735c79308861a428668db2f78764a23b297951f6b7052529dc7d333f41b4","observation_id":"5010d8fd-e5d2-41ba-9a94-0cb6399f6e39","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Jun, and M","venue":null,"work_id":null,"year":2020},"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":29,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:49ec2e16575eca615f55f2abf7237c692409fdad6dbcf48859b7814bb060958f","observation_id":"d1f0728e-4183-4826-b2e6-f94a39bc743e","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Hosgood , Under Spec\\( Z \\) A reader's companion, Dissertation, Oxford University https://thosgood.net/assets/files/under-spec-z.pdf","venue":null,"work_id":null,"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":30,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:8c1b840959442f41253688a659f277380856df735e280a10a60e573d46a93735","observation_id":"bf1e855a-ba2a-4695-8e0e-ab2bb02680ef","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Procesi-Ciampi and R","venue":null,"work_id":null,"year":1987},"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":31,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:1a243b53b35db386b6be9d2fd04262be06e1194d45576d18ed77107832a06581","observation_id":"638fe9fa-5dba-439d-9616-dde644e7f677","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Song , Galois correspondence for Galois coverings of tropical curves, J","venue":null,"work_id":null,"year":2025},"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":32,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:8772fd7148084e345145c1edc764340d8ffda66bb641ff052b6640c770138856","observation_id":"e7019b64-d27f-4698-9995-af7e2a2a509e","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Kurokawa , On some Euler Products I, Proceedings of the Japan Academy, 60A (1984) No.9, 335--338","venue":null,"work_id":null,"year":1984},"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":33,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:ff78aa222d992aa4981bf874cec5682b1caa540fc6d0cc07f857e22e22bf815a","observation_id":"34bdad02-1b02-4413-911c-a493a938ab04","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Kurokawa , Multiple zeta functions: An example, Advanced Studies in Pure Mathematics, 21 (1992), 219--226","venue":null,"work_id":null,"year":1992},"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":34,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:1446d0ba8299359c647864511ec5b177ce4e22ef15ee941d720710c1eb849657","observation_id":"f63c41d9-27b4-4d64-8fd8-6c40acd3510d","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":"Hiranouchi and Y","venue":null,"work_id":null,"year":2007},"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":35,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:2e75b3f7423dfc683d48afc7eb975669b622410d5c43a4c7742d8d29c102dea8","observation_id":"67217274-1520-4165-8b2f-6cc627813fad","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","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":"2026-06-28T16:32:20.499768Z","title":null,"venue":null,"work_id":null,"year":1984},"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":36,"source":"arxiv_source","source_observed_at":"2026-06-28T16:32:20.499768Z"},"links":{"citing_paper":"/paper/2606.01093"},"observation_digest":"sha256:4e48b06ab1c013e8936da351ef6d818e5afb8ce4ce1323463d4826e57632eacd","observation_id":"098e37ed-82bf-49ea-930d-5be7106f31fd","resolution":{"observed_at":"2026-06-28T16:32:20.499768Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.01093","last_updated":"2026-05-31T08:25:31Z","latest_version":1,"primary_category":"math.AG","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"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":34,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":36},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2606.01093."}