{"as_of":"2026-08-08T17:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:92504c84579c6bf1d96921005e71ac8b0a0a4aef1df8350474eb4bcfc1872960","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T13:19:57.187878Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.20820/citation-record","integrity":"/paper/2507.20820/integrity","json":"/paper/2507.20820/citation-record.json","paper":"/paper/2507.20820"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:19:58.181810Z","title":"A theory of quantal sets","venue":null,"work_id":"754f1840-9e20-4698-9aa7-30cbd9417ce6","year":1989},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.260500Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:4b2d01b83bb9e5d046b0cfa998e656ab0e4130eb62c40f519efdda337970f156","observation_id":"4c78fe95-0efd-4c92-900c-e3762bee04c8","resolution":{"observed_at":"2026-08-06T13:19:58.185901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.168910Z","title":"Handbook of categorical algebra","venue":null,"work_id":"b9ab2cea-72c5-445d-a4dc-04b39b1765e6","year":1994},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.338873Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:bf5c1f23db543889e0405c9173579561a0d51729f923a329939cdba5fb86013d","observation_id":"a4a9f62c-43c4-4d2c-adbe-6e71d74fa029","resolution":{"observed_at":"2026-08-06T13:19:58.172777Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf00403411","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:19:57.245184Z","title":"Quantales and their sheaves","venue":null,"work_id":"2db2a555-b1da-4970-b06a-b69195fb9b7b","year":1986},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.513259Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:06048576b6fca56144a56ee111b2b75224d5748405098163f39a5371a5f3f7dd","observation_id":"17c475a2-ffd8-4e46-9cff-1116d4194bf8","resolution":{"observed_at":"2026-08-06T13:19:57.249633Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.142066Z","title":"Cauchy completion in cate- gory theory","venue":null,"work_id":"094c1042-5f56-4d71-af4a-ea3829b9bafb","year":1986},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.594867Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:05d6a6175394ac0a630cb5166f833108b3ae94f32c787d7684a8155bb00a6d01","observation_id":"c7f592f0-e702-4d40-b095-67408d34353c","resolution":{"observed_at":"2026-08-06T13:19:58.146484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.128422Z","title":"Atheoryofenrichedsheaves","venue":null,"work_id":"bec5c60a-422e-4bbd-b852-0b053d8f5897","year":1996},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.673735Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:d4b36ff045a925a8230c0a83bebe2ff8a39b427a71e0ae7555ba045db7a190cf","observation_id":"205c3a98-c947-4001-a370-1ee314ef5bf1","resolution":{"observed_at":"2026-08-06T13:19:58.133232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.114132Z","title":null,"venue":null,"work_id":"13efbed9-bfba-444e-b392-f70293c11cbc","year":null},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.775224Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:aaa47dd88c9fb1dfa01288d6464664014b8487f7d135073ae03da82e7d456ffd","observation_id":"f6b20673-0e90-49d4-abed-107d0e946197","resolution":{"observed_at":"2026-08-06T13:19:58.118607Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.100499Z","title":"Quantal sets and sheaves over quantales","venue":null,"work_id":"d7423ac8-b447-4dc5-89f6-e4e49cf3d146","year":1994},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.971115Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:61f2b393b0ad210e5bc803a7310628bd8a97a5a497b1180fc26c42ee4944105a","observation_id":"309eae7b-557e-46bd-937a-5d2ab565788d","resolution":{"observed_at":"2026-08-06T13:19:58.104591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.087357Z","title":"Sheaves on quantaloids","venue":null,"work_id":"c3f190eb-b617-4dd0-a012-ab1347718de3","year":2000},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.060576Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:075ea57daa942d430fd48cf0911975942ad837fe140a77f9f5d75bf54041d218","observation_id":"89575fbe-e969-4d0e-b63f-d74598ee5335","resolution":{"observed_at":"2026-08-06T13:19:58.091414Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.072857Z","title":"Sheaves on Quantales as Generalized Metric Spaces","venue":null,"work_id":"7b02ca20-b344-4668-93e1-8511ab8106e7","year":2010},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.112366Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:1787231b277191a3c8a870b9bfbbb10d68f7ae5adf7be2768f068e3bdede65e8","observation_id":"99ce195a-37cc-400b-9f20-6d1b4dfad89a","resolution":{"observed_at":"2026-08-06T13:19:58.077426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.058755Z","title":"Sheaves on involutive quantales : Grothendieck quan- tales","venue":null,"work_id":"8126ee4b-d2ff-425f-bdfe-beca87a6738c","year":2014},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.117166Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:225502b5bb1184d5ba3da8edf207c8973c8574e17c40be1b5f82e0d9f2d6d817","observation_id":"1adad17e-bf3c-4f7a-9d80-8ecf93320dd8","resolution":{"observed_at":"2026-08-06T13:19:58.063171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.044873Z","title":"Symmetry and Cauchy completion of quantaloid-enriched categories","venue":null,"work_id":"dc249788-0c88-4b27-9321-92f20343aca2","year":2011},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.121652Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:8a2d08373bed3a0f72877dc87c47a1daeb8c1d391452e12a045fd08e4ff72573","observation_id":"72ad6d36-905e-4718-84d3-bbc9098f637f","resolution":{"observed_at":"2026-08-06T13:19:58.049661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:19:57.126032Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.126032Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:7a9d5614a92053f3c50df5b88af17ea5d386d661c9e0f354b97907105e4aee98","observation_id":"459e9940-c9e2-426d-9df5-7c268528aed3","resolution":{"observed_at":"2026-08-06T13:19:57.126032Z","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":"2026-08-06T13:19:58.031687Z","title":"Basic concepts of enriched category theory","venue":null,"work_id":"b8050b6d-9854-4b05-8570-ebf8bbe923ea","year":2005},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.130394Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:baf689374322f9b30da8ef059a70b681281c0b8c3c95c1007f6e3afec5db3b82","observation_id":"90603d59-3392-40e4-87ff-cbc3e225168f","resolution":{"observed_at":"2026-08-06T13:19:58.035690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:19:57.134598Z","title":"Flat vs. filtered colimits in the enriched context","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.134598Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:9de5434648a840680b8aca11cda7ba3d0ae6594da68220ad0b559df5dc41659d","observation_id":"eb321271-e1a0-4def-bc9a-997cd2d32c74","resolution":{"observed_at":"2026-08-06T13:19:57.134598Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:19:57.138478Z","title":"Metric spaces, generalized logic, and closed categories","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.138478Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:90201207ffbdc939d90d3e2fc4cc835627a2c4d08685b02a367a07240bd96eea","observation_id":"a93bfe18-406f-4e43-931b-8cc250e3dd97","resolution":{"observed_at":"2026-08-06T13:19:57.138478Z","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":"2026-08-06T13:19:58.017653Z","title":null,"venue":null,"work_id":"f782717e-b8c2-46e7-97d1-0ea46206ee1d","year":1986},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.142914Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:1b9ef31e02c9c8df8c408850bedf60593098b67d3e935cb5a67a3df333a1726c","observation_id":"2c00fc3c-8540-4b5d-9f32-1d42b8120aa6","resolution":{"observed_at":"2026-08-06T13:19:58.022166Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.004210Z","title":"Quantales: Quantal sets","venue":null,"work_id":"4b2d4ef9-dd89-4207-9a63-079bc2c08b5f","year":1985},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.147351Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:a47b16a25f150e080276dec11642d03651b25a964e9f39455f7d81df59bd3498","observation_id":"0206a438-6590-4972-a956-b710f2f8cd23","resolution":{"observed_at":"2026-08-06T13:19:58.008315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.991165Z","title":"Cauchy complete category","venue":null,"work_id":"cb1f33ab-df69-4139-9130-b28b25ebcb85","year":2025},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.151597Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:230332f85c32c381ff1307e090f6d27780b7002c6764345324553f30809ae000","observation_id":"c257be47-8edb-4c05-835b-bb027be1ec65","resolution":{"observed_at":"2026-08-06T13:19:57.995371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.977543Z","title":"Rosenthal","venue":null,"work_id":"46936be8-8186-42f8-a4db-3db706f69c54","year":1996},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.155385Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:be10ee4508c0c1935df0232a0e1db59f6b4d0869259c29b87de24eeb8291269f","observation_id":"9af4620a-0db9-43f1-834d-fd01c4868e8d","resolution":{"observed_at":"2026-08-06T13:19:57.982132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.962788Z","title":"Characterization of bicategories of stacks","venue":null,"work_id":"e8e3f1c7-9e91-4fc9-8768-20fb52f95713","year":1982},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.159368Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:fdb77afca29c1f27048a523cc57fa6110e3860486d2cc133798039546d411f63","observation_id":"1bd69a92-b824-468e-8d99-39f07ba74bc4","resolution":{"observed_at":"2026-08-06T13:19:57.967424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.948405Z","title":"Enriched categories and cohomology","venue":null,"work_id":"c5fdaeef-7c57-4504-9f45-4368367a748a","year":2005},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.163087Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:6b0fd4a1a2d355fad41254f6b5dbb6b7fc9a80094fe748c5aca01ed891a12003","observation_id":"f5d61297-910a-4825-b6a2-495b5341bd3b","resolution":{"observed_at":"2026-08-06T13:19:57.952585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.933768Z","title":"Categorical structures enriched in a quantaloid: cate- gories, distributors and functors","venue":null,"work_id":"454ff7c5-46ec-4f80-a4b7-6f07ce04262f","year":2005},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.167411Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:3c97f0ace2a858c088ad7fcb13209014d88d71646139255d258638ea99173d5d","observation_id":"20c4c773-1087-4c0e-be25-364fe2b5aa1c","resolution":{"observed_at":"2026-08-06T13:19:57.938538Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.08351","last_updated":"2023-10-14T15:07:49Z","snapshot_observed_at":"2026-07-06T13:01:19.701734Z","submitted_at":"2022-04-18T14:48:08Z","title":"On sheaves on semicartesian quantales and their truth values","version":2},"cited_work":{"arxiv_id":"2204.08351","doi":null,"metadata_source":"pith","pith_arxiv_id":"2204.08351","snapshot_observed_at":"2026-08-06T13:19:57.265071Z","title":"On sheaves on semicartesian quantales and their truth values","venue":"math.CT","work_id":"1d0fc2c5-ae9b-41a9-b44a-7f94c126bbc0","year":2022},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.171563Z"},"links":{"cited_paper":"/paper/2204.08351","citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:774b953c0752e00696c920f20e62ba429c6efd4ea778769c0e5a40764a2ddef6","observation_id":"5c8bb3db-0756-4075-94f4-27de25692bca","resolution":{"observed_at":"2026-08-06T13:19:57.269682Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.919403Z","title":"Quantaloids and non-commutative ring representations","venue":null,"work_id":"d1ec423a-b5ab-4229-b5c6-a8fe9fa8a349","year":1995},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.176112Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:de001f214b013c2a63ffdaef1c86723b178116d1a33368920be133d390b7455a","observation_id":"ae0e7f6a-f8fb-45fc-b5a4-ea24a6a7f42f","resolution":{"observed_at":"2026-08-06T13:19:57.923868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.739603Z","title":"Sheaves and Cauchy-complete categories","venue":null,"work_id":"740300bc-a65e-4db1-9ab8-573d879b0f96","year":1981},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.180044Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:af306271540ce51c29b1516c746388ada9441d99a82941c925f76826072d5e00","observation_id":"b10a65e2-543b-4e9f-ac09-5703e3148df3","resolution":{"observed_at":"2026-08-06T13:19:57.841674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:57.477219Z","title":"Sheaves on sites as Cauchy-complete categories","venue":null,"work_id":"1984ca81-18a5-40a8-b47b-6710935debc3","year":1982},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.184021Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:0418a3b9162cc13b69182add2442fd205b28b6a67c3e5ec7011e4a3f51074ceb","observation_id":"daeafe06-d306-4aef-b187-1c64e6606891","resolution":{"observed_at":"2026-08-06T13:19:57.607304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:19:58.156080Z","title":null,"venue":null,"work_id":"92df4f7a-acc6-4a0b-b07b-c9ea4892223b","year":null},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.432412Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:faa3fae1ebc88edef5714668429c7a461d4898481b815344927d0aaa24cac9a1","observation_id":"10dffd37-3be2-4261-b980-8362f95590f0","resolution":{"observed_at":"2026-08-06T13:19:58.160385Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2107.04417","last_updated":"2021-07-09T13:04:35Z","snapshot_observed_at":"2026-08-03T15:58:58.115698Z","submitted_at":"2021-07-09T13:04:35Z","title":"Relative topos theory via stacks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.04417","snapshot_observed_at":"2026-08-06T13:19:56.894845Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:56.894845Z"},"links":{"cited_paper":"/paper/2107.04417","citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:9367d97e0770154240d49f2e21efa57456d1d53c000f03d7bc777d2feaa0ec26","observation_id":"5b74c424-e3d9-4a5c-8941-4b93ace692c9","resolution":{"observed_at":"2026-08-06T13:19:56.894845Z","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":"10.1016/0022-4049(82)90061-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:19:57.217606Z","title":"72 Olivia Caramello Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via V alleggio 11, 22100 Como, Italy","venue":null,"work_id":"caa675bb-cba4-451c-ae49-062ceb63cfe0","year":null},"citing_paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory","version":1},"reference_index":4049,"source":"pdf_text","source_observed_at":"2026-08-06T13:19:57.187878Z"},"links":{"citing_paper":"/paper/2507.20820"},"observation_digest":"sha256:8f49229414f4459b64b9cb40dea6333499aef85de6e4140ec3c14ad4b16d27d6","observation_id":"50b6ae61-b346-4659-bfd5-eabfd443d2fe","resolution":{"observed_at":"2026-08-06T13:19:57.224133Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.20820","last_updated":"2025-07-28T13:25:32Z","latest_version":1,"primary_category":"math.CT","snapshot_observed_at":"2026-08-06T13:19:52.897520Z","submitted_at":"2025-07-28T13:25:32Z","title":"Sheaves on a bicategory"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":6,"verified_exact":3,"verified_fuzzy":19},"total_outbound_references":29},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2507.20820."}