{"as_of":"2026-08-08T12:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8dd87b51ed42b334daa9341a5ffe0ea4fa5f594ed05bb854d82d4ba4ad9ee524","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:24:01.555166Z","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":"2026-05-19T06:37:07.255784Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":"2026-08-07T13:24:01.555166Z","title":"Caramello and R","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12050","last_updated":"2025-05-28T06:48:57Z","snapshot_observed_at":"2026-08-07T13:14:37.574330Z","submitted_at":"2025-05-28T06:48:57Z","title":"Stackification via adjunction","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:24:01.555166Z"},"links":{"cited_paper":"/paper/2107.04417","citing_paper":"/paper/2506.12050"},"observation_digest":"sha256:deffab7f3fe1ad64eb7c4f42b6f0e7592ebf879762ed1fac387a5d4cfe1b3990","observation_id":"30c4e9dc-2be1-41e7-803c-d73d5dba4d28","resolution":{"observed_at":"2026-08-07T13:24:01.555166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":"2107.04417","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2107.04417","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Relative topos theory via stacks","venue":null,"work_id":"d2543036-027c-4795-bd04-f9203e3f622a","year":2021},"citing_paper":{"arxiv_id":"2507.01869","last_updated":"2026-04-28T15:36:40Z","snapshot_observed_at":"2026-08-06T00:03:40.452982Z","submitted_at":"2025-07-02T16:35:50Z","title":"De Morgan's law in toposes I","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-19T06:36:22.932893Z"},"links":{"cited_paper":"/paper/2107.04417","citing_paper":"/paper/2507.01869"},"observation_digest":"sha256:e602725f8dcaf0f0f63ddc6889042a90e14fac31f96b32a6387200f3551f22aa","observation_id":"0bf1cf03-29ad-4ee0-b3c0-8fc1e1feb35f","resolution":{"observed_at":"2026-05-19T06:37:07.257727Z","resolver_source":"arxiv_id","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":{"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":"2026-08-06T16:16:45.909837Z","title":"Relative topos theory via stacks","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.14379","last_updated":"2025-07-18T21:58:10Z","snapshot_observed_at":"2026-08-08T06:27:12.903457Z","submitted_at":"2025-07-18T21:58:10Z","title":"Local fibrations and morphisms of relative toposes","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T16:16:45.909837Z"},"links":{"cited_paper":"/paper/2107.04417","citing_paper":"/paper/2507.14379"},"observation_digest":"sha256:2047398c43f9e35868a4a11b0c9f6c3711e2adc5219183ef646cb22dce047055","observation_id":"e45a1d5f-4f33-4800-8a34-404d0440771f","resolution":{"observed_at":"2026-08-06T16:16:45.909837Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":{"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":"2026-08-05T14:46:05.967713Z","title":"Th´ eorie des topos","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2508.21134","last_updated":"2025-08-28T18:08:48Z","snapshot_observed_at":"2026-08-05T18:50:56.625954Z","submitted_at":"2025-08-28T18:08:48Z","title":"Generation of Grothendieck topologies, provability and operations on subtoposes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T14:46:05.967713Z"},"links":{"cited_paper":"/paper/2107.04417","citing_paper":"/paper/2508.21134"},"observation_digest":"sha256:423bc7490dbf2a186085e6dd30e94c10065db7e529d7e6602172e15906940a3f","observation_id":"77075e70-b2b1-4931-84d2-fdbf4b904177","resolution":{"observed_at":"2026-08-05T14:46:05.967713Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":"2026-08-05T14:17:03.034609Z","title":"Th´ eorie des topos","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2508.21609","last_updated":"2025-08-29T13:15:48Z","snapshot_observed_at":"2026-08-05T14:16:42.858355Z","submitted_at":"2025-08-29T13:15:48Z","title":"Sites and Grothendieck toposes: an introduction","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T14:17:03.034609Z"},"links":{"cited_paper":"/paper/2107.04417","citing_paper":"/paper/2508.21609"},"observation_digest":"sha256:363a9dead3a358879512af0f4e1e0204ff5e28782757471d3aed32d9a70bf92f","observation_id":"1fac4fbe-5229-42b2-b728-f561f60b1141","resolution":{"observed_at":"2026-08-05T14:17:03.034609Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2107.04417/citation-record","integrity":"/paper/2107.04417/integrity","json":"/paper/2107.04417/citation-record.json","paper":"/paper/2107.04417"},"outbound":[],"paper":{"arxiv_id":"2107.04417","last_updated":"2021-07-09T13:04:35Z","latest_version":1,"primary_category":"math.AG","snapshot_observed_at":"2026-08-03T15:58:58.115698Z","submitted_at":"2021-07-09T13:04:35Z","title":"Relative topos theory via stacks"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2107.04417."}