{"as_of":"2026-08-09T16:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7af987baca2e6101f8a19b99360bdd221ba58f2845773b4552487a03b9f46f24","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T22:42:54.483452Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2508.06637/citation-record","integrity":"/paper/2508.06637/integrity","json":"/paper/2508.06637/citation-record.json","paper":"/paper/2508.06637"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:42:54.820272Z","title":"Propositional logics for the L awvere quantale","venue":null,"work_id":"2a4d550b-22df-431b-bce4-ee93b0edd312","year":2023},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.398697Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:64e1e12d254b55a4a088d78dd709ced4be40e45502a2b541f780e04978db2875","observation_id":"95602a2b-43ea-4799-a4cb-43d4d914083a","resolution":{"observed_at":"2026-08-05T22:42:54.824790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.805645Z","title":"Spectral M ackey functors and equivariant algebraic K -theory ( I )","venue":null,"work_id":"cd963fd1-5eb5-4c7c-9d16-fb5b8812d4d7","year":2017},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.403602Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:a4aa470505f70a811f75b907cd73ead1c1552921a3d9e5c6e85d44e326d31557","observation_id":"913fe408-db01-4cba-99b0-07748dc1e093","resolution":{"observed_at":"2026-08-05T22:42:54.810307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.791882Z","title":"Adjoining adjoints","venue":null,"work_id":"ba7537b6-9f85-47af-a943-edd7956e6c02","year":2003},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.408289Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:8ca819226394789af9965c79f91b7b5ba7cc21a3c0b835e5791de23ce18596b8","observation_id":"b752542f-425c-4a38-8d95-8a2044aa3dd6","resolution":{"observed_at":"2026-08-05T22:42:54.795985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.777744Z","title":"Universal properties of span","venue":null,"work_id":"36061d66-f18e-4aff-88e9-79a2770d0e21","year":2004},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.413187Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:19a6aa4c368b0aea41aef345a199257597aed2bb9b09cf946832cbbbbb62efb3","observation_id":"4d85a0c4-9eb6-41de-9edc-855431871dff","resolution":{"observed_at":"2026-08-05T22:42:54.782448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.762736Z","title":"The span construction","venue":null,"work_id":"b579878a-4289-4fa4-bb88-b57a7c4df3df","year":2010},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.418122Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:2131e7a1f6e3f747c5e5801c5622009878dbbc3333c5d44a89c5f2a761dfb484","observation_id":"49db4a18-f71f-4bba-a769-71a16613f831","resolution":{"observed_at":"2026-08-05T22:42:54.767676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.05765","last_updated":"2019-06-20T17:28:00Z","snapshot_observed_at":"2026-07-06T07:21:06.980572Z","submitted_at":"2018-12-14T03:07:29Z","title":"Graphical Regular Logic","version":3},"cited_work":{"arxiv_id":"1812.05765","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.05765","snapshot_observed_at":"2026-08-05T22:42:54.571081Z","title":"Graphical Regular Logic","venue":"math.CT","work_id":"314cc2d8-9de2-40cd-be18-8c037d47f9fb","year":2018},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.422821Z"},"links":{"cited_paper":"/paper/1812.05765","citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:5e006a464651f9347a07c0e2f99b1a8f4f71d4cbb820f50f510ff57d78660f08","observation_id":"26bdb906-6f08-4f72-88e2-dbff0c7f456e","resolution":{"observed_at":"2026-08-05T22:42:54.577212Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.748554Z","title":null,"venue":null,"work_id":"6d65f42d-9fdb-429f-939e-27aedf2c614a","year":2019},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.428350Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:99f0a7da799b33cce80fded16235619589648a3954eb9b634bc154b3fdb0ad15","observation_id":"b62825c6-a727-4ef1-8846-db38328740e1","resolution":{"observed_at":"2026-08-05T22:42:54.753045Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.733725Z","title":"Limits in double categories","venue":null,"work_id":"4f37edcf-46f0-45b5-82e3-170831b86558","year":1999},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.432794Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:e64a21eea16a8fadd595ed2b45196d315e5df8183b02020d583d825d90e6c085","observation_id":"de8dcc61-65be-4a34-8f7f-99c5689ffb97","resolution":{"observed_at":"2026-08-05T22:42:54.738249Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.719379Z","title":"Higher Dimensional Categories: From Double to Multiple Categories","venue":null,"work_id":"c101351c-5347-42af-9d92-f9c2b4511ab1","year":2019},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.436951Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:2eaabffc8b91e19dfd6501abca55593e09edde92f3b2a57a2babf0a83ac4722d","observation_id":"698487f9-16ef-4185-8aee-375b5c6ac49d","resolution":{"observed_at":"2026-08-05T22:42:54.723757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.705456Z","title":"Two-variable fibrations, factorisation systems and categories of spans","venue":null,"work_id":"6c9361dd-31df-4840-8752-d3b020503af4","year":2023},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.441221Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:6338ea5fd082018b33e2b7b2d821e52fa6a9321ccfe0ecaa8770cbbed0ee074b","observation_id":"994d754d-b58d-4fd6-a695-6a925a59c450","resolution":{"observed_at":"2026-08-05T22:42:54.709705Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.690235Z","title":"Representable multicategories","venue":null,"work_id":"fd39d0c5-86a6-4c2f-bf52-491d8295d1e4","year":2000},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.445426Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:63a147ffbdd28ca9cf796673d70348e84dcbcff4df9cff83a14365ed94065dd4","observation_id":"507ccb8f-2476-4f25-a468-8eca214a65b3","resolution":{"observed_at":"2026-08-05T22:42:54.694995Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.674619Z","title":"Cartesian double theories: A double-categorical framework for categorical doctrines","venue":null,"work_id":"49bd6106-36fb-4bfc-b498-2963b268db5f","year":2024},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.449581Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:b86ca500dd353dd346ff072d91e36c8f5067406cbb926e84567d20d13ea5aa6c","observation_id":"ac3bc372-ded7-4fdf-917a-52744eb3e332","resolution":{"observed_at":"2026-08-05T22:42:54.679819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.654833Z","title":"William Lawvere","venue":null,"work_id":"d4b5efdc-0134-4881-8b9c-0e8e9217bb62","year":2006},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.453866Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:cedb34013c29a57c41ee612b225f618471f18edd9e5a2f664181ac9d26cf2299","observation_id":"58cd532b-700e-418d-b590-e0dae1fc04a1","resolution":{"observed_at":"2026-08-05T22:42:54.661861Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.18329","last_updated":"2025-05-28T19:20:26Z","snapshot_observed_at":"2026-08-07T14:30:50.138764Z","submitted_at":"2025-05-23T19:35:57Z","title":"Towards a double operadic theory of systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.18329","snapshot_observed_at":"2026-08-05T22:42:54.457955Z","title":"Towards a double operadic theory of systems","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.457955Z"},"links":{"cited_paper":"/paper/2505.18329","citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:99bb3e0fab8831dffe4b10af8bf23e661aa4ec659c83ce94bea18f4cd8a7b9b2","observation_id":"4d6d1ecc-e3f7-4c5e-baa9-bbfc8f728bc1","resolution":{"observed_at":"2026-08-05T22:42:54.457955Z","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":"2026-08-05T22:42:54.637406Z","title":"Monoidal G rothendieck C onstruction","venue":null,"work_id":"d8904e84-9f57-4880-b754-4edf67df878c","year":2020},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.462494Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:584d4bed2b6960396c6b0aa031e99720ccca0e0300cf64a3b4b69bea2615f2eb","observation_id":"f21d2045-4ed5-40a7-b355-843de66d2639","resolution":{"observed_at":"2026-08-05T22:42:54.642815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.621732Z","title":"Retrocells","venue":null,"work_id":"8e7bd739-1976-4c4a-8316-799b4439b679","year":2024},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.466844Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:456844406e26a4c40b0cb39c0937bfdd95ad5dd821b76661ae2c0593e6f00603","observation_id":"1f8a06c5-3cad-4a58-a2ed-f79cb7670737","resolution":{"observed_at":"2026-08-05T22:42:54.626107Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.606125Z","title":null,"venue":null,"work_id":"3f556fda-4d8c-4a08-9435-e32568c2a5d1","year":2008},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.470930Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:1892888fab971dd1146c0fb2e6a5163b8dd4a12c5a7cc94276b73d956d6b2fcc","observation_id":"aeb99dea-9334-49e2-8242-adab0ec6e153","resolution":{"observed_at":"2026-08-05T22:42:54.610647Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-05T22:42:54.588644Z","title":"Comparing composites of left and right derived functors","venue":null,"work_id":"a446d966-91a6-46cf-aeb2-532f811d8426","year":2011},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.474905Z"},"links":{"citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:b932d8b53ff5d34c5230e765c277bab870eebcbad9df0f9ee6f9c6a14c7c7f76","observation_id":"588a306c-8c1f-4b82-9c0c-4c7b3086b4a0","resolution":{"observed_at":"2026-08-05T22:42:54.594614Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1305.0297","last_updated":"2013-05-01T21:24:17Z","snapshot_observed_at":"2026-08-01T16:12:31.103197Z","submitted_at":"2013-05-01T21:24:17Z","title":"The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1305.0297","snapshot_observed_at":"2026-08-05T22:42:54.479152Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.479152Z"},"links":{"cited_paper":"/paper/1305.0297","citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:3912f4eed62eb682a0f82c6ed752999e594e884650daf4f40ea218d7855b5348","observation_id":"d50ab691-68f3-4d6e-8b5c-ccdc6918c427","resolution":{"observed_at":"2026-08-05T22:42:54.479152Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02202","last_updated":"2022-03-17T02:03:28Z","snapshot_observed_at":"2026-08-05T17:38:44.020489Z","submitted_at":"2019-08-06T15:10:42Z","title":"Generalized Lens Categories via functors $\\mathcal{C}^{\\rm op}\\to\\mathsf{Cat}$","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02202","snapshot_observed_at":"2026-08-05T22:42:54.483452Z","title":null,"venue":null,"work_id":null,"year":1908},"citing_paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines","version":3},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-05T22:42:54.483452Z"},"links":{"cited_paper":"/paper/1908.02202","citing_paper":"/paper/2508.06637"},"observation_digest":"sha256:bd37ec09c0c12831303ddfb6d713cf81526dd286b8e86dd8bb46f842b20dfc14","observation_id":"40d1399e-05de-48c8-81f7-abdeaa00b430","resolution":{"observed_at":"2026-08-05T22:42:54.483452Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2508.06637","last_updated":"2026-06-24T15:57:13Z","latest_version":3,"primary_category":"math.CT","snapshot_observed_at":"2026-08-07T16:38:57.553847Z","submitted_at":"2025-08-08T18:34:36Z","title":"Double-functorial representation of regular hyperdoctrines"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":1,"verified_fuzzy":14},"total_outbound_references":20},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2508.06637."}