{"as_of":"2026-08-13T06:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f49f0700a4fc02967abfc2bba06af6e291d4726cf59b1eabdf4754f2980aa73c","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T06:07:04.472732Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2607.27541/citation-record","integrity":"/paper/2607.27541/integrity","json":"/paper/2607.27541/citation-record.json","paper":"/paper/2607.27541"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T06:07:02.076194Z","title":"Max Kelly, and A","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.076194Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:5b369a01d85e7ff1bac2b95dc7156c007ab32775f0fd39adb7c39fe3631b0e2e","observation_id":"368e1cc1-973b-4c1a-9e8e-9d4efadb6ba0","resolution":{"observed_at":"2026-08-01T06:07:02.076194Z","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":"2026-08-01T06:07:02.155464Z","title":"Fibred 2-categories and bicategories.J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.155464Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:04f92c679b6daba5030682931db63ef47e3b0fba26afc6bdd9e3bee3d4f18835","observation_id":"658cb241-ddfe-44f8-9f80-1e5b5c7f2953","resolution":{"observed_at":"2026-08-01T06:07:02.155464Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1503.06469","last_updated":"2016-09-09T21:10:25Z","snapshot_observed_at":"2026-07-06T04:12:46.762963Z","submitted_at":"2015-03-22T19:39:44Z","title":"Lax orthogonal factorisation systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1503.06469","snapshot_observed_at":"2026-08-01T06:07:02.399302Z","title":"Lax orthogonal factorisation systems","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.399302Z"},"links":{"cited_paper":"/paper/1503.06469","citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:d2efbee84eaf19769cdc1c72ff28b5b005915f59dfc3ed3e4746b8c4b0a9f1a3","observation_id":"5e73d00d-2161-4675-9a17-79ea52334206","resolution":{"observed_at":"2026-08-01T06:07:02.399302Z","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":"10.70930/tac/re3rk47b","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Lax comma 2-categories and admissible 2-functors.Theory Appl","venue":"Theory and applications of categories","work_id":"50e6bf1e-34b2-4e19-a8b8-e87067c5f575","year":2024},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.453459Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:93c2c2e86fe7b6c2cf6f8eb3fdd50ea3682fae6f16b0c7c131dd72d0dd0c5b23","observation_id":"d14f0e86-4ff1-469c-bb3f-a203d9a561a2","resolution":{"observed_at":"2026-08-01T06:08:28.719179Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.70930/tac/3d9q6q64","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A comonad for Grothendieck fibrations.Theory Appl","venue":"Theory and applications of categories","work_id":"39d9d7c2-7485-4983-bdf0-d897de3c498b","year":2024},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.547075Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:15a2d617c047c710193f134cb3df162681b167e08453b69de49cb5d21c72f242","observation_id":"6678b2dc-2421-4843-b2d2-d1443b50c59a","resolution":{"observed_at":"2026-08-01T06:08:28.642323Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1411.2457","last_updated":"2014-11-10T15:27:26Z","snapshot_observed_at":"2026-07-06T04:00:03.359445Z","submitted_at":"2014-11-10T15:27:26Z","title":"Geometric constructions preserve fibrations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.2457","snapshot_observed_at":"2026-08-01T06:07:02.625755Z","title":"Geometric constructions preserve fibrations","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.625755Z"},"links":{"cited_paper":"/paper/1411.2457","citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:816e2b1746ce08cd6cf347e1c95e819904b28a257c0063792ac6859d60b4ef8a","observation_id":"aaac3324-1661-4f79-9559-793970b11a9f","resolution":{"observed_at":"2026-08-01T06:07:02.625755Z","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":"2026-08-01T06:07:02.715279Z","title":"Natural weak factorization systems.Arch","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.715279Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:da49cfba6829ab7b6dce57507cd5c56b681b5087043737efa4c1b1edd098b050","observation_id":"f55608b4-8d33-4789-b9b2-6f0e92cbce71","resolution":{"observed_at":"2026-08-01T06:07:02.715279Z","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":"10.1007/978-3-642-99902-4_","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T06:08:28.495145Z","title":null,"venue":null,"work_id":"6326d8e7-8219-4efb-a4c5-f64ef4ddebf5","year":1965},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.802289Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:d32fe9151a71dca142b93b75f73423c58acc14bfaa77c0076e9159762e46647c","observation_id":"40d312ef-0308-43fe-85bb-4df8ae5e0085","resolution":{"observed_at":"2026-08-01T06:08:28.569422Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bfb0058662","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Catégories fibrées et descente","venue":"Lecture notes in mathematics","work_id":"7c89661b-8444-4c8b-b929-632f968708e4","year":1971},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.864079Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:9813c0e22aab77be0627f257ce0205b67627f230e9360cd6c49ec0d6be877ed0","observation_id":"55ff2b06-e6dd-4ee0-8ae7-70928a11958c","resolution":{"observed_at":"2026-08-01T06:08:28.387020Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-01T06:07:02.943715Z","title":"Some properties of Fib as a fibred 2-category.J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.943715Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:33b020c8bcb4152caaf54cbd8faa73b7bdf4d4bbd05e914531849eff922644f1","observation_id":"4234ea09-690d-4568-bc4d-e5242aa215fa","resolution":{"observed_at":"2026-08-01T06:07:02.943715Z","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":"2026-08-01T06:07:03.031706Z","title":"North-Holland, Amsterdam, 1999","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.031706Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:99f4821a32cfb8e4d59e64ede553391717a2d6cc29a32e04e1a123ba7939baca","observation_id":"95f942c1-4f27-430b-81b1-f6795ac01f41","resolution":{"observed_at":"2026-08-01T06:07:03.031706Z","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/s0022-4049(98)00095-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Functorial factorization, well-pointedness and separabil- ity.J","venue":"Journal of Pure and Applied Algebra","work_id":"b3b4350a-2834-4a20-9dd4-602ad8336875","year":1999},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.092742Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:0299b961b88d14183b1efe0f261f5b32b36fa8a0f25361edd45493b6209386fb","observation_id":"548e4ea1-375b-4bc8-8bf0-fc59022221e1","resolution":{"observed_at":"2026-08-01T06:08:28.113684Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bfb0063101","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Max Kelly and Ross Street","venue":"Lecture notes in mathematics","work_id":"cfe14e96-19ab-4d22-8e10-42e46d906b43","year":1972},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.190370Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:fa5cf10e2d09ebcc3c4beda2104009b60834446c7736db0ea1d749761aec145b","observation_id":"eb8586f8-7ed4-4ab4-b1be-8cbc5681950f","resolution":{"observed_at":"2026-08-01T06:08:28.040709Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0022-4049(94)00111-u","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Monads for which structures are adjoint to units.J","venue":"Journal of Pure and Applied Algebra","work_id":"9ddc44d2-eb4e-42ed-9e9c-4106f99b4aaf","year":1995},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.260751Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:b85e6336b023c70a8efd27da9ddec3d48e2f701bf6a4114c5470d62c5e5bea87","observation_id":"bfad3a3c-0a6f-43f8-ab81-74c37517dbb5","resolution":{"observed_at":"2026-08-01T06:08:27.971342Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0022-4049(93)90171-o","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Factorization systems as Eilenberg–Moore algebras.J","venue":"Journal of Pure and Applied Algebra","work_id":"44229b81-e48f-4a51-a201-284dfdb40dd7","year":1993},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.314635Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:ea42ba47baa1a26cd1c1a5152d16b81e85d459d3f0674d5468d8ddf3bf4ab2da","observation_id":"1861b444-4935-48b5-8887-3cff0b1c8f6b","resolution":{"observed_at":"2026-08-01T06:08:27.886527Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10485-018-9541-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Pseudoalgebras and non-canonical isomorphisms.Appl","venue":"Applied Categorical Structures","work_id":"a56c1a89-2dab-43ad-888d-c60017515d97","year":2019},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.392138Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:6e9ab4051d2b80c7c7fb5a28777961611e196d3c62275a2ff3bc5ed35802f978","observation_id":"97e3c18f-2b8d-41fe-9749-38561b2cecf3","resolution":{"observed_at":"2026-08-01T06:08:27.798306Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2110.00446","last_updated":"2023-04-03T10:29:41Z","snapshot_observed_at":"2026-07-06T11:53:31.073250Z","submitted_at":"2021-10-01T14:30:30Z","title":"CHAD for Expressive Total Languages","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.00446","snapshot_observed_at":"2026-08-01T06:07:03.451316Z","title":"CHAD for expressive total languages.Math","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.451316Z"},"links":{"cited_paper":"/paper/2110.00446","citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:747f44458a52288afd85a84b4f9e4bc82adc252c35fa15912c756c782f82b92b","observation_id":"4cd1005a-f19e-4113-9474-2fbc6547354d","resolution":{"observed_at":"2026-08-01T06:07:03.451316Z","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":"2026-08-01T06:07:03.511421Z","title":"Monoidal closure of Grothendieck constructions via Σ-tractable monoidal structures and Dialectica formulas.Theory Appl","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.511421Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:240c5a16e7d57c5e3da5a09d9f0f939c6a3f065595851fdf90324f3aefad5bce","observation_id":"98635e90-a624-4aaf-bdec-ac65142644ae","resolution":{"observed_at":"2026-08-01T06:07:03.511421Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2210.12021","last_updated":"2023-02-05T00:37:37Z","snapshot_observed_at":"2026-07-06T14:08:45.786397Z","submitted_at":"2022-10-21T15:09:04Z","title":"Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.12021","snapshot_observed_at":"2026-08-01T06:07:03.570319Z","title":"Cauchy completeness, lax epi- morphisms and effective descent for split fibrations.Bull","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.570319Z"},"links":{"cited_paper":"/paper/2210.12021","citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:649f3c8c7b80aa0fc09663617530c2e9c3fb0b7725f4ed0d704d9ff5a32d6199","observation_id":"5fdaeb10-f0be-4bf1-b0d7-a7bbfaa76b26","resolution":{"observed_at":"2026-08-01T06:07:03.570319Z","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":"2026-08-01T06:07:03.624532Z","title":"Monoidal Grothendieck construction.Theory Appl","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.624532Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:794dd87a64ef81123befedb8e99260830e78cf156d6a39247f946ea9db47b36e","observation_id":"9676bf18-2887-41bc-853d-e493fe9f0ae6","resolution":{"observed_at":"2026-08-01T06:07:03.624532Z","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":"10.1007/s10485-021-09671-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kan extensions are partial colimits.Appl","venue":"Applied Categorical Structures","work_id":"6c22153b-8b71-4997-9dfc-e7b770c0229e","year":2022},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.679076Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:ecc36ac1b9029bf0454353d3209f4ba3b4eb013e026efedb0c28e704f66fff5a","observation_id":"df6af39f-f7e5-42d8-81c4-3db585a0e740","resolution":{"observed_at":"2026-08-01T06:08:27.717173Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.10890","last_updated":"2021-03-08T03:40:52Z","snapshot_observed_at":"2026-07-06T09:30:38.493338Z","submitted_at":"2020-06-18T22:57:30Z","title":"Diagrams, Fibrations, and the Decomposition of Colimits","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.10890","snapshot_observed_at":"2026-08-01T06:07:03.738394Z","title":"Diagrams, fibrations, and the decomposition of colimits","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.738394Z"},"links":{"cited_paper":"/paper/2006.10890","citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:88576538e3c3dc2f3d3fbfd6f511639ed22395a4fe28de6846f38909179a782d","observation_id":"4c1ccfa4-0f95-4fb1-814a-4731b434fb5b","resolution":{"observed_at":"2026-08-01T06:07:03.738394Z","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":"10.70930/tac/g0lqukuu","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Theory and applications of categories","work_id":"fdffa9f2-a41f-464f-9b54-b2b247360870","year":2002},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.787064Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:a20a367f7714c05c56769f285e455666c02689d862b30c302463ccd53a5c8f1e","observation_id":"1c019079-99e3-4275-b075-d757a42be896","resolution":{"observed_at":"2026-08-01T06:08:27.610778Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0022-4049(02)00140-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Pure and Applied Algebra","work_id":"be7e6a84-45ac-44ff-92b8-56f909fe78a2","year":2002},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.848421Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:867cfe6ca44dcbff80b3552b95a47b8b8c3858d9fe1def517162a1ec51682c53","observation_id":"05a4c8f5-4314-41f7-8657-94c86c36c389","resolution":{"observed_at":"2026-08-01T06:08:27.506171Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0022-4049(02)00141-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Lax factorization algebras.J","venue":"Journal of Pure and Applied Algebra","work_id":"94b5afca-1e3f-4a98-be41-158c03daa0dc","year":2002},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.902442Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:a44ffa332eabb0c298ef9ae4a7801b9b95366f941d481c2d6ce8146c5a1e753f","observation_id":"6a5ec911-6377-4480-bdc4-71301f16baaf","resolution":{"observed_at":"2026-08-01T06:08:27.410116Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-01T06:07:03.959148Z","title":"Factorization, fibration and torsion.J","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:03.959148Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:5171434124c1e8a4afd235dd401e591669c66d46c8c0564fd581ff8973f7aea2","observation_id":"f227b68a-9194-4ae6-8c98-d9e4d14d700d","resolution":{"observed_at":"2026-08-01T06:07:03.959148Z","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":"2026-08-01T06:07:04.058500Z","title":"The formal theory of monads.J","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:04.058500Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:4427090a0cef799526bf2b7dc34cb6914f17ccd8c1d8b5f951c33bcbfac1b033","observation_id":"96580f36-d978-487f-9a43-b99b62f6bc3f","resolution":{"observed_at":"2026-08-01T06:07:04.058500Z","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":"2026-08-01T06:07:04.163265Z","title":"Fibrations and Yoneda’s lemma in a 2-category","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:04.163265Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:b5606223d6598c963feec419da37df686d1faf43bc317014adff93d8077085ab","observation_id":"8810755f-9d27-4bb0-a1a4-9b3a09b5b08e","resolution":{"observed_at":"2026-08-01T06:07:04.163265Z","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":"2026-08-01T06:07:04.247760Z","title":"Fibrations in bicategories.Cah","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:04.247760Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:3436a27f32e6ea446b2da2b231c964f43ccea09092dac5faa027ae21a9888964","observation_id":"a933a98d-ec24-43ae-bd59-b2d5e9f0c5ab","resolution":{"observed_at":"2026-08-01T06:07:04.247760Z","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":"10.1090/s0002-9904-1973-13268-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Bulletin of the American Mathematical Society","work_id":"2cdc5db0-8489-4d9c-b77f-65cbfc3c3bd7","year":1973},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:04.332493Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:db457ff341fe0f7bd00d9b8aa2e7afa26b66b29ac10032c17fa3d54c8895c336","observation_id":"6a5c4f47-32bb-4f60-9926-7e1cd9930e73","resolution":{"observed_at":"2026-08-01T06:08:27.301888Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-01T06:07:04.418692Z","title":"On enriched fibrations.Cah","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:04.418692Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:8de57948909cb8c8e0aba79d67f755cf9fe2f724f91f26d13108c38d16b217f2","observation_id":"b7d4949b-c056-4f81-8891-020488445c37","resolution":{"observed_at":"2026-08-01T06:07:04.418692Z","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":"2026-08-01T06:07:04.472732Z","title":"Doctrines on 2-categories.Math","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:04.472732Z"},"links":{"citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:61b644f2e56ced4cb59c1fe1c13cb11e245376589c807c1f2759bdf47fe7e266","observation_id":"e78a959a-20db-4274-9b66-fb804e88759f","resolution":{"observed_at":"2026-08-01T06:07:04.472732Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1212.6283","last_updated":"2013-03-25T00:37:55Z","snapshot_observed_at":"2026-08-11T09:50:48.741541Z","submitted_at":"2012-12-27T00:45:17Z","title":"Fibred 2-categories and bicategories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1212.6283","snapshot_observed_at":"2026-08-01T06:07:02.279535Z","title":"URLhttps://arxiv.org/abs/1212.6283","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-01T06:07:02.279535Z"},"links":{"cited_paper":"/paper/1212.6283","citing_paper":"/paper/2607.27541"},"observation_digest":"sha256:f01d972893a9d14d9e52bde094ef4ac76bdc77849eb8f68a3f42566227a399b9","observation_id":"86fb25cc-ab7c-448f-802c-52e73fb1cd9f","resolution":{"observed_at":"2026-08-01T06:07:02.279535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.27541","last_updated":"2026-07-30T00:22:45Z","latest_version":1,"primary_category":"math.CT","snapshot_observed_at":"2026-08-03T18:47:23.702454Z","submitted_at":"2026-07-30T00:22:45Z","title":"From Grothendieck cofibrations to factorization systems: a formal 2-monadic account"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":14,"verified_fuzzy":0},"total_outbound_references":33},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2607.27541."}