{"paper":{"title":"Bousfield Localizations on the Nonmodular Lattice $N_5$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The nonmodular lattice N5 admits exactly those model category structures that arise from transfer systems, all connected by Bousfield localizations.","cross_cats":[],"primary_cat":"math.AT","authors_text":"Constanze Roitzheim, Sof\\'ia Mart\\'inez Alberga","submitted_at":"2026-05-12T20:48:18Z","abstract_excerpt":"We provide a complete description of the model category structures on the nonmodular lattice $N_5$. Furthermore we explain how these model category structures are related to each other via Bousfield localization. This work heavily relies on the use of combinatorical objects from equivariant homotopy theory known as \\emph{transfer systems}, and it results in a wealth of interesting interactions between combinatorial and homotopical methods."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We provide a complete description of the model category structures on the nonmodular lattice N5.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That transfer systems from equivariant homotopy theory suffice to enumerate and relate all model structures on this specific lattice.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"All model structures on the lattice N5 are classified and related via Bousfield localizations using transfer systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The nonmodular lattice N5 admits exactly those model category structures that arise from transfer systems, all connected by Bousfield localizations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6abf6702537613e8000a7fc1a699ebfefc6ae30e562bc39f9d1cd08aa6951ced"},"source":{"id":"2605.12744","kind":"arxiv","version":1},"verdict":{"id":"786bdaaa-6963-45e1-a553-77c4c8f64330","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:00:31.631715Z","strongest_claim":"We provide a complete description of the model category structures on the nonmodular lattice N5.","one_line_summary":"All model structures on the lattice N5 are classified and related via Bousfield localizations using transfer systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That transfer systems from equivariant homotopy theory suffice to enumerate and relate all model structures on this specific lattice.","pith_extraction_headline":"The nonmodular lattice N5 admits exactly those model category structures that arise from transfer systems, all connected by Bousfield localizations."},"references":{"count":28,"sample":[{"doi":"10.1017/9781108636575","year":2020,"title":"Barnes, D. and Roitzheim, C. , TITLE =. 2020 , PAGES =. doi:10.1017/9781108636575 , URL =","work_id":"25d0aa9a-2419-41e6-9e7b-21e926e28d25","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Mazur, K. and Osorno, A.M. and Roitzheim, C. and Santhanam, R. and Van Niel, D. and Zapata Castro, V. , TITLE =. Topology and its Applications , YEAR =","work_id":"e4adc13a-8f14-4984-adb2-a7790468e234","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Mazur, K. and Osorno, A.M. and Roitzheim, C. and Santhanam, R. and Van Niel, D. and Zapata Castro, V. , TITLE =. arXiv preprint , YEAR =","work_id":"982bf00d-2e91-40ea-a6ed-7c86f4499a7c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Carnero Bravo, A. and Goyal, S. and Mart. Left and right Bousfield Localization on Lattices , JOURNAL =. 2025 , PAGES =","work_id":"c052c416-38e2-4ceb-acce-3dfec5692ad5","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1090/surv/099","year":2003,"title":"Hirschhorn,Model categories and their localizations, Mathematical Surveys and Monographs, vol","work_id":"3bd12657-fc70-4e44-9c29-6f8443f748b3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"29861fd2051869ae5692daf0732ce6e36bd791ea1b7f3c07f30f734b3ebab0f8","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"dd38840c7020a08575390de1d138b46e13e4585e01e828f2f9b7b8f7e56452dd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}