{"paper":{"title":"Scattering diagrams for Artin algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hipolito Treffinger","submitted_at":"2026-08-04T21:19:12Z","abstract_excerpt":"For an arbitrary Artin algebra $A$, we construct a minimal and consistent scattering diagram by approximating its module category $\\mathrm{mod}\\,A$ using the subcategories $(\\mathrm{mod}\\,A)_\\ell$ of modules of length at most $\\ell \\in \\mathbb{N}$. We prove that each subcategory $(\\operatorname{mod}A)_\\ell$ possesses a well-behaved lattice of torsion classes, a finite wall-and-chamber structure $\\mathfrak{D}_\\ell(A)$ and an associated picture group $G_\\ell(A)$ with a natural categorical interpretation. Using these properties, we build a finite, minimal, consistent scattering diagram for each $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04233","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04233/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}