{"paper":{"title":"Fibre stability for dominated self-affine sets","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.DS","authors_text":"Alex Rutar, Roope Anttila","submitted_at":"2024-12-09T15:33:04Z","abstract_excerpt":"Let $K$ be a planar self-affine set. Assuming a weak domination condition on the matrix parts, we prove for all backward Furstenberg directions $V$ that $$\\max_{E\\in\\operatorname{Tan}(K)} \\max_{x\\in \\pi_{V^\\bot}(E)} \\operatorname{dim_H} (\\pi_{V^\\bot}^{-1}(x)\\cap E) = \\operatorname{dim_A} K - \\operatorname{dim_A} \\pi_{V^\\bot}(K).$$ Here, $\\operatorname{Tan}(K)$ denotes the space of weak tangents of $K$. Unlike previous work on this topic, we require no separation or irreducibility assumptions. However, if in addition the strong separation condition holds, then there exists a $V\\in X_F$ so that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06579","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/2412.06579/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"}