{"paper":{"title":"Dimension of diagonal self-affine sets and measures via non-conformal partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ariel Rapaport","submitted_at":"2023-09-07T19:36:21Z","abstract_excerpt":"Let $\\Phi:=\\left\\{ (x_{1},...,x_{d})\\rightarrow\\left(r_{i,1}x_{1}+a_{i,1},...,r_{i,d}x_{d}+a_{i,d}\\right)\\right\\} _{i\\in\\Lambda}$ be an affine diagonal IFS on $\\mathbb{R}^{d}$. Suppose that for each $1\\le j_{1}<j_{2}\\le d$ there exists $i\\in\\Lambda$ so that $|r_{i,j_{1}}|\\ne|r_{i,j_{2}}|$, and that for each $1\\le j\\le d$ the IFS $\\left\\{ t\\rightarrow r_{i,j}t+a_{i,j}\\right\\} _{i\\in\\Lambda}$ on the real line is exponentially separated. Under these assumptions we show that the Hausdorff dimension of the attractor of $\\Phi$ is equal to $\\min\\left\\{ \\dim_{A}\\Phi,d\\right\\} $, where $\\dim_{A}\\Phi$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.03985","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/2309.03985/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"}