{"paper":{"title":"Dimension of diagonal self-affine measures with exponentially separated projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhou Feng","submitted_at":"2025-01-29T02:19:09Z","abstract_excerpt":"Let $ \\mu $ be a self-affine measure associated with a diagonal affine iterated function system (IFS) $ \\Phi = \\{ (x_{1}, \\ldots, x_{d}) \\mapsto ( r_{i, 1}x_{1} + t_{i,1}, \\ldots, r_{i,d}x_{d} + t_{i,d}) \\}_{i\\in\\Lambda} $ on $ \\mathbb{R}^{d} $ and a probability vector $ p = (p_{i})_{i\\in\\Lambda}$. For $ 1 \\leq j \\leq d $, denote the $ j $-th the Lyapunov exponent by $ \\chi_{j} := \\sum_{i\\in\\Lambda} - p_{i} \\log | r_{i,j} |$, and define the IFS induced by $ \\Phi $ on the $j$-th coordinate as $ \\Phi_{j} := \\{ x \\mapsto r_{i,j}x + t_{i,j}\\}_{i\\in\\Lambda}$. We prove that if $ \\chi_{j_{1}} \\neq \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.17378","kind":"arxiv","version":2},"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/2501.17378/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"}