Assouad-type Dimensions of Overlapping Self-affine Sets

The paper’s Theorem A (equations (1.2)–(1.3)) and its proof (Theorem 2.10) establish the exact Assouad-dimension formula for dominated rectangular self-affine sets, with a lower bound via carefully aligned weak tangents and a matching upper bound under the WSC, plus a slice/symbolic-fibre identification of suprema under WSC . The candidate solution replicates the headline statements but its proof contains serious errors: (i) it constructs a purported weak tangent π(K) × E′η by applying inverses to unions of full rectangles Un⊂K—yet Un⊂K is false; (ii) it asserts a general product rule dimA(A×B)=dimA A+dimA B, which the paper explicitly notes is false in general (only holds in the self-similar–times–compact setting) ; (iii) it claims Eη equals the geometric fibre Kxη for all η, whereas the paper only proves {xη}×Eη⊂K and equality of the suprema under WSC, not set equality in general ; and (iv) it assumes uniform fibre-covering constants without invoking the uniformity proposition (Proposition 2.6) that the paper develops for this purpose . Net: the paper’s argument is sound; the model’s is not.