Tangents and slices of self-affine carpets

The paper proves precise tangent and pointwise Assouad-dimension formulas for Gatzouras–Lalley carpets and the full-dimension level-set result, via approximate squares, symbolic slices K_η(γ), and a product-containment argument for tangents (Proposition 3.6), culminating in Theorem 3.12 and Theorem 3.14; see also Theorem A in the introduction. The candidate solution reproduces the main statements but its key upper bound for tangent dimensions relies on an invalid inequality that attempts to bound sup_u dim_H(G∩η^{-1}{u}) by the dimension of the slice at η(x). This logical misstep is critical because it is used to assert equality in the maximal tangent dimension at x. The paper’s correct route avoids this by proving h(F) ⊂ η(K)×E for any tangent F (with E a weak tangent of the vertical slice), which yields the needed upper bound. Thus, while the candidate’s conclusions align with the paper, its proof contains a fundamental gap.