FINER GEOMETRY OF PLANAR SELF-AFFINE SETS

The paper proves the slicing formula for the Assouad dimension in the dominated, strongly separated planar self-affine setting (Theorem 3.2) and the strict bound < 2, via weak tangents, a uniform subunit upper bound for all slices (Lemma 5.1), a carefully constructed tangent with 1-dimensional slices in a Furstenberg direction (Lemma 5.2), Marstrand’s slicing theorem, and the identity dim_A(X) = max_{T in Tan(X)} dim_H(T) (Lemma 2.1). This chain is explicit and correct in the PDF. By contrast, the candidate solution claims a strong, unreferenced “tangent decomposition” that every microset is contained in a finite union of bi-Lipschitz images of products I × Y, and uses this as a black box for the upper bound. That product-structure statement is not asserted in the paper and, as stated, is stronger than what is used or established there. The model’s lower-bound construction is plausible in spirit but not justified at the level of detail provided. Consequently, although the model’s final conclusion matches the paper, its proof relies on unproven claims and mis-citations, so we deem the model’s argument incorrect.