On an abrasion motivated fractal model

The paper proves: (i) existence of a unique Hausdorff limit X for the edge nets under regular chipping; (ii) an explicit formula for dim_B(X)=s0 via the singular value function, with 1 ≤ dim_B(X) ≤ 2; and (iii) in the constant-rate case p∈(0,1/2), dim_H(X)=s0, by invoking modern self-affine dimension results which require proximality and strong irreducibility as well as separation. These are all stated and proved (or reduced to established theorems) in the manuscript’s Theorem 1 and Theorem 2, with the affine encoding via the matrices Cj,σ,p from (2) and the IFS representation, the use of adapted charts, and a careful separation analysis via projection to V= {(x1,x2,x3): x1+x2+x3=0} (Section 3) . By contrast, the candidate solution’s upper bound aligns with Falconer-style covering, but the lower bound relies on an unproven “bounded overlap” of same-level cylinders and a Gibbs–type mass distribution without establishing the key separation/overlap lemmas which the paper supplies. More seriously, for the constant-rate case it claims dim_H(X)=s0 from a classical Carathéodory construction under strong separation alone; in 3D this is not generally valid and the paper instead uses stronger hypotheses (proximality, strong irreducibility) and recent theorems to conclude equality . The candidate also misstates all step matrices as upper–triangular (only one of the three forms is upper triangular; the others are not) .