Regularity of non-autonomous self-similar sets

The paper proves that for non-autonomous self-similar IFSs satisfying the bounded neighbourhood condition (BNC), the Assouad dimension equals several limit forms built from the unique zeros θ(n,m) of block pressure functions ϕn,m, see Theorem A and Theorem 4.3 (dim_A K = lim_m sup_n θ(n,m) = lim_m limsup_n θ(n,m) = inf_m limsup_n θ(n,m)) under BNC . The candidate solution establishes the same formula via a block-pressure P(t) := lim_m sup_n ϕn,m(t) and a covering argument that uses BNC directly. The model’s subadditivity/weighted-counting proof is sound and aligns with the paper’s setting and assumptions (BNC, definitions of T(r), π, and ϕn,m) . While the paper proceeds via bi-Lipschitz decomposability and a disc-packing characterization of Assouad dimension , the model’s approach is a valid alternative. Minor nit: the model asserts P(t) is strictly decreasing and continuous; monotonicity suffices and strictness/continuity need not be invoked. Overall, both reach the same result; the proofs are different but compatible.