Lower box dimension of infinitely generated self-conformal sets

The paper proves only an upper identity and sharp two-sided bounds for the lower box dimension, not the lower identity asserted by the model. Specifically, it shows max{dim_H Λ, dim_B F} ≤ dim_B Λ ≤ dim_B Λ = max{dim_H Λ, dim_B F} (their equation (1.4)) and classifies existence of box dimension by dim_B Λ = dim_B Λ iff dim_B F ≤ max{dim_H Λ, dim_B F} (Theorem B). It further provides an asymptotic formula for log N_r(Λ) that demonstrates the lower box dimension can strictly exceed max{dim_H Λ, dim_B F} in general. Thus the model’s Step 1 equalities (claiming dim_B Λ = max{dim_H Λ, dim_B F}) are false; the model’s final criterion matches the paper’s Theorem B but is derived from an incorrect premise. See the paper’s (1.4), Theorem B, and Theorem C for the correct statements and proof strategy.