INTERMEDIATE DIMENSIONS OF INFINITELY GENERATED ATTRACTORS

The paper’s Theorem 3.5 establishes, for a conformal IFS (with OSC, cone condition, conformality, bounded distortion), the identities dim_B F = dim_P F = max{h, dim_B P}, dim_θ F = max{h, dim_θ P} for θ ∈ [0,1], and dim_Φ F = max{h, dim_Φ P} for monotonically admissible Φ, where h = dim_H F is given by the pressure zero via Mauldin–Urbański . The candidate solution proves the same max formulae by a different route: using δ-stopping cylinders, bounded clustering (their M) and standard thermodynamic tools for CIFS (conformal measure/Gibbs-type estimates), together with pressure negativity for t>h. This aligns with the paper’s geometric lemmas (e.g. Lemma 2.9 and the finite clustering Lemma 2.11) and the general upper-bound scheme in Theorem 3.2, though the candidate’s proof does not rely on the paper’s inductive covering construction . Two small issues: (i) an inequality used to interpolate between s and t-costs in the upper bound should read diam^s ≤ δ^{s−t} diam^t (since diam ≤ δ), not with Φ(δ) (a minor slip that does not affect the conclusion); and (ii) the paper assumes Φ is monotonically admissible for the Φ-intermediate identity, whereas the candidate states it for “admissible” Φ; tightening to the monotone case aligns fully with the paper .