Dimensions and Dimension Spectra of Non-Autonomous Iterated Function Systems

The paper proves that, for a non‑autonomous conformal IFS satisfying OSC and the regularity (1.11), the upper and lower θ‑intermediate dimensions equal the jump points of the corresponding upper/lower pressure functions defined via δ‑cut sets. The key ingredients are the bounded‑distortion geometry (|Ju| ≍ ∥Dφu∥), the stopping‑time cut sets M(δ,θ), and a careful cover–to–cut/cut–to–cover construction used in the proof of Theorem 2.1, together with (1.11) to control scale transitions. The candidate solution follows the same high‑level plan (pressures via δ‑admissible cut sets) and is substantively correct; it differs mainly in presenting a more symmetric ‘two‑sided comparability’ between restricted intermediate contents and cut‑set sums, whereas the paper’s proof implements this comparison with a small exponent slack and direct combinatorial estimates. No contradiction arises, but the model’s Step (3) asserts a stronger uniform comparability than is explicitly established in the paper.