Maximizing dimension for Bernoulli measures and the Gauss map

The paper proves existence of a Bernoulli measure maximizing dimension for the Gauss map, identifies its power-law tail p_k ≍ k^{-2D}, and establishes ergodicity via transfer-operator methods. The candidate solution reaches the same conclusions using a different variational route (maximizing F_s = h − sλ and sending s ↗ D), plus a KKT-type argument to obtain the tail. While the model’s proof contains some steps that would benefit from tighter justification (notably compactness/tail control from KL bounds and a heuristic derivative of λ), the core logic aligns with the paper’s rigorous framework and conclusions.