ON THE GAUSS-KUZMIN-LÉVY PROBLEM FOR NEAREST INTEGER CONTINUED FRACTIONS

The paper proves Gauss–Kuzmin–Lévy-type asymptotics for the three nearest-integer CF maps T, To, Te with explicit rates q=0.291 (T, To) and q=0.246 (Te), by analyzing the normalized Perron–Frobenius operator U = M_{1/h} P M_h, proving a derivative contraction, and applying a mean value estimate; To is reduced to T by a symmetry operator V; Te is handled via a conjugation T̃e to [0,1] and an analogous derivative bound (Corollary 11) leading to the same scheme (Theorem 1 and its proofs) . The candidate solution follows essentially the same normalized-operator/MVT strategy and arrives at the paper’s rates; it also proposes explicit multiplicative constants C1, C2, C3 by bounding sup-norms via derivatives/variation. Minor issues: it cites slightly stronger contraction rates (0.288, 0.234) not found in the uploaded paper and uses a heuristic “×2” reduction for To that the paper replaces with a precise operator symmetry. These are small and fixable; the core argument and conclusions match the paper.