Mean and variance of finite 2-adic complexity (Question 3.1)

The manuscript claims both requested results: the exact mean upper bound for every N>=1 and an explicit finite arithmetic-logarithmic variance formula obtained from the complete distribution. It also evaluates the limiting variance as 0.892302571204274625294755... . The all-length mean proof combines a written lattice argument with exact finite certificates. The variance and asymptotic arguments use finite counting, marked-lattice equidistribution and uniform integrability. The limiting geometric law is explicitly credited to Boca-Gologan. The finite answer is a sum, not a short elementary expression in N; no convergence rate or raw-height variance theorem is claimed.

The manuscript claims both requested results: the exact mean upper bound for every N>=1 and an explicit finite arithmetic-logarithmic variance formula obtained from the complete distribution. It also evaluates the limiting variance as 0.892302571204274625294755... . The all-length mean proof combines a written lattice argument with exact finite certificates. The variance and asymptotic arguments use finite counting, marked-lattice equidistribution and uniform integrability. The limiting geometric law is explicitly credited to Boca-Gologan. The finite answer is a sum, not a short elementary expression in N; no convergence rate or raw-height variance theorem is claimed.