COUNTING IN GENERIC LATTICES AND HIGHER RANK ACTIONS

The paper explicitly proves a central limit theorem for the discrepancy DT(Λ) over the domains ΩT(I,B) when k ≥ 2 and d ≥ 9, including the exact variance constant σ(I,B)^2 and convergence of the normalized discrepancy to a Gaussian law; see Theorem 1.2 and the displayed formula for σ(I,B)^2, which matches the candidate’s constant . The proof proceeds by approximating χΩT with functional averages and applying a general CLT (Theorem 3.17) based on effective exponential mixing of all orders for the higher-rank diagonal action, after verifying variance convergence via Rogers’ mean-square identity and establishing the needed bounds; see the axiomatic framework and Theorem 3.17 and the final verification implying d ≥ 9 suffices , together with the variance computation via Rogers’ theorem (Corollary 4.5) . Consequently, the result is not “likely open as of cutoff”; the model’s claim about openness and reliance on unavailable higher-order Rogers formulas is incorrect.