A Recursive Tower Sieve Method Based on Uniform Distribution Correction: Proof of the Twin Prime Conjecture

This paper develops a recursive tower sieve method based on uniform distribution correction and applies it to prove the twin prime conjecture. The method removes at most two fixed residue classes modulo each prime at each step, while the surviving set maintains a complete periodic structure. We rigorously prove the recursive relation \(N_i = N_{i-1}(1 - d_i/P_i) + E_i\), where \(|E_i|\) is bounded by an absolute constant. Furthermore, we construct the interval \(U = [1, Q_t + P_t^2]\) and use translation invariance and complement decomposition to obtain a lower bound \(N(A) \ge P_t^2 A_t - Dt\), where \(A_t = \frac12\prod_{i=2}^t (1-2/P_i)\). By Mertens' theorem, the main term \(\sim c t^2\) tends to infinity, thus proving the twin prime conjecture. The proof is elementary, self-contained, and uses no unproven conjectures.