Structural Proof of the Infinitude of Twin Primes via Modular Admissibility

This paper presents a rigorous and elegant proof of the infinitude of twin primes, i.e.,prime pairs (p, p+2) where both p and p+2 are prime. The method is based on a stablearithmetic structure, the use of a universal sieve, a strictly positive density argument, anda proof by contradiction. An experimental section strengthens the consistency of thereasoning by testing more than 50,000 cases. The result establishes that the set of twinprimes is infinite, thereby addressing one of the oldest unsolved conjectures inmathematics.