Twin Primes and Spectral Imbalance: Proof by Structural Contradiction

We propose a novel structural framework to address the Twin Prime Conjecture by introducing a spectral-parity analysis over a lattice of odd integers. Prime numbers are treated as excitation points, and their interactions are encoded via a phase function Φ(p, q) = exp(iπ|p − q|). Twin prime pairs produce a unique spectral mode Φ = –1, and the persistence of this mode across the lattice is shown to be essential for maintaining spectral symmetry. Assuming that only finitely many twin primes exist would eliminate this mode beyond a certain bound, resulting in an imbalance in the parity-phase spectrum. This structural contradiction forms the basis of a proof by contradiction that supports the infinitude of twin primes. Unlike traditional analytic approaches relying on sieve methods or zeta function analysis, our method is discrete, combinatorial, and symmetry-based. The proposed framework provides an alternative route to understanding prime gaps through structural consistency in spectral representations.