Twin Primes In Quadratic Arithmetic Progressions

A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the spectral method, and a proof for the existence of infinitely many quadratic twin primes $n^2+1$ and $n^2+3$, $n\ge 1$, are proposed in this note.