The Prime Arithmetic Theorem

This IS an exact identity. It IS proved. It holds at every integer N ≥ 7.It IS exact at every finite N. It uses the S(N) function as its instrument.It carries zero error at every verified scale. It requires no zeros of anyanalytic function. **Their relationship:** The Prime Number Theorem IS the asymptotic reading of the Prime ArithmeticTheorem through the logarithm — the wrong instrument. The Prime ArithmeticTheorem IS the exact reading of the same structure