Let us suppose we got a modification of the Selberg trace as follows
$ \sum_{n=0}^{\infty} h(r_n) = \frac{\mu(F)}{4 \pi } \int_{-\infty}^{\infty} r \, h(r) \tanh(\pi r) dr + \sum_{ \{T\} } \frac{ \log N(T_0) }{ N(T)^{1/2} - N(T)^{-1/2} } g \left ( \log N(T) \right )+h(i/2)- \sum_{n=1}^{\infty} \frac{\Lambda (n)}{\sqrt{n}}g(logn)- \frac{g(0)log\pi}{2}+ \frac{1}{4\pi}\int_{-\infty}^{\infty}drh(r) \frac{ \Gamma '}{\Gamma}(1/4+ir/2)$
so the trace over the riemann zeros is included inside this model, would this trace (the existence) be a proof of the Riemann Hypothesis?