  The function $S_n (t) = \pi \left( \frac{3}{2} - {frac} \left(
\frac{\vartheta(t)}{\pi} \right) + \left( \lfloor \frac{t \ln \left( \frac{t}{2
\pi e}\right)}{2 \pi} + \frac{7}{8} \rfloor - n \right) \right)$ is conjectured
to be equal to $S (t_n)_{} = \arg \zeta \left( \frac{1}{2} + i t_n \right)$
when $t=t_n$ is the imaginary part of the n-th zero of $\zeta$ on the critical
line. If $S(t_n)=S_n(t_n)$ then the exact transcendental equation for the
Riemann zeros has a solution for each positive integer $n$ which proves that
Riemann's hypothesis is true since the counting function for zeros on the
critical line is equal to the counting function for zeros on the critical strip
if the transcendental equation has a solution for each $n$.
