Maximal clusters of zeros of the zeta-function

Random matrix theory predicts that at a height $T$, the closest that two zeros of $\zeta(s)$ could be is about $T^{-1/3}$. (Unlike the situation of large gaps, where the primes enter into the picture in a critical way, the random matirx prediction is expected to give the right answer here.) Now the question is, how many zeros could be clustered together in a small region? Clearly, this question is related to large values of $S(T)$. Let $M_S(T) =\max_{t<T}S(t)$. Is it reasobale to believe that for certain $T$ there will be $\gg M_S(T)$ zeros clustered together in an interval $(T,T+T^{-1/3+\epsilon})$?

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