In this question here:
Upper bound on differences of consecutive zeta zeros
by Charles it is said that: "There are many papers giving lower bounds to:
$$\limsup_n\ \delta_n\frac{\log\gamma_n}{2\pi}$$
unconditionally or on RH or GRH." RH stands of course for the Riemann hypothesis.
Therefore I am asking: What is the best unconditional effective lower bound for gaps $$\delta_n=|\gamma_{n+1}-\gamma_n|$$ between consecutive non-trivial Riemann zeta function zeros?
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