quantum Hamlet

The arXiv blog reports about a new proposed effect called Quantum Hamlet Effect. According to the author "It represents a complete destruction of the quantum predictions on the decay probability of an unstable quantum system by frequent measurement".

But I think there is a problem with it. The Hamlet state is prepared by a series of subsequent measurements, happening at decreasing time intervals tau/sqrt(n), with n
going to infinity. This leads to a divergent sum in the probability, which then leads to the "complete destruction of predictability".

But, of course, in reality the limit n to infinity cannot be taken (e.g. as the author notices himself he neglects time - energy uncertainty!), so we have to assume the procedure stops at n = N, with some finite but perhaps large N. Unfortunately, the divergent Hamlet term is the harmonic series, which increases only with log(N),
i.e. it increases much slower than sqrt(N).

Therefore I doubt that the Hamlet effect will "turn out to be more useful and famous than [the Zeno effect]" as suggested on the arXiv blog.