I think they misunderstood in this article. The cable would extend to the _height_ of the geostationary orbit. It will not actually be in the geostationary orbit as it would be anchored to the moon.
Т.е. начало троса будет притягивать к Луне, а большую его часть - к Земле, и трос должен выдерживать эти напряжения (включая вес грузов и противовесов)
No need for counterweights, that was one of the important points. You can check the computations in the paper, they are probably not too difficult to follow with a bit of math.
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