Kaledin mentioned in https://arxiv.org/abs/2004.04279 Remark 11.5 that, in a letter to Waldhausen by Goodwillie in 1988, Goodwillie showed that the cyclic K-theory can be computed by the geometric realization of the cyclic nerve.
It might be some simple observation, but so far I do not see the reason. Furthermore, I cannot find a copy of Goodwillie's letter in 1988.
I look forward to an explanation, and/or a summary of Goodwillie's letter in 1988 in question.
