Greenberg's finiteness conjecture for the plus Iwasawa module

For general $N>1$, let $X^+$ denote the plus part of the relevant cyclotomic Iwasawa module. Greenberg's conjecture. The module $X^+$ is finite. This is a finiteness form of Greenberg's conjecture for cyclotomic class groups. The source notes that $X^+$ need not vanish, but records finiteness as conjectural and mentions that it holds in all known examples discussed there.