Shelah's pcf conjecture for limits of limit cardinals

Let $\mu$ be a limit of limit cardinals, and let $\lambda<\mu$ range over arbitrarily large regular cardinals. Write $\forall^*$ for “for every large enough.” Shelah's pcf conjecture for limits of limit cardinals. For arbitrarily large regular $\lambda<\mu$, we have

$$(\forall^*\mu_1<\mu)[\operatorname{cf}(\mu_1)=\lambda\ \Rightarrow\ \operatorname{pp}_{\Gamma(\lambda)}(\mu_1)<\mu].$$

The paper says this conjecture would simplify answers concerning universal objects and pcf theory; no resolution is supplied.