= Solution
The <Bukovský-Hechler theorem> states: if $\kappa$ is singular and there are a <cardinal> $\rho<\kappa$ and a <cardinal> $\tau$ such that $2^\mu=\tau$ for every <cardinal> $\mu$ with $\rho\le\mu<\kappa$, then
$$
\boxed{2^\kappa=\tau.}
$$
Thus an eventual plateau of the power-set <function> below a <singular cardinal> continues at that <cardinal>. One can see the mechanism by decomposing $\kappa$ into $\operatorname{cf}(\kappa)$ bounded pieces: $2^\kappa=(2^{<\kappa})^{\operatorname{cf}(\kappa)}$. On the plateau choose $\mu\ge\operatorname{cf}(\kappa)$, so $\tau^{\operatorname{cf}(\kappa)}=(2^\mu)^{\operatorname{cf}(\kappa)}=2^\mu=\tau$.
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