  This article is Part I in a series of three papers devoted to determining the
minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part
I, we shall complete our development of a fine structure theory for
$K(\mathbb{R})$ which is essential for our work in Parts II and III. In
particular, we prove the following fundamental theorem which supports our
analysis of scales in $K(\mathbb{R})$: If $\mathcal{M}$ is an iterable real
premouse, then $\mathcal{M}$ is acceptable above the reals. This theorem will
be used in Parts II and III to solve the problem of finding scales of minimal
complexity in $K(\mathbb{R})$.
