  We show that Quillen's resolution theorem for K-theory also applies to exact
$\infty$-categories. We introduce heart structures on a stable
$\infty$-category, generalizing weight structures, and using resolution ideas,
we show that the category of stable $\infty$-categories equipped with a heart
structure fully-faithfully embeds into the category of exact
$\infty$-categories. Consequently, we show a generalized theorem of the heart
for K-theory, which is equivalent to its invariance under passage to the stable
envelope of exact $\infty$-category in the image of the heart functor. Finally,
leveraging the above, we show that K-theory of endomorphisms satisfies the
theorem of the heart for weight structures, even allowing coefficients in a
suitable bimodule.
