  One of the most intriguing aspects of $f$-electron systems is their
homogeneous mixed valence (MV) behavior. Despite extensive efforts, a
fundamental aspect which remains unsettled is the determination of the limiting
cases for which MV emerges, as highlighted by Haldane's theoretical proposal of
the occurrence of a MV state for a single $f$-type impurity in a Fermi sea of
$d$-electrons. Here we address this open question for SmB$_6$, a prototypical
system characterized by the interplay between two nearly-degenerate Sm$^{2+}$
and Sm$^{3+}$ configurations. By combining La substitution with angle resolved
photoemission (ARPES) and x-ray absorption spectroscopy (XAS), we track the
evolution of the mean Sm valence for the $f$-shell, $v_{Sm}$, in the
Sm$_x$La$_{1-x}$B$_6$ series. Upon substitution of Sm ions by trivalent
La$^{3+}$, we observe a linear decrease of valence fluctuations to an almost
complete suppression at $x$$\,$=$\,$0.2, with $v_{Sm}$$\,$$\sim$$\,$2;
surprisingly, by further reducing $x$, a re-entrant increase of $v_{Sm}$
develops for $x$$\,$<$\,$0.2, approaching a single-impurity-limit value of
$v_{imp}$$\,$$\sim$$\,$2.35. Such observation marks a stark deviation from a
monotonic evolution of $v_{Sm}$ across the entire series, as well as from the
expectation of its convergence to an integer value for
$x$$\,$$\rightarrow$$\,$0. Our study suggests the realization of a
$\textit{mixed-valence single-impurity state}$ in Sm$_x$La$_{1-x}$B$_6$, paving
the way to further considerations on the concept of MV and its influence on the
macroscopic properties of rare-earth compounds in the dilute-to-intermediate
impurity regime.
