  We address the one-parameter minmax construction, via Allen--Cahn energy,
that has recently lead to a new proof of the existence of a closed minimal
hypersurface in an arbitrary compact Riemannian manifold $N^{n+1}$ with $n\geq
2$ (see Guaraco's 2018 work). We obtain the following multiplicity-$1$ result:
if the Ricci curvature of $N$ is positive then the minmax Allen--Cahn solutions
concentrate around a multiplicity-$1$ hypersurface, that may have a singular
set of dimension $\leq n-7$. This result is new for $n\geq 3$ (for $n=2$ it is
also implied by the recent work by Chodosh--Mantoulidis). The argument
developed here is geometric in flavour and exploits directly the minmax
characterization of the solutions. An immediate corollary is that every compact
Riemannian manifold $N^{n+1}$ with $n\geq 2$ and positive Ricci curvature
admits a two-sided closed minimal hypersurface, possibly with a singular set of
dimension at most $n-7$. This existence result also follows from
multiplicity-$1$ results developed within the Almgren--Pitts framework, see
works by Ketover-Marques-Neves, Zhou, Marques-Neves, Ramirez-Luna.
