  The arboreal gas is the random (unrooted) spanning forest of a graph in which
each forest is sampled with probability proportional to $\beta^{\#
\text{edges}}$ for some $\beta\geq 0$, which arises as the $q\to 0$ limit of
the Fortuin-Kastelyn random cluster model with $p=\beta q$.
  We study the infinite-volume limits of the arboreal gas on the hypercubic
lattice $\mathbb{Z}^d$, and prove that when $d\leq 4$, any
translation-invariant infinite volume Gibbs measure contains at most one
infinite tree almost surely. Together with the existence theorem of
Bauerschmidt, Crawford and Helmuth (2021), this establishes that for $d=3,4$
there exists a value of $\beta$ above which subsequential weak limits of the
$\beta$-arboreal gas on tori have exactly one infinite tree almost surely. We
also show that the infinite trees of any translation-invariant Gibbs measure on
$\mathbb{Z}^d$ are one-ended almost surely in every dimension.
  The proof has two main ingredients:
  First, we prove a resampling property for translation-invariant arboreal gas
Gibbs measures in every dimension, stating that the restriction of the arboreal
gas to the trace of the union of its infinite trees is distributed as the
uniform spanning forest on this same trace.
  Second, we prove that the uniform spanning forest of any
translation-invariant random connected subgraph of $\mathbb{Z}^d$ is connected
almost surely when $d\leq 4$. This proof also provides strong heuristic
evidence for the conjecture that the supercritical arboreal gas contains
infinitely many infinite trees in dimensions $d\geq 5$. Along the way, we give
the first systematic and axiomatic treatment of Gibbs measures for models of
this form including the random cluster model and the uniform spanning tree.
