  We compute the relative symplectic cohomology sheaf in degree $0$ on the
bases of nodal Lagrangian torus fibrations on four dimensional symplectic
cluster manifolds. We show that it is the pushforward of the structure sheaf of
a certain rigid analytic manifold under a non-archimedean torus fibration. The
rigid analytic manifold is constructed in a canonical way from the relative SH
sheaf and is referred as the \emph{closed string mirror}. The construction
relies on computing relative SH for local models by applying general axiomatic
properties rather than ad hoc analysis of holomorphic curves. These axiomatic
properties include previously established ones such as the Mayer-Vietoris
property and locality for complete embeddings; and new ones such as the Hartogs
property and the holomorphic volume form preservation property of wall crossing
in relative $SH$.

Symplectic Geometry