  For a finite-dimensional algebra $A$ over a field $K$ with $n$ simple
modules, the real Grothendieck group $K_0(\operatorname{\mathsf{proj}}
A)_\mathbb{R}:=K_0(\operatorname{\mathsf{proj}} A) \otimes_\mathbb{Z}
\mathbb{R} \cong \mathbb{R}^n$ gives stability conditions of King. We study the
associated wall-chamber structure of $K_0(\operatorname{\mathsf{proj}}
A)_\mathbb{R}$ by using the Koenig--Yang correspondences in silting theory.
First, we introduce an equivalence relation on
$K_0(\operatorname{\mathsf{proj}} A)_\mathbb{R}$ called TF equivalence by using
numerical torsion pairs of Baumann--Kamnitzer--Tingley. Second, we show that
the open cone in $K_0(\operatorname{\mathsf{proj}} A)_\mathbb{R}$ spanned by
the g-vectors of each 2-term silting object gives a TF equivalence class, and
this gives a one-to-one correspondence between the basic 2-term silting objects
and the TF equivalence classes of full dimension. Finally, we determine the
wall-chamber structure of $K_0(\operatorname{\mathsf{proj}} A)_\mathbb{R}$ in
the case that $A$ is a path algebra of an acyclic quiver.
