  A minimal model based on the Co-varying Physical Couplings (CPC) framework
for gravity is proposed. The CPC framework is based on the assumptions of a
metric-compatible four-dimensional Riemannian manifold where a covariantly
conserved stress-energy tensor acts as source of the field equations which are
formally the same as Einstein field equations, but where the couplings $\{ G,
c,\Lambda \}$ are allowed to vary simultaneously. The minimal CPC model takes
$\Lambda$ as a genuine constant while $c$ and $G$ vary in an entangled way that
is consistent with Bianchi identity and the aforementioned assumptions. The
model is constrained using the most recent galaxy cluster gas mass fraction
observational data. Our result indicates that the functions $c(z)$ and
$G\left(z\right)=G_{0}\left(c/c_{0}\right)^{4}$ are compatible with constant
couplings for the three different parameterizations of $c=c(z)$ adopted here.
