= Solution
There is a literal domain error in the printed formula. A <semivariogram> indexed by a signed displacement must satisfy $\gamma(h)=\gamma(-h)$, since reversing the two observations leaves the squared increment unchanged. For positive $\sigma^2$ or $\tau^2$, the displayed positive-lag value is nonzero whereas the displayed negative-lag value is zero. Thus the claim on all of $\mathbb R$ is false as written.
Interpret the argument as a nonnegative distance, or use the even extension of the <Gaussian semivariogram>. For $\sigma^2,\tau^2\ge0$ and $\phi>0$, the intended model is
$$
\gamma(h)=\tau^2\mathbf1_{\{h\ne0\}}+\sigma^2(1-e^{-\phi^2h^2}).
$$
It admits the <covariogram>
$$
\boxed{C(h)=\sigma^2e^{-\phi^2h^2}+\tau^2\mathbf1_{\{h=0\}}.}
$$
The <Gaussian kernel> is a <positive-definite kernel>, as can be seen from the <Fourier transform of a Gaussian>: in one dimension
$$
e^{-\phi^2h^2}=\int_{\mathbb R}e^{i\omega h}\frac{e^{-\omega^2/(4\phi^2)}}{2\phi\sqrt\pi}\,d\omega,
$$
and the nonnegative spectral density makes every finite <covariance> quadratic form nonnegative. In higher dimensions use the product Gaussian density. Adding independent Gaussian <white noise> of <variance> $\tau^2$ adds the diagonal nugget <covariance>. Thus a zero-mean <stationary Gaussian random field> exists with this <covariance>, and $C(0)-C(h)$ gives the corrected <semivariogram>.
For nonzero structured <variance>, the <nugget effect> is the right limit $\tau^2$ at zero, the <sill of a semivariogram> is $\tau^2+\sigma^2$, and the <range of a semivariogram> is infinite if defined as the distance at which the sill is exactly reached. A 95-percent <practical range> solves $1-e^{-\phi^2h^2}=0.95$:
$$
\boxed{h_{0.95}=\sqrt{\log20}/\phi.}
$$
The scale $1/\phi$ is sometimes called the range parameter; it is neither the exact range nor the 95-percent practical range. If $\sigma^2=0$, there is no nontrivial structured range.
The fact that <a semivariogram does not determine stationarity> is a further distinction: a <semivariogram> specifies increment variation, not a unique process or absolute <covariance>. Adding an independent random constant adds a constant to $C$ without changing $\gamma$. More strongly, subtracting $W(0)$ from a stationary field $W(s)$ preserves its <semivariogram> but generally makes its <variance> depend on $s$. The corrected statement is that this <semivariogram> admits a second-order stationary model, with the displayed <covariance> using the usual convention $C(h)\to0$ at large distance; it does not force every compatible process to be stationary.
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