= Solution
$\boxed{(c)\longleftrightarrow P1}$. A <periodic covariance function> gives identical latent values one period apart: if $p$ is its period, $\operatorname{Var}(f(t+p)-f(t))=k(t+p,t+p)+k(t,t)-2k(t+p,t)=0$. The smooth repeating P1 trace is therefore the appropriate match.
The original PDF has $\ell^2$ in the prefactor, not the TeX transcription's $t'^2$. It prints $\sin^2(2\pi|t-t'|/T)$; this kernel repeats at $\boxed{p=T/2}$ because $\sin^2(x+\pi)=\sin^2x$. To parameterize the period itself by $P$, use $\sin^2(\pi(t-t')/P)$ as below. The absolute value is immaterial inside the squared sine.
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