= Solution
Assume the usual <Semileptonic decay>[semileptonic] <Flavor eigenstate>[flavour] selection rule $\Delta S=\Delta Q$, negligible wrong-sign decay <probability amplitudes>, and equal magnitudes for CP-conjugate allowed <probability amplitudes>. Then $f_+=\pi^-\ell^+\nu$ is reached directly only from $K^0$, and $f_-=\pi^+\ell^-\bar\nu$ only from $\bar K^0$. Put $|A_{f_+}|=|\bar A_{f_-}|=|A|$. The four rates are
$$
\boxed{\begin{aligned}
\Gamma(K(t)\to f_+)&=|A|^2|g_+|^2,&\Gamma(\bar K(t)\to f_-)&=|A|^2|g_+|^2,\\
\Gamma(K(t)\to f_-)&=|A|^2|q/p|^2|g_-|^2,&\Gamma(\bar K(t)\to f_+)&=|A|^2|p/q|^2|g_-|^2.
\end{aligned}}
$$
There is only one path to each tagged <Semileptonic decay>[semileptonic] channel, so no direct/mixed decay <interference> survives. The <semileptonic wrong-sign mixing asymmetry> is
$$
\boxed{a_{\mathrm{SL}}=\frac{\Gamma(\bar K(t)\to f_+)-\Gamma(K(t)\to f_-)}{\Gamma(\bar K(t)\to f_+)+\Gamma(K(t)\to f_-)}
=\frac{1-|q/p|^4}{1+|q/p|^4}.}
$$
It isolates <CP violation in neutral-meson mixing>[CP violation in mixing] under the stated assumptions. Allowing direct <Semileptonic decay>[semileptonic] <CP violation> or wrong-sign <probability amplitudes> would spoil that isolation.<Review of Particle Physics by Particle Data Group (2022)>[<CP violation> in the <Quark> Sector, §13.1.3, equations (13.22)–(13.24): mixing and <Semileptonic decay>[semileptonic] wrong-sign asymmetry]{ref}
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