the superscripts indicates generic formulas that are valid for all three meson systems.

In order to understand better the anatomy of the $\Delta I=1/2$ rule we use again the form $$\begin{aligned}
\frac{A_0}{A_2} &= B + C e^{i\delta}\,, \label{eq:DeltaI12-generic}\end{aligned}$$ analogously to Eq. (\[eq:defC\]) in Sec. \[sec:deltau0rule\] for the $\Delta U=0$ rule. Here, $B$ is again the contribution in the limit of no QCD, and $C e^{i\delta}$ contains the corrections to that limit. Now, as discussed in Refs. [@Buras:1988ky; @Buras:2014maa], in the limit of no strong interactions only the $Q_2$ operator contributes in Eq. (\[eq:DeltaI12-generic\]). Note that the operator $Q_1$ is only generated from QCD corrections. When we switch off QCD, the amplitude into neutral pions vanishes and we have for $K,D,B\rightarrow \pi\pi$ equally [@Buras:1988ky; @Buras:2014maa] $$\begin{aligned}
B &= \sqrt{2}\,. \label{eq:kaon-deltaI12-rule-no-qcd}\end{aligned}$$ This corresponds to the limit $\tilde{p}_0 = 1$ that we considered in Sec. \[sec:deltau0rule\] for the $\Delta U=0$ rule. The exact numerical value in Eq. (\[eq:kaon-deltaI12-rule-no-qcd\]) of course depends on the convention used for the normalization of $A_{0,2}$ in the isospin decomposition Eq. (\[eq:kaondata\]), where we use the one present in the literature.

For the isospin decomposition of $D^+\rightarrow \pi^+\pi^0$, $D^0\rightarrow \pi^+\pi^-$ and $D^0\rightarrow \pi^0\pi^0$, we simply combine the fit of Ref. [@Franco:2012ck] to get $$\begin{aligned}
\left|\frac{A_0^D}{A_2^D}\right| &= 2.47\pm 0.07\,, \qquad  
\delta_0^D - \delta_2^D = (\pm 93 \pm 3)^{\circ}\,.  \label{eq:charm-deltaI12-rule}\end{aligned}$$ Reproducing the $\Delta I=1/2$ rule for charm Eq. (\[eq:charm-deltaI12-rule\]) is an optimal future testing ground for emerging new interesting non-perturbative methods [@Khodjamirian:2017zdu]. Very promising steps on a conceptual level are also taken by lattice QCD [@Hansen:2012tf].

In $K$ and $D$ decays the contributions of penguin operators t