Then, we have the relation of $$\begin{aligned}
\left( M_V[t] \right)_{\rm template} 
&=& \left( M'_V[t'] \right)_{\rm target} \cr
&=& \left( M_V[t/f_{\rm s}]-2.5\log f_{\rm s} \right)_{\rm target}
\label{time-stretching_general}\end{aligned}$$ between $(t', M'_V)$ and $(t, M_V)$ coordinates systems [see Appendix A of @hac16k], where $M_V[t]$ means that $M_V$ is a function of time $t$. The color $(B-V)_0$ is not affected by this time-stretch because the both fluxes of $B$ and $V$ are shifted by the same quantities, $-2.5\log f_{\rm s}$ [@hac18k]. We thus examine each nova evolution in the $(B-V)_0$-$(M_V-2.5\log f_{\rm s})$ diagram. The above two reasons, Equation (\[time-stretching\_general\]) and that the color $(B-V)_0$ is not affected by time-stretch, are the theoretical background for the property that each nova track overlaps in the time-stretched color-magnitude diagram.

To summarize the theoretical background, both the colors $(B-V)_0$ and $(U-B)_0$ are not affected by time-stretch. Therefore, the $(t/f_{\rm s})$-$(B-V)_0$ and $(t/f_{\rm s})$-$(U-B)_0$ color curves overlap each other after time-stretch. As a result, many novae in outburst evolve on a common path in the usual $(B-V)_0$-$(U-B)_0$ color-color diagram. This is the reason why @hac14k found a common track in the $(B-V)_0$-$(U-B)_0$ diagram. On the other hand, the $(t/f_{\rm s})$-$M_V$ light curves do not overlap because the absolute $M_V$ 