The respective sums of the potentials coincide at the transition point, i.e. $U_p^{FMV} + U_e|_{\theta=0} = U_p^{AFMV} + U_e|_{\theta=\pi/2}$, which leads to $$\gamma_p \sin\Psi_c = (\gamma_p- \gamma_e) \cos\Psi_c,$$ where $\gamma_p- \gamma_e$ indicates the suppression of AFMV pairing by chiral edge current. Hence, $\Delta_c/R=2\cos\Psi_c$ at which FMV and AFMV pairings occur at equal probability is $$\label{chiral_geometric rule}
\frac{\Delta_c}{R} = \frac{2}{\sqrt{1+(1-\gamma_e/\gamma_p)^2}}\simeq \sqrt{2} \Bigl( 1 + \frac{\gamma_e}{2\gamma_p}\Bigr).$$ FMV pattern is stabilized in $\Delta/R \geq \sqrt{2}$ and the relative strength of the edge current $\gamma_e/\gamma_p$ determines the shift of the transition point.

To test those chirality effects, we examined the pairing of doublets of chiral vortices with $R = \SI{19}{\micro\meter}$ within the range of $0 \leq \Delta < 2R = \SI{38}{\micro\meter}$. FMV pattern of chiral vortices is dominant in $0 \leq \Delta/R \leq 1.9$ and exhibits CCW rotation (Fig. \[fig5\](c)). The pairing order transition is also analyzed by using the order parameter of FMV pairing $\Phi_{FMV}$ [@supplement]. $\Phi_{FMV}$, which reaches 1 for FMV while it goes down to 0 for AFMV, is defined as $\vert \langle \bm{p}_i \cdot \bm{u}_i \rangle \vert$ with the orientation of velocity $\bm{p}_i$ measured experimentally at site $i$ and the expected orientation of FMV pattern $\bm{u}_i$ calculated numerically at corresponding 