$R\cdot R$ and $-1/2$ from each disk $D_{i}$, so $\Psi_{n} \cdot \Psi_{n} = 2 - n/2$. The term $\tau$ is the number of tetrahedral points, which is $n(n-1)/2$, and the Euler number $\chi$ is $1+n$. The formula in the lemma follows.

For each of the cases in the previous lemma, we can now consider the non-empty moduli spaces of smallest possible action. For appropriate choices of metrics, we can identify these completely.

On the bifolds corresponding to $(S^{4}, \Psi_{n})$, the smallest-action non-empty moduli spaces of anti-self-dual bifold connections are as follows, for $n\le 2$.

1.  For $n=0$ or $n=2$, there is a unique solution with $\kappa=0$: a flat connection whose holonomy group has order $2$ for $n=0$ and is the Klein $4$-group, $V_{4}$, for $n=2$. The automorphism group of the connection is $O(2)$ (respectively, $V_{4}$), and it is an unobstructed solution in a moduli space of formal dimension $-1$ (respectively, dimension $0$).

2.  For $n=1$ and $n=3$, the smallest non-empty moduli spaces have $\kappa=1/32$ and formal dimension $0$. In both cases, with suitable choices of bifold metrics, the moduli space consists of a unique unobstructed solution with holonomy group $O(2)$.

The complement $S^{4}\sminus R$ deformation-retracts onto another copy of $\RP^{2}$ 