Determination of the $C\!P$-even fraction of $D^0\rightarrow K_S^0π^+π^-π^0$
Quantum-correlated $D\bar{D}$ pairs collected by the BESIII experiment at the $ψ(3770)$ resonance, corresponding to an integrated luminosity of 2.93 fb$^{-1}$, are used to study the $D^0 \rightarrow K^{0}_Sπ^{+} π^{-} π^{0}$ decay mode. The $C\!P$-even fraction of $D^0 \rightarrow K^{0}_Sπ^{+} π^{-} π^{0}$ decays is determined to be $0.235\pm 0.010\pm 0.002$, where the first uncertainty is statistical and the second is systematic.