The involution rank of a group generated by group involutions is the least number of such group generators. Each generator must have order exactly two (Guo and Sun 2026).
Guo and Sun (2026) proved that the orientation-preserving mapping class group of a closed connected orientable surface of genus 3 has involution rank 4. Thus four group involutions suffice and three do not.
Is Four." 16 Oct 2026.