This note isolates the minimal structural assumptions underlying the Two-Type restriction (dim (V/H) ≤ 1) derived in v3. 1. We systematically remove field structure and finiteness assumptions and show that they are not essential for two-face forcing. We then prove that commutativity and involution (a² = b² = e) are minimal structural requirements for the canonical four-cycle in the two-face x, xa, xb, xab. Consequently, without arbitrary language extension, the maximal class reachable by reduction is the class of commutative 2-groups containing at least two distinct involutions.
Minehiro Iriguchi (Tue,) studied this question.