M-theory requires exactly eleven spacetime dimensions, conventionally split as four large and seven compact, with the seven compact dimensions carried on a manifold of G2 holonomy. The number eleven, and the 7+4 split, are inputs to M-theory rather than outputs. We show that within the G2 algebraic framework established in prior work, this dimension count arises naturally from the structure of the algebra. The seven compact dimensions correspond to the fundamental representation of G2, on which the rank-2 Cartan subalgebra acts; the coset SO(7)/G2 has dimension 7, the tangent space of a G2- holonomy manifold. The four large dimensions arise from the antisymmetric tensor product of the fundamental representation: 7 7 antisymmetric = 7 + 14 = 21 = dim(SO(7)), and SO(7) contains SO(4), ⊗ whose Lie algebra is that of the four-dimensional Lorentz group. The total, 7 + 4 = 11, matches the Mtheory dimension. We present this as a structural compatibility, not a derivation of spacetime: we state explicitly the three gaps — the framework supplies no principle selecting which four dimensions become large, the passage SO(4) to SO(3,1) requires Wick rotation rather than an algebraic identity, and no dynamical mechanism for the compactification is given. The dimension count, however, is exact and follows from the representation theory of a single algebra. Keywords: M-theory, eleven dimensions, G2 holonomy, compactification, exceptional Lie algebras, Lorentz group, spacetime dimensions, Kaluza-Klein
Vali Ilyas (Sat,) studied this question.