A multiplicative universal property for real algebraic $K$-theory

We prove that the real $K$-theory functor is lax symmetric monoidal. Moreover, it is initial among those real functors ${\mathsf{W}\mathsf{a}\mathsf{l}\mathsf{d}}_{\mathrm{\infty }}^{\mathrm{g}\mathrm{d}}\to {\mathsf{S}\mathsf{p}}^{C_2}$ that are additive and lax symmetric monoidal.