Conjecture on quantity structures of special relativity with approximate motion

Let $n$ be the spacetime dimension, let $\mathsf{SpecRel}$ be the theory of special relativity, and let $\mathsf{AxThExp^-}$ be the axiom expressing that inertial observers can move roughly with any speed less than the speed of light, roughly in any direction. For a theory $T$, let $\operatorname{Num}_{n}(T)$ denote the class of quantity structures of its $n$-dimensional models. Quantity-structure conjecture. There is a model of $\mathsf{SpecRel}+\mathsf{AxThExp^-}$ over every ordered field, equivalently,

$$\operatorname{Num}_{n}(\mathsf{SpecRel}+\mathsf{AxThExp^-})=\{\text{ordered fields}\}.$$

The paper presents determining these quantity structures as an open question; the conjecture would extend the known rational and Archimedean ordered-field examples to all ordered fields.