This preprint develops a geometric framework for mixed-variable optimisation in which categorical variables are endowed with transient cyclic-ordering-induced metrics. The mixed search space is formalised as a weighted Cartesian product of metric spaces, and it is shown that dynamic rotation of the categorical component preserves metric validity and induces uniform metric equivalence across epochs. A hierarchy of local optimality (instantaneous, robust, and categorical) is introduced, together with explicit coverage bounds establishing that ⌈(k−1)/2⌉ cyclic orderings suffice for full categorical adjacency coverage for a k-level variable. The results provide structural foundations for mixed-variable optimisation independent of any particular algorithmic paradigm.