New Applications of the Universal Kink Quantisation Theorem: Explicit examples beyond the standard models

The universal kink quantisation theorem proved in the geometric subsystem programme states that for any relativistic scalar field theory in $(1+1)$ dimensions with a smooth potential possessing at least two degenerate global minima, the translational moduli space of a boosted kink carries the canonical symplectic form dP da with P = Mγ v and the mass M given by the Bogomolny integral over the potential. No closed‑form kink profile or integrability is required. We illustrate this theorem with several new, previously unexplored potentials that support topological kinks, explicitly computing their masses and confirming the universal symplectic structure. The examples include an octic double‑double‑well model, an asymmetric double‑well potential, and a non‑integrable periodic potential. The results demonstrate the broad applicability of the geometric subsystem programme.