Anti-soliton Symmetry, Topological Unwinding, and Constrained Annihilation Dynamics in the Coupled SU(2) Skyrme–Dilaton Model

Abstract We investigate antisolitons, zero-degree soliton–antisoliton trial configurations, and constrained collision dynamics in the classical coupled SU(2) Skyrme–Dilaton prototype of One Fundamental Geometric Field Theory (OFGFT). The inversion involution (U,p) -> (U†,p) exactly preserves the classical action and energy while reversing the winding degree. It maps any degree-one solution into a degree-minus-one solution with the same dilaton profile and symmetry-equivalent Hessian. We then construct a degree-zero two-center product ansatz and explicitly deform it to the vacuum. For a numerically reconstructed degree-one background, three-dimensional static quadrature exhibits a nonmonotonic energy along this chosen unrelaxed pair family, including a sampled maximum near separation d=0.85. A single collective-coordinate reduction yields an ansatz-dependent threshold for reaching overlap, and a separately prescribed post-cancellation scalar field obeys the exactly solvable massive Klein–Gordon equation and disperses. None of these results demonstrates the full nonlinear time-dependent annihilation of initially separated solitons, and no electromagnetic photon production or physical antiparticle identification follows. We provide derivations, numerical methods, convergence checks, explicit limitations, and reproducibility directions appropriate to a preliminary research preprint.