The Hyperspheric Wave Front (HWF): A Geometric-Dynamic Framework in C7.

An integrated formulation of the Hyperspheric Wave Front (HWF) framework is presented as a geometric-dynamic theory defined on a propagating pseudo-hypersphere embedded in seven dimensions. The model combines a fundamental complex scalar dynamics with an effective emergent tensor structure formulated on the manifold C7. The propagating radial coordinate λ is introduced explicitly as the fundamental temporal parameter of the framework, conceptually distinct from conventional time in standard physics, although related to it through λ=ct. The framework suggests that observable electromagnetic interactions may correspond to effective three-dimensional projections of a deeper propagating magneto-geometric dynamics associated with the global hyperspheric wave front. Geometric invariants, fundamental dynamical equations, emergent tensor structures, a variational formulation, and conserved currents are introduced. It is further proposed that several known physical theories may emerge as approximate effective limits of HWF dynamics under specific geometric and dynamical regimes.