The n-Dimensional Period-Basin Bijection: Geometry Encodes Arithmetic on N^{n-1}

We extend the Period-Basin Bijection to n symbolic sequences. The underlying space isnon-metrizable but uniformizable; periodic structure is extracted via entourage filtration onthe uniform structure, not distance. Joint periods in n sequences correspond bijectively tobasins in the n-dimensional coordination surface. The divisibility lattice on N^{n-1} manifestsgeometrically as sphere-like structures (positive curvature basins). The product Möbiusfunction governs the extraction of primitive joint periods fromharmonic structure. Morse-Bott theory reveals that the critical point structure encodesthe homology of the divisor poset, explaining the deep connection between arithmetic andgeometry. This unifies arithmetic on the product lattice N^{n-1} with Riemannian geometryon R^{n+1} and algebraic topology—all derived from a non-metric uniform foundation.