Toroidal Boundary

The Toroidal Boundary is the closed, pulsing torus surface on which the book places all physical information and energy, with a null interior, so that information is conserved across collapse and expansion cycles. The book models the universe's pulsing boundary as a standard torus whose major and minor radii oscillate at the Prime Pulse frequency. At the Zinf limit the boundary is discretized into Zinf quanta: its minimal surface area scales with the square of the discretization parameter and of the spatial quantum, and it holds N▫ = A⥥/(ℓ_z)² = (N⥥)² cells, the computational degrees of freedom of a Zinf universe. Below these bounds the torus cannot host stable standing waves, just as a signal cannot be sampled below the Nyquist rate without aliasing, so the minimal closed torus is the lowest geometry on which recursive computation and physical law can emerge. Standing waves on it have a discrete frequency spectrum set by the Pulse Rhythm. It is parametrized by the Toroidal Position Vector and Radius Evolution, and connects to Strict Interior Nulling, Minimal Surface Area, Toroidal Pulse Manifold and Information Conservation.