Abstract: This paper formalizes a 4th-spatial dimension model (w) to resolve the "embedding paradox" inherent in standard cosmological singularities. It posits that the 3D universe exists as a hypersurface within a 4-dimensional substrate termed Hyper-Space, redefining gravity as an inward pressure gradient caused by volumetric displacement. The work introduces the Law of Instantaneous Requirement to account for superluminal inflation and resolves mathematical singularities by redefining division by zero as a trans-dimensional geometric transformation.
H. P. Muller (2025) studied this question.