Primordial 4D Torus Hypothesis: A Pre-Big Bang Cosmological Model

This paper presents a mathematical formalization of the Primordial 4D Torus Hypothesis, proposing a closed four dimensional toroidal geometric structure as a pre Big Bang cosmological state. The hypothesis suggests that before the emergence of linear time and conventional spacetime, the universe existed as a self contained non orientable four manifold with topology K2×T2K^2 \times T^2K2×T2 (Klein bottle × two torus), undergoing a signature transition from Euclidean to Lorentzian geometry. Key Contributions Primordial topology: The model proposes a non orientable four dimensional primordial manifold with Klein bottle like topology, providing a well defined geometric pre Big Bang state. Emergent spacetime: The observable universe arises through a geometric transition from a timeless Euclidean regime to Lorentzian spacetime, giving rise to causal structure and physical time. Topological information content: Information is encoded in the global topology of the primordial manifold, allowing entropy to accumulate independently of local geometry. Zero energy universe: Topological pair creation enforces exact global energy cancellation, reframing the Big Bang as an information release rather than an energetic explosion. Consistency with known physics: The framework is constructed to be compatible with established gravitational principles while operating outside the assumptions of classical spacetime. Testable signatures: The hypothesis leads to observational predictions in cosmology and gravitational physics, enabling potential empirical validation. This work originates from questions raised during The Atlas project and the writing of The Procedural Universe: A Philosophical Quantum and Computational Analysis of Cosmos Simulations via AI (doi:10.5281/zenodo.18112886), where implementing a procedural universe simulation within Einstein’s block universe motivated the search for a formal description of a primordial state without conventional spacetime.