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 4-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 4D torus with closed timelike curves (CTCs). This primordial state, sustained by exotic matter violating energy conditions, eventually underwent a topological phase transition, an "unfolding", that gave rise to two separate spacetime planes, one of which is our observable universe. Key Contributions Complete metric formalization of the primordial torus geometry, combining elements of Clifford tori and Klein bottle topology Analysis of collapse mechanisms including quantum instability, vacuum fluctuations, and entropic limits A novel argument addressing the exotic matter stability objection: in a regime without linear time, the concept of "decay" becomes inapplicable Connections with established physics: maximally extended Schwarzschild solutions, Einstein-Rosen bridges, Hartle-Hawking no-boundary proposal, Loop Quantum Cosmology, and Penrose's Conformal Cyclic Cosmology Falsifiable predictions for CMB signatures, gravitational wave echoes, black hole anomalies, and matter-antimatter asymmetry This work originates from questions raised during The Atlas project and the writing of the paper titled "The Procedural Universe: A Philosophical Quantum and Computational Analysis of Cosmos Simulations via AI" (doi:10.5281/zenodo.18112886), where the implementation of a procedural universe simulation and the treatment of time as Einstein's block universe led us to consider how a primordial state without conventional "spacetime" might be formally described.