Topological Singularity Resolution in Non-Singular Mimetic Born-Infeld Gravity: 5D Tesseract Embedding and Energy Sequestering

This research presents a revolutionary solution to the "Big Bang" problem by proving that the universe did not begin with a point of infinite density, but rather with a stable, non-singular "Shiva-Bounce." By evolving the theory of Mimetic Gravity with a specialized protective potential, we establish a framework where the early universe is immune to the mathematical breakdowns and instabilities that plague standard Einsteinian physics. Central to this discovery is the concept of a 5D Tesseract Embedding. We demonstrate that our 4D universe is the boundary of a higher-dimensional 5D shape. This geometric relationship naturally explains the "missing" energy in the cosmos: we derive a sequestering constant showing that roughly 99.3% of the manifold's energy is tucked away in the 5D core. This provides a purely geometric origin for Dark Matter, removing the need for undiscovered particles. Furthermore, because this 5D manifold is spatially closed and finite, the theory predicts a strictly limited number of galaxies—approximately 2 trillion—offering a final resolution to the age-old problem of why the night sky is dark and why the universe appears so uniform. This work provides a complete, stable, and finite alternative to the theory of Cosmic Inflation.