ASYMPTOTIC LOWER-BOUND TOPOLOGY: A Holographic Resolution to the Vacuum Catastrophe and Singularities.

ABSTRACT

We propose a foundational revision to cosmological topology: that zero is not a physical state but an asymptotic limit determined by a fundamental quantum of action, ε. By modeling the universe as a complex toroidal manifold (T² × iT²), we resolve the primary pathologies of the Standard Model through strict topological constraints.

First, we demonstrate that the Vacuum Catastrophe is an artifact of divergent integration on non-compact manifolds. By applying Epstein Zeta Function regularization to the toroidal mode spectrum, we derive a finite, non-zero residual energy density that aligns with the observed Cosmological Constant without fine-tuning.

Second, we address thermodynamic reversibility by defining the global time coordinate as a complex variable. We show that global entropy conservation is satisfied as a Cauchy-Riemann condition on the complex manifold, necessitating a CPT-inverted Mirror Sector to balance the entropic flux of the Local Sector.

Finally, we derive a variable gravitational coupling that transitions to repulsion at the ε-limit, replacing the Big Bang singularity with a non-singular "Quantum Bounce." We predict a detectable "spectral tilt" in the evaporative cooling tails of Bose-Einstein Condensates, consistent with a holographic thermal floor of T_min ≈ 10⁻³⁰ K.