Quantum Excess: Resolving Planck-Scale Singularities through Geometric Degeneration

Abstract

Quantum Excess establishes a non-singular, flat-universe cosmology by integrating Kalimuthu’s 2013 spherical triangle theorem into Planck-scale physics. Standard quantum gravity models struggle to reconcile local quantum fluctuations with the observed global flatness of the universe. This paper resolves the paradox by applying Kalimuthu’s geometric proof, which establishes that a spherical triangle's interior angle sum can equal exactly 360 degrees. By utilising this specific geometric constraint, we demonstrate that Planck-scale spatial curvature dynamically self-corrects to mirror Euclidean flatness. This topological mechanism distributes infinite energy densities across degenerate boundaries, completely neutralising gravitational singularities in black holes and the early universe. The resulting framework provides a smooth, singularity-free description of space-time that naturally explains cosmic inflation without fine-tuning parameters. Ultimately, this approach bridges non-Euclidean geometry and quantum mechanics, offering a scalable foundation for quantum gravity and unique predictions for primordial gravitational wave signatures.
MSC: 83C45, 1M014, 83F05,
PACS: 04.60.-m, 04.20.Dw, 04.50.Kd