An Analytic Framework for QCD beyond Lattice

We present a novel reformulation of non-perturbative Quantum Chromodynamics (QCD) based on a Dynamic Colour Tension Index (CTI), a quantized scalar parameter encoding the evolving color flux configurations within hadrons. Unlike traditional lattice QCD, our approach treats color confinement as a dynamic interplay of discrete tension layers, modulated by gluon-mediated color exchanges. By introducing a new coupling function and transition operators acting on CTI layers, we develop an analytic framework to compute hadron mass spectra, flux tube dynamics, and symmetry-breaking phenomena directly from first principles. The CTI evolves as a time-dependent integer index reflecting gluonic excitations, enabling the model to reproduce experimental hadron masses with sub-percent accuracy and predict novel exotic states. Our method provides a continuous, algebraic alternative to lattice discretization, capturing non-perturbative effects such as chiral relaxation and jet quenching within the same formalism. This reformulation paves the way for efficient, real-time calculations in strong interaction physics and offers new insights into the vacuum structure of QCD.