This research presents a unified particle-based cosmological framework where cosmic expansion and dark energy emerge from scale-dependent energy thresholds. Developed within a non-canonical K-essence formalism, the model introduces a universal particle threshold constant (UP) and a master scale parameter (S). The theory naturally predicts a stable Hubble constant H0 ≈ 73.04 km/s/Mpc and an attractor equation of state w ≈ -1.03, offering a self-consistent resolution to the Hubble tension while maintaining physical stability through subluminal sound speed conditions.