Generalized Uncertainty Principle (GUP) from an Invariant Mass Cutoff of 10⁷ GeV

Traditional quantum mechanics allows spatial resolution to approach zero (Δx → 0) as momentum approaches infinity (Δp → ∞). However, quantum gravity predicts the existence of a fundamental minimum length, leading to the Generalized Uncertainty Principle (GUP). In this letter, we demonstrate that the cutoff Λ_SVL ≈ 1.2 × 10⁷ GeV derived phenomenologically from the decay width of the Higgs boson naturally establishes a minimum length a₀ ≈ 5.15 × 10⁻²³ m. Applying this invariant mass cutoff to the quantum commutator reveals that particles cannot be localized more precisely than a₀. Rather than discarding the Planck scale (10¹⁹ GeV), this result provides a robust phenomenological foundation for GUP as a dynamical cutoff within the framework of Effective Field Theory (EFT).