Discovery of an Empirical Geometric Pattern in Fundamental Coupling Constants

We report a remarkable empirical regularity concerning the fundamental coupling constants of the Standard Model. Analysis reveals that the reciprocal of the fine-structure constant α⁻¹, the high-energy-scale limiting deviation of the electroweak mixing angle θ_W, and the ultraviolet boundary value of the strong coupling constant α_s collectively obey a simple geometric pattern constructed from the minimal integer sequence {1, 2, 3, 4, 5} and its combinatorial number 5! = 120. Specifically, the optimal fitted value for α⁻¹ is 4π√120 ≈ 137.040, which deviates from the current experimental value of 137.035999084(21) by less than 3×10⁻⁵; the high-energy deviation of the electroweak mixing angle is related to (8π√15)⁻¹; and the ultraviolet scale of α_s is predominantly governed by 2π√120. Bayesian analysis indicates an extremely high probability that this pattern is non-random. Existing Grand Unified Theories or the string theory landscape struggle to naturally explain this concise integer-based regularity. We propose that the emerging “self-constructive theory” — a quantum gravity framework based on spacetime quantum units whose intrinsic quantum numbers are precisely {1, 2, 3, 4, 5} — provides a natural explanatory context for this pattern. Using the high-energy parameters fitted from this pattern and running them via the Standard Model renormalization group, we predict that the top quark mass should be greater than 173.2 GeV, offering a clear target for verification by next-generation high-energy experiments.