An Algebraic Closed Form for the Higgs Self-Coupling from Icosahedral Symmetry

This paper proposes a parameter-free, closed-form algebraic expression for the dimensionless Higgs self-coupling, lambda_H = K1 + phi^-5, derived from the representation theory of the icosahedral symmetry group A5. The constant K1 is defined as a canonical normalization of a four-dimensional representation channel, weighted by the inverse fine-structure integer 137, while phi^-5 represents the minimal self-similar scale of the five-dimensional representation slot.

 

Using the measured electroweak vacuum expectation value v = 246.220 GeV, the framework yields a precise prediction for the Higgs boson mass of mH = 125.112 GeV. This result is consistent with the current world average (mH = 125.20 +/- 0.11 GeV) within 0.80 standard deviations.

 

Furthermore, the paper derives a corollary for the top-to-Higgs mass ratio as the irrational number phi^(2/3) approx 1.37824, which matches experimental data to within 0.008 percent.

 

The construction is motivated by the requirement of a non-solvable simple internal symmetry group and provides a rigorous falsification protocol based on future collider measurements of Higgs-pair production. A self-contained Python script is provided to verify all numerical claims from first principles.