E₈ is the largest and most symmetrical of the exceptional Lie algebras. Various approaches to unification — string theory, heterotic models — assume E₈ as a starting point. Pentagon Physics shows that E₈ is not a starting point but an endpoint: it is a necessary consequence of the self-referential axiom. The McKay correspondence maps the binary icosahedral group 2I (the symmetry group of the 600-cell) to the E₈ Dynkin diagram. This mapping is not a coincidence — it is forced by the algebraic structure of ℚ(√5). E₈ is what the axiom produces when its symmetry is fully unfolded.