The Friedmann equations govern the expansion of the universe in general relativity. They are derived from Einstein's field equations with the cosmological constant Λ as a free parameter. This paper shows that the same action that derives α, G, and Λ from the axiom σ = 1/(1+σ) also produces Friedmann dynamics. The de Sitter solution (exponential expansion) emerges as the long-time attractor of the self-referential field equation. The Hubble parameter H₀ = 70.5 km/s/Mpc follows from the fixed-point structure without fitting to observations.