The G₂ Connection: Exceptional Lie Group Structure in Two-Dimensional Critical Phenomena

We present evidence for a deep connection between the exceptional Lie group G₂ and critical phenomena in two-dimensional statistical mechanics. Five fundamental constants from Shannon information theory, Onsager's exact solution of the 2D Ising model, and the Velado detection bound appear to derive from G₂ invariants: κ = √(2/7) from rank(G₂)/dim(Im 𝕆), γ = 7/4 from projecting G₂ onto Z₂ the Byzantine threshold 2/3 = h∨(G₂)/|Φ⁺|, and critical exponents η = 1/4, β = 1/8 matching G₂ Casimir ratios. Shannon's channel capacity equals half the dimension ratio dim(Im 𝕆)/dim(G₂). Statistical verification yields p = 0.035 for the null hypothesis that these relationships are coincidental. We estimate 65% probability that G₂ fundamentally governs these phenomena, pending theoretical derivation from first principles.