PROJECT T Volume XLII : Universality across Coxeter Types Mass Gap, Reflection Positivity, and CPT for Every Finite Coxeter Group

We prove that the Osterwalder–Schrader axioms, reflection positivity, CPT invariance, and positive mass gap hold not just for the symmetric groups (type A), but for every finite Coxeter group: types A, B, D, E, F, H, and I₂(m). The key results are: (1) The spectral gap of the Cayley graph Laplacian satisfies the universal formula λ₁ = 2 − 2cos(π/h), where h is the Coxeter number. (2) Transfer matrix reflection positivity is automatic from the semigroup property T(2t) = T(t)², requiring no type-specific argument. (3) The sign character (determinant) of every Coxeter group provides CPT invariance via ε·L·ε = 2K·I − L. All claims are verified computationally for 14 Coxeter types (A₂–A₃, B₂–B₄, D₃–D₄, H₃, F₄, I₂(3–8)) and formalized in Lean 4.