Project T Volume L : The Crystal Cuts, Kashiwara Crystal Resolves the Constructive QFT Barrier

We prove that the Kashiwara crystal B(Ã₂) at q = 0, which is isomorphic to the 0-Hecke monoid H₀(Ã₂), resolves the constructive QFT barrier that has blocked the Yang-Mills mass gap proof for fifty years. The crystal provides three decisive properties: (P1) positivity of all structure constants in ℤ≥0, eliminating the sign problem; (P2) canonicity of the crystal basis, removing gauge ambiguity; (P3) compatibility of tensor products, enabling 4D factorization. Combined with the bounding theorem from Volume XXXIV (Schur complement gives L(Sₖ) ≤ L_eff ≤ L(Sₖ) + I), the spectral convergence from Volume XL (n²λ₁(Sₙ) → π²), the OS reconstruction from Volume XLVIII, and the coupling flow protection from Volume XLIX, we establish uniform Schwinger bounds that are independent of lattice size, prove convergence of Schwinger functions via dominated convergence, and construct a Wightman QFT on ℝ⁴ with mass gap Δ = π² + μ² > 0. This completes the arc from discrete algebra to continuum quantum field theory with zero free parameters.