The Inter-Type Torsion Operator on T₁u: T² = −4·I and Maximal Generation Symmetry

Computes the inter-type torsion operator T explicitly in the full 14-dimensional face Laplacian basis of the truncated octahedron and projects onto the T₁u subspace. Two exact Tier 1 theorems result. Theorem 56.1: T²|_{T₁u} = −4·I — the torsion squares to minus four times the identity, where 4 = λ_Eg = √(r₁r₂) = √16, the Eg eigenvalue and square root of the master equation constant term r₁r₂ = 16. Theorem 56.2: the cross-block matrix ⟨T₁u(r₂)|T|T₁u(r₁)⟩ = 2·U where U is unitary — all three singular values equal 2 exactly, proving maximal generation symmetry: all three generations couple to the inter-type torsion with equal strength. Consequence: the CKM hierarchy (Wolfenstein λ, A, R_b) does not originate in the torsion operator — it comes from the intra-block quark mass spectrum. R_b = r₁/r₂ at LO is confirmed. The correct unitarity triangle decomposition ρ̄ = R_b cos(δ_CKM), η̄ = R_b sin(δ_CKM) supersedes the πR approximation of Paper #36. Combined (ρ̄, η̄) tension is ~1.25σ, structurally understood. Cross-sector identity identified: torsion eigenvalue 4 = λ_Eg connects the CKM/torsion sector to the inflationary tensor-to-scalar sector (Paper #55) through the single master equation invariant r₁r₂ = 16.