Sharp Norms of Rectangular Majorana Matrices and a Two-Matrix Obstruction to Strong Convergence

Let C_(m,n) be an m by n matrix whose entries are distinct self-adjoint Clifford generators, each squaring to one. We prove that its squared operator norm is 2(m+n-2) for m,n at least 2; the one-row and one-column cases have squared norm max(m,n). The argument uses a vector-spin Casimir identity and an attaining highest-weight summand. The square case gives the optimal uniform bound 2 for the normalized arrays in the explicit CAR subquestion of the AIM Free Analysis problem list. Several arrays of distinct generators converge jointly in star moments to a standard free circular family. For N at least 2, the norm of the sum of d normalized array products X_r X_r^* is exactly 2(d+1)-4/N, while the free-limit norm is at most (1+sqrt(d))^2. Strong convergence therefore fails already for two arrays. The broader q-Gaussian approximation question is not resolved. The imported square calculation and Shlyakhtenko's prior work on a different Hermitian fermionic ensemble are credited. This is a self-audited, AI-assisted, unrefereed preprint; no independent review, formal verification or absolute priority is claimed.