Strong convergence for a repeated GUE interaction on three tensor legs

Let $X_N$ be a normalized Gaussian unitary ensemble matrix of size $N^2$. We place the same realization on two adjacent pairs of tensor factors, as $X_N\otimes I_N$ and $I_N\otimes X_N$ on $(\C^N)^{\otimes3}$. For every fixed complex noncommutative polynomial, its operator norm converges in probability to the norm of that polynomial in two free variance-one semicircular elements. The argument computes the covariance of the dependent pair and applies existing Gaussian spectral comparison and operator-valued free convergence results. A direct Gaussian variance estimate supplies the trace convergence needed for the norm lower bound.