A 3×3 interval matrix with at least four real-eigenvalue components

A two-parameter $3\times3$ interval matrix with integer endpoints has at least four connected components in its real eigenvalue set. The matrix has rows $(25,a,b)$, $(1,-1,0)$ and $(1,0,1)$, with $a\in[-166,-16]$ and $b\in[9,159]$ varying independently. Its characteristic polynomial is affine in each parameter, with no mixed term. So for each real $\lambda$ its exact range over the box is an explicit interval, and $\lambda$ is a real eigenvalue of some member exactly when that interval contains zero. Four exact integer eigenpairs, at $\lambda=-3,0,3,25$, and three excluded real numbers, $-1$, $1$ and $12$, separate four components. This disproves the bound of $n$ components for a general $n\times n$ interval matrix.