  Mignosi, Restivo, and Salemi (1998) proved that for all $\epsilon > 0$ there
exists an integer $N$ such that all prefixes of the Fibonacci word of length
$\geq N$ contain a suffix of exponent $\alpha^2-\epsilon$, where $\alpha =
(1+\sqrt{5})/2$ is the golden ratio. In this note we show how to prove an
explicit version of this theorem with tools from automata theory and logic.
Along the way we gain a better understanding of the repetitive structure of the
Fibonacci word.
