  In 2005, the second author and Todorov introduced an upper bound on the
finitistic dimension of an Artin algebra, now known as the {\phi}-dimension.
The {\phi}-dimension conjecture states that this upper bound is always finite,
a fact that would imply the finitistic dimension conjecture. In this paper, we
present a counterexample to the {\phi}-dimension conjecture and explain where
it comes from. We also discuss implications for further research and the
finitistic dimension conjecture.
