  There is a conjecture that renormalizable higher-derivative gravity has a
finite classical potential at the origin. In this work we show clearly that the
scale-invariant gravity (SIG) satisfies the conjecture. This gravity produces
the better-behaved $1/k^4$ UV behavior as needed for renormalizability. It
turns out that the SIG has the linear classical potential of $V\propto r$ and
it is a UV complete theory.
