  This paper establishes closed-string mirror symmetry for all log Calabi-Yau
surfaces with generic parameters, where the exceptional divisor are
sufficiently small. We demonstrate that blowing down a $(-1)$-divisor removes a
single geometric critical point, ensuring that the resulting potential remains
a Morse function. Additionally, we show that the critical values are distinct,
which implies that the quantum cohomology $QH^{\ast}(X)$ is semi-simple.
