The true statement about the Sui dynasty is:
It was short-lived but set the foundation for the Tang dynasty.
The Sui dynasty (581–618 AD) was indeed short-lived, lasting only about 37 years, but it played a critical role in unifying China and laying the groundwork for the succeeding Tang dynasty, which became one of the most prosperous and culturally vibrant periods in Chinese history. The other statements are not accurate: the Sui dynasty was not particularly known for military dominance over Korea, it did not last over 300 years, and while there were some cultural developments, it was not marked by extensive cultural achievements like those seen in the Tang dynasty.