Why did the Treaty of Verdun signal the decline of Charlemagne's empire?

The Treaty of Verdun, signed in 843, marked the division of Charlemagne's vast empire among his three grandsons, leading to fragmentation and the establishment of distinct kingdoms. This division weakened central authority, as each grandson focused on consolidating power within their own territory, fostering rivalry and conflict. Consequently, the lack of a unified leadership made the empire more vulnerable to external threats and internal strife, ultimately contributing to its decline. The treaty thus set the stage for the political disintegration that followed in the ensuing centuries.