The US empire arc (1750–present): post-WWII dominance was the peak (empire score ~1.0 in 1950); the decline has been gradual since, as China rises from near-zero. The US still leads on innovation, military, and financial center metrics — but cost competitiveness and trade balance have deteriorated. The Digital Revolution (1990–2021) produced another innovation burst that slowed the relative decline. The critical question is whether AI/tech continues to sustain US innovation leadership or whether China closes the gap.