The Thomsen stratification intersection-number conjecture for smooth proper toric varieties

Let $X$ be a smooth proper toric variety, and consider its Thomsen stratification and the associated intersection numbers. Thomsen stratification intersection-number conjecture. For any smooth proper toric variety, the Thomsen stratification intersection-number condition holds. The condition is verified in several basic families, but the source says that no conceptual or general method is currently known for establishing it for an arbitrary smooth toric variety.