Extensions and Shadows (13)

With the double inequality (1.1) on 7/21/25 now available, let’s prove Theorem 2.1: \( \kappa[ Shd (\mathcal{F}, r) ] < \frac{r}{m} \kappa(\mathcal{F}) + \frac{m^2}{n} \) for powers \( m, r \) of 2 in this post. We first confirm it when \( r=m/2 \). It’s a case to pivot all other \( r \) as […]