Remark: What the complementary comparison does and does not say

The complementary term in (eq:basicSandwich) exceeds $t^2/2$ when $\eta >\sqrt{2}-1$. At $\eta =1/2$, those two terms are $9/64$ and $1/8$. Neither is the best local witness available here: the equatorial pair gives $1/4$, and the optimized Bell witness below gives $5/16$. All these are proved lower bounds, not intermediate recovery optima.