Midpoint lenses in segment spaces

For a real segment-forest dual with unbounded finite component heights and the real infinite-height coordinate predual, we bound the tail of an arbitrary displacement in a symmetric lens by $2\sqrt{R^2-\Vert x{\Vert }^2}$, where R is the lens radius and x is its finitely supported center. Both given norms are asymptotically midpoint uniformly convex, although neither space admits an equivalent asymptotically uniformly convex norm. The finite-height forest dual is reflexive.