Exact asymptotic moduli in a Daugavet subspace of L1

For an infinite-dimensional real subspace of L${}^1$ whose unit ball is totally bounded in measure and whose norm has the Daugavet property, we compute the averaged midpoint and one-sided asymptotic moduli at every unit center. They are $\max \{t/2,t-1\}$ and $\max \{0,t-2\}$, respectively. The same weak-neighborhood geometry excludes every equivalent asymptotically uniformly convex norm. A quantitative realization of the Kadets–Werner construction supplies a space with both hypotheses.