We show that \(\textrm{TR}_{2i-1}(S)=0\) for all \(i\in \mathbb {N} \) and all S quasiregular semiperfect. We show this by computing the algebraic K-theory of truncated polynomial algebras over certain quaisregular semiperfect rings and showing that for these rings the topological restriction homology is even via the curves on K-theory description of [9]. We then use prismatic cohomology to go from these cases to the general case.
