Big Finitistic Dimensions of Radical-Cube-Zero Algebras

We construct, over any field, a ten-dimensional algebra $A$ with $(\operatorname{rad}A)^3=0$ such that $\operatorname{findim}A=2$, $\operatorname{Findim}A=\infty$, and $\operatorname{Findim}(A^{\mathrm{op}})=0$. An explicit inverse-syzygy construction gives countably generated right modules of every