Infinitely many accumulation points of codegree Turán densities

The codegree Turán density $\gamma (F)$ of a $k$-graph $F$ is the smallest $\gamma \in [0,1)$ such that every $k$-graph $H$ with ${\delta }_{k-1}(H)\ge (\gamma +o(1))\mathrm{\mid }V(H)\mathrm{\mid }$ contains a copy of $F$. We prove that for all $k,r\in \mathbb{N}$ with $k\ge 3$, $\frac{r-1}{r}$ is an accumulation point of ${\mathrm{\Gamma }}^{(k)}=\{\gamma (F):F\text{ is a }k\text{-graph}\}$. This makes progress on a problem posed by Mubayi and Zhao.