Győri–Salia–Tompkins–Zamora path extremal graph conjecture

For odd $k\geq5$, let $H_{n,k}$ be the graph obtained from a clique $K_{\lfloor k/2\rfloor}$ by choosing a vertex $v$, adding $m$ independent vertices adjacent to $v$, and adding $n-m-\lfloor k/2\rfloor$ independent vertices adjacent to every clique vertex except $v$, where $m$ is chosen to maximize the number of copies of $P_{k-1}$. The Győri–Salia–Tompkins–Zamora conjecture. The extremal number ${\mathrm{ex}}(n,P_{k-1},P_k)$ is attained by $H_{n,k}$. The source presents this as a conjecture for the first open path case and gives no resolution evidence.