Cleanliness conjecture for t-clock-free graphs

A hole is an induced cycle on four or more vertices. A t-clock is a clock consisting of a hole $C$ and a vertex $v$ such that there are two neighbours $x,y\in V(C)$ of $v$ where the distance between $x$ and $y$ along $C$ is at least $t$. A graph is t-clock-free if it contains no induced subgraph that is a t-clock. A graph class is clean if there is a function $f:\mathbb{N}\rightarrow\mathbb{N}$ such that, for every $s$, each $s$-clean graph $G$ in the class satisfies $\operatorname{tw}(G)\leq f(s)$. Cleanliness conjecture for t-clock-free graphs. For every fixed $t\geq 1$, the family of t-clock-free graphs is clean. This would strengthen the known result that the class of clock-free graphs is clean and the previously proved cleanliness of the class of (clock, prism, pyramid)-free graphs; whether the stated strengthening holds is left open in the source.