The multicolour size Ramsey number of a path

In this paper, we determine the $r$-colour size Ramsey number of the path $P_k$, up to constants. In particular, for every fixed $r\ge 2$ and $k\ge 100\log r$, we have $${\widehat{R}}_r(P_k)=\mathrm{\Theta }((r^2\log r)k)\mathrm{.}$$ Perhaps surprisingly, we do this by improving the lower bound on ${\widehat{R}}_r(P_k)$.