Polynomial-exponent upper-bound conjecture for linear hypergraph Ramsey numbers

A $3$-graph $F$ is linear if any two of its edges share at most one vertex. For fixed $F$, let $r(F,K_n^{(3)})$ be the least $N$ such that every red-blue coloring of $K_N^{(3)}$ contains a red copy of $F$ or a blue copy of $K_n^{(3)}$. Polynomial-exponent upper-bound conjecture. There is an absolute constant $C>0$ such that, for every fixed linear $3$-graph $F$,

$$r(F,K_n^{(3)})\le 2^{O_F(n^C)}.$$

The source records this as a proposed uniform upper bound. It follows stronger bounds for linear $F$ from existing methods, but does not establish an absolute exponent valid for every fixed linear $3$-graph.