Low-complexity encoding conjecture for hypergraph Ramsey colorings

A pair construction of a $3$-graph coloring is a coloring of $K_N^{(3)}$ obtained from functions $f:\binom{[N]}{2}\to[p]$ and $g:[p]^3\to\{\operatorname{red},\operatorname{blue}\}$ by setting

$$\chi_{f,g}(\{i,j,k\})=g(f(i,j),f(j,k),f(k,i))$$

for $i<j<k$. Its complexity is $p$. For $3$-graphs $G,H$, let $r^p(G,H)$ be the smallest $n$ such that every $2$-edge-coloring of $K_n^{(3)}$ of complexity at most $p$ contains a red copy of $G$ or a blue copy of $H$. Low-complexity encoding conjecture. There exists an absolute constant $a>0$ such that, for all $3$-graphs $G$ and $H$,

$$r^p(G,H)\ge r(G,H)^a$$

whenever $p>r(G,H)^{o(1)}$. This conjecture asks whether Ramsey colorings can retain a polynomial fraction of the unrestricted Ramsey number while using subpolynomial pair-construction complexity. The source gives no resolution.