The c-unbounded lower-bound conjecture for hypergraph Ramsey numbers

Let $k\geq 10$ be an integer, and let $p$ and $q$ be integers satisfying $p\geq k+2$ and $q\geq k+1$. Write $r_k(p,q)$ for the smallest integer $n$ such that every red-blue coloring of the $k$-element subsets of an $n$-element set contains either a red $p$-element set or a blue $q$-element set. The c-unbounded lower-bound conjecture. For every such $k$, $p$, and $q$,

$$r_k(p,q)\geq (p-1)\bigl(r_k(p-1,q)-1\bigr)+1.$$

This conjecture extends the lower-bound recurrence proved computationally in the paper, removing the fixed upper bound on the parameter $c$ from the corresponding theorem. It is motivated by the expectation that constructing additional SAT instances for larger values of $k$ would improve the established lower bound.