Conjectured threshold for product-Schur subsets of random integer sets

Let $[n]_p$ be the binomial random subset of $[n]$, obtained by retaining each integer independently with probability $p$, and call $[n]_p$ product-Schur if every $2$-colouring of it contains a monochromatic product relation of the type studied in the paper. The paper proves that the threshold for this property lies between $n^{-1/9-o(1)}$ and $n^{-1/11}$. Product-Schur threshold conjecture. The threshold for $[n]_p$ to be product-Schur lies at $n^{-1/11}$. This conjecture asserts that the paper's upper bound gives the true threshold; the supplied source does not state that it has been resolved.