Hong's power LCM matrix size-threshold conjecture

Let $t$ be a positive integer, let $S=\{x_1,x_2,\ldots,x_n\}$ be a GCD-closed set of positive integers, and let the power LCM matrix be the matrix

$$[(\operatorname{lcm}(x_i,x_j))^t].$$

The Hong conjecture. There exists a positive integer $k(t)$ depending only on $t$ such that this matrix is nonsingular for every GCD-closed set $S$ with $n\leq k(t)$, whereas for every $n\geq k(t)+1$ there exists a GCD-closed set $S$ of size $n$ for which the matrix is singular. The source presents this as a conjecture concerning the transition from universal nonsingularity at small cardinalities to the existence of singular examples at all larger cardinalities; no resolution is given in the supplied text.