The 3MIN threshold conjecture for reliable noisy computation

Let $\delta^*_{\operatorname{3MIN}}$ denote the threshold for reliable computation with noisy circuits of 3MIN gates, and let $\delta^*(3)$ denote the threshold for reliable computation with noisy circuits of fan-in $3$. 3MIN threshold conjecture. The thresholds are equal:

$$\delta^*_{\operatorname{3MIN}}=\delta^*(3).$$

This conjecture asserts that restricting noisy circuits of fan-in three to the single functionally complete 3MIN gate does not change the reliable-computation threshold, analogously to the equality of the thresholds for NAND formulas and fan-in-two formulas. The paper presents it as a conjecture motivated by the known fan-in-two result; no resolution is given here.