Asymptotic equality conjecture for real monopole Floer invariants

Let $K$ be a knot, let $\#_nK$ denote the connected sum of $n$ copies of $K$, and let $\underline{\delta}_R$, $\bar{\delta}_R$, and $\delta(K)$ be the invariants used in the paper. Asymptotic equality conjecture. For every knot $K$,

$$\lim_{n \to \infty}\frac{\underline{\delta}_R(\#_nK)}{n}=\delta(K) \quad\text{and}\quad \lim_{n \to \infty}\frac{\bar{\delta}_R(\#_nK)}{n}=\delta(K).$$

The conjecture proposes that both real monopole Floer invariants have the same stable average as $\delta(K)$ under repeated connected sum. The supplied text presents this as an analogue of earlier asymptotic results, but gives no resolution.