The interrupted convergence conjecture for truth seekers

Let $K$ be the set of truth seekers and let $\overline{K}$ be the set of ignorants in a generalized weighted asynchronous bounded-confidence opinion system (WASBOCOS) with structural parameters $\varepsilon$, $\alpha$, $\beta$, and $n$. Let $\alpha_i(t)$ denote the truth-seeking parameter of individual $i$ at time $t$, and let $|\overline{K}|$ denote the number of ignorants. The truth seekers are said to be $r$-fold convergent when their convergence to the truth is interrupted at most $r$ times. Interrupted convergence conjecture. If the condition $\alpha_i(t)=0$ for all $i\in\overline{K}$ in the interrupted-convergence theorem is dropped, then the truth seekers have $|\overline{K}|$-fold convergence. The preceding lemma shows that without this condition each ignorant can in general cause an interruption, so the conjecture asserts the corresponding upper bound; the source gives no resolution status.