Berman's cyclic-module characterization of infinity-operads

Let $\text{Fin}^{\text{op}}$ be the opposite category of finite sets, and let $\text{Burn}^{\text{eff}}$ denote the effective Burnside 2-category, or spans of finite sets. A cyclic module over $\text{Fin}^{\text{op}}$ is understood in the thesis's framework. Berman's characterization conjecture. An $\infty$-operad is a cyclic module over $\text{Fin}^{\text{op}}$ which is trivial over $\text{Burn}^{\text{eff}}$. The thesis presents this as an algebraic characterization, while noting that the terminology in the statement has not yet been defined at that point and that only a weak variant is proved.