Fiedorowicz–Pirashvili–Schwänzl–Vogt–Waldhausen conjecture on MacLane's Q-construction

Let $R$ be a discrete ring. Write $Q(R)$ for the spectrum associated with MacLane's $Q$-construction, let $\mathbb{Z}$ denote the Eilenberg–Mac Lane spectrum of the integers, and let $\otimes$ denote the smash product of spectra. Fiedorowicz–Pirashvili–Schwänzl–Vogt–Waldhausen conjecture. There is an equivalence

$$Q(R)\simeq \mathbb{Z}\otimes R$$

as $A_\infty$ ring spectra. The conjecture is the key spectral-level comparison underlying the equivalence between MacLane homology and topological Hochschild homology; the paper's abstract states that it proves this conjecture by constructing a symmetric monoidal structure on $Q$.