Extrapolated multilevel computational-work conjecture

Let $\prescript{\mathrm{Ext}}{}{\Phi}^{\ell}$ and $\prescript{\mathrm{Ext}}{}{\Psi}^{\ell}$ denote the extrapolated fine- and coarse-level quantities at level $\ell$. Extrapolated multilevel computational-work conjecture. The computational work required for one realization satisfies

$$\operatorname{Work}\left[\prescript{\mathrm{Ext}}{}{\Phi}^{\ell}-\prescript{\mathrm{Ext}}{}{\Psi}^{\ell}\right]=\mathcal{O}(2^{-3\ell}).$$

The source motivates this by noting that extrapolation improves the time-difference rate while the computational cost per sample remains the same; the stated work law is an assumption rather than an established result.