Tight Bayesian optimal uniform reserve approximation for quasi-regular buyers

Let asymmetric and symmetric buyers have quasi-regular valuation distributions, and let $\calC_{{\sf BOM}}^{\textsf{Bayesian Optimal Uniform Reserve}}$ denote the revenue approximation ratio of Bayesian Optimal Uniform Reserve to Bayesian Optimal Mechanism. Bayesian Optimal Uniform Reserve conjecture. For asymmetric quasi-regular buyers, the tight ratio equals the regular-buyer bound

$$\calC_{{\sf BOM}}^{\textsf{Bayesian Optimal Uniform Reserve}}\in[0.3817,0.4630],$$

while for symmetric quasi-regular buyers it equals

$$\calC_{{\sf BOM}}^{\textsf{Bayesian Optimal Uniform Reserve}}=1+\left(W_{-1}\left(-\frac{1}{e^2}\right)\right)^{-1}\approx0.6822.$$

The conjecture would extend the known asymmetric regular-buyer bounds to asymmetric quasi-regular buyers and identify the symmetric quasi-regular worst case; the proposed reduction from quasi-regular to regular buyers remains to be established.