“…Most importantly, such redox-triggered carbonyl additions enable transformations and strategies beyond those accessible via conventional carbanion chemistry. Indeed, as borne out in total syntheses of roxaticin, 7a bryostatin 7, 7b trienomycins A and F, 7c cyanolide A, 7d and 6-deoxyerythronolide B, 7e application of these methods have availed a “step-function increase” in efficiency – in each case, the synthetic route was significantly more concise than in any prior approach. 4b These studies brought to light an especially powerful protocol for the direct assembly of acetate- or propionate-based triketide stereopolyads 2a or 2b involving the bidirectional enantioselective double allylation 8a or anti -crotylation 8b of 1,3-diols 1a or 1b , respectively (eq.…”