A comprehensive account of the cosmic star-formation history demands an accurate census of dust-enshrouded star formation over cosmic time. We provide strong new constraints from a large sample of 777 red galaxies, selected based on their dust-reddened, rest-frame UV-optical emission. This sample of 777 galaxies spans 1 10 at z = 3. 3, rising to 91\% by z 7 (albeit with large uncertainties at the highest redshifts). Crucially, we find that the number density of massive red star-forming galaxies at z 6 is sufficient to explain the abundance of quiescent galaxies at z > 3, consistent with typical quenching timescales allowed in the 1Gyr interval from z 6 to z 3. This large abundance yields a substantial contribution to the cosmic star-formation rate density: at z 4, red galaxies provide ρₒ₅ₑ = 3. 9^{+0. 6-₀. ₅ 10^-2 M_ yr^-1Mpc^-3}, and at z 5 they supply nearly 40 \% of the total ρₒ₅ₑ. This exceeds the contribution of bright sub (mm) -selected dusty star-forming galaxies by more than an order of magnitude. Future deeper and wider ALMA surveys will provide further opportunities to strengthen and extend our results in our quest to fully quantify the contribution of dust-obscured activity to ρₒ₅ₑ at high redshifts.
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