  We carried out extremely sensitive Submillimeter Array (SMA) 340 GHz (860
micron) continuum imaging of a complete sample of SCUBA 850 micron sources (>4
sigma) with fluxes >3 mJy in the GOODS-N. Using these data and new SCUBA-2
data, we do not detect 4 of the 16 SCUBA sources, and we rule out the original
SCUBA fluxes at the 4 sigma level. Three more resolve into multiple fainter SMA
galaxies, suggesting that our understanding of the most luminous high-redshift
dusty galaxies may not be as reliable as we thought. 10 of the 16 independent
SMA sources have spectroscopic redshifts (optical/infrared or CO) to z=5.18.
Using a new, ultradeep 20 cm image obtained with the Karl G. Jansky Very Large
Array (rms of 2.5 microJy), we find that all 16 of the SMA sources are detected
at >5 sigma. Using Herschel far-infrared (FIR) data, we show that the five
isolated SMA sources with Herschel detections are well described by an Arp 220
spectral energy distribution template in the FIR. They also closely obey the
local FIR-radio correlation, a result that does not suffer from a radio bias.
We compute the contribution from the 16 SMA sources to the universal star
formation rate (SFR) per comoving volume. With individual SFRs in the range
700-5000 solar masses per year, they contribute ~30% of the
extinction-corrected ultraviolet-selected SFR density from z=1 to at least z=5.
Star formation histories determined from extinction-corrected ultraviolet
populations and from submillimeter galaxy populations only partially overlap,
due to the extreme ultraviolet faintness of some submillimeter galaxies.
