We present the detailed characterization of two extremely red submillimeter galaxies (SMGs), ASXDF1100.053.1 and 231.1, with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Jansky Very Large Array (VLA). These SMGs were selected originally using AzTEC at 1100 micron, and are observed by Herschel to be faint at 100--500 micron. Their (sub)millimeter colors are as red as -- or redder -- than known z>~5 SMGs; indeed, ASXDF1100.053.1 is redder than HFLS 3, which lies at z=6.3. They are also faint and red in the near-/mid-infrared: ~1 microJy at IRAC 4.5 micron and <0.2 microJy in the Ks filter. These SMGs are also faint in the radio waveband, where F_6GHz=4.5 microJy for ASXDF1100.053.1 and F_1.4GHz=28 microJy for ASXDF1100.231.1, suggestive of z=6.5^{+1.4}_{-1.1} and z=4.1^{+0.6}_{-0.7} for ASXDF1100.053.1 and 231.1, respectively. ASXDF1100.231.1 has a flux excess in the 3.6-micron filter, probably due to H$alpha$ emission at z=4--5. Derived properties of ASXDF1100.053.1 for z=5.5--7.5 and 231.1 for z=3.5--5.5 are as follows: their infrared luminosities are [6.5-7.4]x10^{12} and [4.2-4.5]x10^{12} L_sun; their stellar masses are [0.9-2]x10^{11} and [0.4-3]x10^{10} M_sun; their circularized half-light radii in the ALMA maps are ~1 and <~0.2 kpc (~2--3 kpc for 90% of the total flux). Lastly, their surface infrared luminosity densities, Sigma_IR, are ~1x10^{12} and >~1.5x10^{13} L_sun kpc^{-2}, similar to values seen for local (U)LIRGs. These data suggest that ASXDF1100.053.1 and 231.1 are compact SMGs at z>~4 and can plausibly evolve into z>~3 compact quiescent galaxies.
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