  We combine archival ALMA data targeting the Hubble Ultra Deep Field (HUDF) to
produce the deepest currently attainable 1-mm maps of this key region. Our
deepest map covers 4.2arcmin^2, with a beamsize of 1.49''x1.07'' at an
effective frequency of 243GHz (1.23mm). It reaches an rms of 4.6uJy/beam, with
1.5arcmin^2 below 9.0uJy/beam, an improvement of >5% (and up to 50% in some
regions) over the best previous map. We also make a wider, shallower map,
covering 25.4arcmin^2. We detect 45 galaxies in the deep map down to 3.6sigma,
10 more than previously detected, and 39 of these galaxies have JWST
counterparts. A stacking analysis on the positions of ALMA-undetected JWST
galaxies with z<4 and stellar masses from 10^8.4 to 10^10.4 M_sun yields 10%
more signal compared to previous stacking analyses, and we find that detected
sources plus stacking contribute (10.0+/-0.5)Jy/deg^2 to the cosmic infrared
background (CIB) at 1.23mm. Although this is short of the (uncertain)
background level of about 20Jy/deg^2, we show that our measurement is
consistent with the background if the HUDF is a mild (~2sigma) negative CIB
fluctuation, and that the contribution from faint undetected objects is small
and converging. In particular, we predict that the field contains about 60
additional 15uJy galaxies, and over 300 galaxies at the few uJy level. This
suggests that JWST has detected essentially all of the galaxies that contribute
to the CIB, as anticipated from the strong correlation between galaxy stellar
mass and obscured star formation.
