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We combine archival ALMA data targeting the Hubble Ultra Deep Field (HUDF) toproduce the deepest currently attainable 1-mm maps of this key, extragalacticsurvey field. Combining all existing data in Band 6, our deepest map covers4.2arcmin^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% over the best previously published map and 50%improvement in some regions. We also make a wider, but shallower map, covering25.4arcmin^2. We detect 45 galaxies in the deep map down to 3.6sigma, including10 more 1-mm sources than previously detected. 39 of these galaxies have a JWSTID from the JADES NIRCam imaging and the new sources are typically faint andred. A stacking analysis on the positions of ALMA-undetected JADES galaxiesyields detections for z<4 and stellar masses from 10^(8.4) to 10^(10.4)Msun,extracting 10% of additional stacked signal from our map compared to previousanalyses. Detected sources and stacking contribute (10.0+/-0.5)Jy/deg^2 of thecosmic infrared background (CIB) at 1.23mm. Although this is short of the(uncertain) background level of about 20Jy/deg^2, after taking into accountintrinsic fluctuations in the CIB, our measurement is consistent with thebackground if the HUDF is a mild (~2sigma) negative fluctuation. This suggeststhat within the HUDF, JWST may have detected essentially all of the galaxiesthat contribute to the CIB. Our stacking analysis predicts that the fieldcontains around 60 additional galaxies with 1.23mm flux densities averagingaround 15uJy, and over 300 galaxies at the few uJy level. However, thecontribution of these fainter more modestly-obscured objects to the backgroundis small, and converging, as anticipated from the now well-established strongcorrelation between galaxy stellar mass and obscured star formation.

An optimal ALMA image of the Hubble Ultra Deep Field in the era of JWST: obscured star formation and the cosmic far-infrared background