The ALMA Survey of Gas Evolution of PROtoplanetary Disks (AGE-PRO): X. Dust Substructures, Disk Geometries, and Dust-disk Radii

We perform visibility fitting to the dust continuum Band 6 1.3 mm data of the 30 protoplanetary disks in the AGE-PRO ALMA Large Program. We obtain disk geometries, dust-disk radii, and azimuthally symmetric radial profiles of the intensity of the dust continuum emission. We examine the presence of continuum substructures in the AGE-PRO sample by using these radial profiles and their residuals. We detect substructures in 15 out of 30 disks. We report five disks with large ($>$15 au) inner dust cavities. The Ophiuchus Class I disks show dust-disk substructures in $\sim80\%$ of the resolved sources. This evidences the early formation of substructures in protoplanetary disks. A spiral is identified in IRS 63, hinting to gravitational instability in this massive disk. We compare our dust-disk brightness radial profiles with gas-disk brightness radial profiles and discuss colocal substructures in both tracers. In addition, we discuss the evolution of dust-disk radii and substructures across Ophiuchus, Lupus, and Upper Scorpius. We find that disks in Lupus and Upper Scorpius with large inner dust cavities have typical gas-disk masses, suggesting an abundance of dust cavities in these regions. The prevalence of pressure dust traps at later ages is supported by a potential trend with time with more disks with large inner dust cavities (or "transition disks") in Upper Scorpius and the absence of evolution of dust-disk sizes with time in the AGE-PRO sample. We propose this is caused by an evolutionary sequence with a high fraction of protoplanetary disks with inner protoplanets carving dust cavities.