New Tests of Millilensing in the Blazar PKS 1413+135
  Symmetric Achromatic Variability (SAV) is a rare form of radio variability in
blazars that has been attributed to gravitational millilensing by a ~$10^2 -
10^5$ $M_\odot$ mass condensate. Four SAVs have been identified between 1980
and 2020 in the long-term radio monitoring data of the blazar PKS 1413+135. We
show that all four can be fitted with the same, unchanging, gravitational lens
model. If SAV is due to gravitational millilensing, PKS 1413+135 provides a
unique system for studying active galactic nuclei with unprecedented
microarcsecond resolution, as well as for studying the nature of the millilens
itself. We discuss two possible candidates for the putative millilens: a giant
molecular cloud hosted in the intervening edge-on spiral galaxy, and an
undetected dwarf galaxy with a massive black hole. We find a significant
dependence of SAV crossing time on frequency, which could indicate a fast shock
moving in a slower underlying flow. We also find tentative evidence for a
989-day periodicity in the SAVs, which, if real, makes possible the prediction
of future SAVs: the next three windows for possible SAVs begin in August 2022,
May 2025, and February 2028.
