  Kepler-444 is a five planet system around a host-star approximately 11
billion years old. The five transiting planets all have sub-Earth radii and are
in a compact configuration with orbital periods between 3 and 10 days. Here we
present a transit-timing analysis of the system using the full Kepler data set
in order to determine the masses of the planets. Two planets, Kepler-444 d
($M_\mathrm{d}=0.036^{+0.065}_{-0.020}M_\oplus$) and Kepler-444 e
($M_\mathrm{e}=0.034^{+0.059}_{-0.019}M_\oplus $), have confidently detected
masses due to their proximity to resonance which creates transit timing
variations. The mass ratio of these planets combined with the magnitude of
possible star-planet tidal effects suggests that smooth disk migration over a
significant distance is unlikely to have brought the system to its currently
observed orbital architecture without significant post-formation perturbations.
