  Uncovering the formation process that reproduces the distinct properties of
compact super-Earth exoplanet systems is a major goal of planet formation
theory. The most successful model argues that non-resonant systems begin as
resonant chains of planets that later experience a dynamical instability.
However, both the boundary of stability in resonant chains and the mechanism of
the instability itself are poorly understood. Previous work postulated that a
secondary resonance between the fastest libration frequency and a difference in
synodic frequencies destabilizes the system. Here, we use that hypothesis to
produce a simple and general criterion for resonant chain stability that
depends only on planet orbital periods and masses. We show that the criterion
accurately predicts the maximum mass of planets in synthetic resonant chains up
to six planets. More complicated resonant chains produced in population
synthesis simulations are found to be less stable than expected, although our
criterion remains useful and superior to machine learning models.
