  Using analytic modeling and simulations, we address the origin of an
abundance of star-forming, clumpy, extended gas rings about massive central
bodies in massive galaxies at $z \!<\! 4$. Rings form by high-angular-momentum
streams and survive in galaxies of $M_{\rm star} \!>\! 10^{9.5-10} M_\odot$
where merger-driven spin flips and supernova feedback are ineffective. The
rings survive after events of compaction to central nuggets. Ring longevity was
unexpected based on inward mass transport driven by torques from violent disc
instability. However, evaluating the torques from a tightly wound spiral
structure, we find that the timescale for transport per orbital time is long
and $\propto\! \delta_{\rm d}^{-3}$, with $\delta_{\rm d}$ the cold-to-total
mass ratio interior to the ring. A long-lived ring forms when the ring
transport is slower than its replenishment by accretion and the interior
depletion by SFR, both valid for $\delta_{\rm d} \!<\! 0.3$. The central mass
that lowers $\delta_{\rm d}$ is a compaction-driven bulge and/or dark matter,
aided by the lower gas fraction at $z \!<\! 4$, provided that it is not too
low. The ring is Toomre unstable for clump and star formation. The high-$z$
dynamic rings are not likely to arise form secular resonances or collisions.
AGN feedback is not expected to affect the rings. Mock images of simulated
rings through dust indicate qualitative consistency with observed rings about
bulges in massive $z\!\sim\!0.5\!-\!3$ galaxies, in $H_{\alpha}$ and deep HST
imaging. ALMA mock images indicate that $z\!\sim\!0.5\!-\!1$ rings should be
detectable. We quote expected observable properties of rings and their central
nuggets.
