  We explore whether close-in super-Earths were formed as rocky bodies that
failed to grow fast enough to become the cores of gas giants before the natal
protostellar disk dispersed. We model the failed cores' inward orbital
migration in the low-mass or type I regime, to stopping points at distances
where the tidal interaction with the protostellar disk applies zero net torque.
The three kinds of migration traps considered are those due to the dead zone's
outer edge, the ice line, and the transition from accretion to starlight as the
disk's main heat source. As the disk disperses, the traps move toward final
positions near or just outside 1~au. Planets at this location exceeding about
3~M$_\oplus$ open a gap, decouple from their host trap, and migrate inward in
the high-mass or type II regime to reach the vicinity of the star. We
synthesize the population of planets formed in this scenario, finding that some
fraction of the observed super-Earths can be failed cores. Most super-Earths
formed this way have more than 4~M$_\oplus$, so their orbits when the disk
disperses are governed by type II migration. These planets have solid cores
surrounded by gaseous envelopes. Their subsequent photoevaporative mass loss is
most effective for masses originally below about 6 M$_\oplus$. The failed core
scenario suggests a division of the observed super-Earth mass-radius diagram
into five zones according to the inferred formation history.
