  Stars originate from the dense interstellar medium, which exhibits
filamentary structure to scales of $\sim 1$ kpc in galaxies like our Milky Way.
We explore quantitatively how much resulting large-scale correlation there is
among different stellar clusters and associations in \emph{orbit phase space},
characterized here by actions and angles. As a starting point, we identified 55
prominent stellar overdensities in the 6D space of orbit (actions) and orbital
phase (angles), among the $\sim$ 2.8 million stars with radial velocities from
Gaia EDR3 and $d \leq 800$ pc. We then explored the orbital \emph{phase}
distribution of all sample stars in the same \emph{orbit} patch as any one of
these 55 overdensities. We find that very commonly numerous other distinct
orbital phase overdensities exist along these same orbits, like pearls on a
string. These `pearls' range from known stellar clusters to loose, unrecognized
associations. Among orbit patches defined by one initial orbit-phase
overdensity 50\% contain at least 8 additional orbital-phase pearls of 10
cataloged members; 20\% of them contain 20 additional pearls. This is in
contrast to matching orbit patches sampled from a smooth mock catalog, or
offset nearby orbit patches, where there are only 2 (or 5, respectively)
comparable pearls. Our findings quantify for the first time how common it is
for star clusters and associations to form at distinct orbital phases of nearly
the same orbit. This may eventually offer a new way to probe the 6D orbit
structure of the filamentary interstellar medium.
