  The planet-metallicity correlation serves as a potential link between
exoplanet systems as we observe them today and the effects of bulk composition
on the planet formation process. Many observers have noted a tendency for
Jovian planets to form around stars with higher metallicities; however, there
is no consensus on a trend for smaller planets. Here, we investigate the
planet-metallicity correlation for rocky planets in single and multi-planet
systems around Kepler M-dwarf and late K-dwarf stars. Due to molecular
blanketing and the dim nature of these low mass stars, it is difficult to make
direct elemental abundance measurements via spectroscopy. We instead use a
combination of accurate and uniformly measured parallaxes and photometry to
obtain relative metallicities and validate this method with a subsample of
spectroscopically determined metallicities. We use the Kolmogorov-Smirnov (KS)
test, Mann-Whitney U test, and Anderson-Darling test to compare the compact
multiple planetary systems with single transiting planet systems and systems
with no detected transiting planets. We find that the compact multiple
planetary systems are derived from a statistically more metal-poor population,
with a p-value of 0.015 in the KS test, a p-value of 0.005 in the Mann-Whitney
U test, and a value of 2.574 in the Anderson-Darling test statistic, which
exceeds the derived threshold for significance by a factor of 25. We conclude
that metallicity plays a significant role in determining the architecture of
rocky planet systems. Compact multiples either form more readily, or are more
likely to survive on Gyr timescales, around metal-poor stars.
