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We report the discovery of a cold Super-Earth planet (m_p=4.4 +/- 0.5M_Earth) orbiting a low-mass (M=0.23 +/- 0.03 M_Sun) M dwarf at projectedseparation a_perp = 1.18 +/- 0.10 AU, i.e., about 1.9 times the snow line. Thesystem is quite nearby for a microlensing planet, D_Lens = 0.86 +/- 0.09 kpc.Indeed, it was the large lens-source relative parallax pi_rel=1.0 mas (combinedwith the low mass M) that gave rise to the large, and thus well-measured,"microlens parallax" that enabled these precise measurements.OGLE-2017-BLG-1434Lb is the eighth microlensing planet with planet-host massratio q < 1 * 10^-4.  We apply a new planet-detection sensitivity method, which is a variant of"V/V_max", to seven of these eight planets to derive the mass-ratio function inthis regime. We find dN/d(ln q) ~ q^p, with p = 1.05 (+0.78,-0.68), whichconfirms the "turnover" in the mass function found by Suzuki et al. relative tothe power law of opposite sign n = -0.93 +/- 0.13 at higher mass ratios q >~ 2* 10^-4. We combine our result with that of Suzuki et al. to obtain p = 0.73(+0.42,-0.34).

OGLE-2017-BLG-1434Lb: Eighth q < 1 * 10^-4 Mass-Ratio Microlens Planet Confirms Turnover in Planet Mass-Ratio Function