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Description
We report the discovery of one newly confirmed planet (P=66.06 days, R_P_=2.68+/-0.17 R_{Earth}_) and mass determinations of two previously validated Kepler planets, Kepler-289 b (P=34.55 days, R_P_=2.15+/-0.10 R_{Earth}_) and Kepler-289-c (P=125.85 days, R_P_=11.59+/-0.10 R_{Earth}_), through their transit timing variations (TTVs). We also exclude the possibility that these three planets reside in a 1:2:4 Laplace resonance. The outer planet has very deep (~1.3%), high signal-to-noise transits, which puts extremely tight constraints on its host star's stellar properties via Kepler's Third Law. The star PH3 is a young (~1 Gyr as determined by isochrones and gyrochronology), Sun-like star with M_*_=1.08+/-0.02 M_{sun}_, R_*_=1.00+/-0.02 R_{sun}_, and T_eff_=5990+/-38 K. The middle planet's large TTV amplitude (~5 hr) resulted either in non-detections or inaccurate detections in previous searches. A strong chopping signal, a shorter period sinusoid in the TTVs, allows us to break the mass-eccentricity degeneracy and uniquely determine the masses of the inner, middle, and outer planets to be M=7.3+/-6.8 M_{oplus}_, 4.0+/-0.9M_{oplus}_, and M=132+/-17 M_{oplus}_, which we designate PH3 b, c, and d, respectively. Furthermore, the middle planet, PH3 c, has a relatively low density, {rho}=1.2+/-0.3 g/cm3 for a planet of its mass, requiring a substantial H/He atmosphere of 2.1_-0.3_^+0.8^% by mass, and joins a growing population of low-mass, low-density planets.
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