Fraction of USP planets formed (i.e., reaching ﹩{a}_{1}(1-{e}_{1}^{2})\lt 0.02﹩ au) as a function of time for Kepler-10 systems where the innermost planet starts with a random semimajor axis in ﹩{a}_{1}\in [0.06,0.1]﹩ au. In our fiducial run (blue line), all planets have initial eccentricities and inclinations drawn from a Rayleigh distribution with parameter σ = 0.1 (﹩{e}_{\mathrm{rms}}={i}_{\mathrm{rms}}=0.14﹩), and the masses and semimajor axes of the outer planets are the same as in Figure 5. The green line indicates a simulation in which we decrease the dispersions by setting σ = 0.08 (﹩{e}_{\mathrm{rms}}={i}_{\mathrm{rms}}=0.11﹩); 2 out of 500 become USP planets. The orange line shows a set where we decrease the masses of all the planets by a factor of 3 (﹩{M}_{\mathrm{USP}}=1.5\,{M}_{\oplus }﹩ and ﹩{M}_{\mathrm{outer}}\sim 5\,{M}_{\oplus }﹩) and the red line shows a set where we only decrease the mass of the outer planets by a factor of 2 (﹩{M}_{\mathrm{USP}}=3\,{M}_{\oplus }﹩ and ﹩{M}_{\mathrm{outer}}\sim 7.5\,{M}_{\oplus }﹩). The integrations include GR precession and nondissipative tidal bulges.