Solar-type binaries with short orbital periods ($P_{rm close}$ $equiv$ 1 - 10 days; $a$ $lesssim$ 0.1 AU) cannot form directly via fragmentation of molecular clouds or protostellar disks, yet their component masses are highly correlated, suggesting interaction during the pre-main-sequence (pre-MS) phase. Moreover, the close binary fraction of pre-MS stars is consistent with that of their MS counterparts in the field ($F_{rm close}$ = 2.1%). Thus we can infer that some migration mechanism operates during the early pre-MS phase ($tau$ $lesssim$ 5 Myr) that reshapes the primordial separation distribution. We test the feasibility of this hypothesis by carrying out a population synthesis calculation which accounts for two formation channels: Kozai-Lidov (KL) oscillations and dynamical instability in triple systems. Our models incorporate (1) more realistic initial conditions compared to previous studies, (2) octupole-level effects in the secular evolution, (3) tidal energy dissipation via weak-friction equilibrium tides at small eccentricities and via non-radial dynamical oscillations at large eccentricities, and (4) the larger tidal radius of a pre-MS primary. Given a 15% triple star fraction, we simulate a close binary fraction from KL oscillations alone of $F_{rm close}$ $approx$ 0.4% after $tau$ = 5 Myr, which increases to $F_{rm close}$ $approx$ 0.8% by $tau$ = 5 Gyr. Dynamical ejections and disruptions of unstable coplanar triples in the disk produce solitary binaries with slightly longer periods $P$ $approx$ 10 - 100 days. The remaining $approx$60% of close binaries with outer tertiaries, particularly those in compact coplanar configurations with log $P_{rm out}$ (days) $approx$ 2 - 5 ($a_{rm out}$ $<$ 50 AU), can be explained only with substantial extra energy dissipation due to interactions with primordial gas.
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