Proposal for an Extended Run of T2K to 20×102120\times10^{21} POT

68 pages, 31 figures68 pages, 31 figures68 pages, 31 figuresRecent measurements by the T2K neutrino oscillation experiment indicate that CP violation in neutrino mixing may be observed in the future by long-baseline neutrino oscillation experiments. We propose an extension to the currently approved T2K running from 7.8\times 10^{21}~\mbox{POT} to 20\times 10^{21}~\mbox{POT}, aiming at initial observation of CP violation with 3$\,\sigma$ or higher significance for the case of maximum CP violation. The program also contains a measurement of mixing parameters, $\theta_{23}$ and $\Delta m^2_{32}$, with a precision of 1.7$^\circ$ or better and 1%, respectively. With accelerator and beamline upgrades, as well as analysis improvements, this program would occur before the next generation of long-baseline neutrino oscillation experiments that are expected to start operation in 2026