CSST Cosmological Emulator I: Matter Power Spectrum Emulation with one percent accuracy to k = 10 h/Mpc

In the near future, the China Space Station Telescope (CSST) will obtain unprecedented imaging and spectroscopic data. The statistical errors in the cosmological parameter constraints will be reduced significantly. The corresponding theoretical tools must meet the percent-level accuracy required to extract as much cosmological information as possible from the observations. We present the CSST Emulator to provide nonlinear power spectrum predictions in the eight cosmological parameter space $\Omega_\mathrm{cb},\Omega_\mathrm{b},H_{0},n_{s},A_{s},w_{0}, w_{a}$, and $m_\nu$. It is constructed based on the Kun simulation suite, consisting of 129 high-resolution simulations with box size $L=1\,h^{-1} {\rm Gpc}$ and evolving $3072^3$ particles. The determinations of parameter ranges, sampling method, and emulation strategy in the whole construction have been optimized exquisitely. This enables our prediction for $k\leq 10\,h {\rm Mpc}^{-1}$ and $z\leq 2.0$ to reach $1\%$ accuracy validated through internal and external simulations. We also compare our results with recent BACCO, EuclidEmulator2, and Mira-Titan IV emulators, which demonstrate the CSST Emulator's excellent performance across a wide cosmological parameter range in the nonlinear regime. CSST Emulator is publicly released at https://github.com/czymh/csstemu, and provides a fundamental theoretical tool for accurate cosmological inference with future CSST observations.