PMO Polaris CO survey. I. A 100 deg$^2$ view of the Polaris Flare
Large-area CO surveys are essential for studying molecular cloud dynamics and evolution; however, most have focused on the Galactic plane, leaving high-latitude clouds less explored. We present the PMO Polaris CO Survey (PPCOS), which maps a 100~deg$^2$ region of the Polaris Flare in the $J=1-0$ transitions of $^{12}$CO, $^{13}$CO, and C$^{18}$O using the Delingha 13.7~m telescope. As the first large-area CO survey at high Galactic latitude ($|b| > 20^{\circ}$) with sub-arcminute resolution, PPCOS achieves sensitivities of $\sim$0.46~K for $^{12}$CO and $\sim$0.23~K for $^{13}$CO and C$^{18}$O at a spectral resolution of 0.16~km~s$^{-1}$ and an angular resolution of 50\arcsec. The $^{12}$CO emission reveals seven distinct complexes, where only $\sim$10\% of pixels display multiple velocity components, alongside a global velocity gradient of 0.18~km~s$^{-1}$~pc$^{-1}$. Typical line widths are $1.2 \pm 0.6$~\mbox{km~s$^{-1}$} for $^{12}$CO, while $^{13}$CO components are systematically narrower ($\lesssim 0.7\,\Delta V_{\rm ^{12}CO}$). The $^{12}$CO/$^{13}$CO intensity ratios (5--25) indicate widespread $^{12}$CO optical thickness, resembling conditions found in giant molecular clouds (GMCs). Globally, the CO emission divides into two groups: a major group aligned with the velocity gradient and a secondary group elongated perpendicular to it, possibly regulated by large-scale coherent dynamics. We propose a three-layer hierarchy: a dynamically assembling and dispersing periphery traced by $^{12}$CO, a more stable intermediate kernel traced by $^{13}$CO, and gravitationally bound compact cores traced by C$^{18}$O. No young stellar objects are firmly associated with the molecular gas. PPCOS provides an ideal laboratory for studying turbulence, hierarchical structure, and early cloud evolution in a nearby, relatively simple molecular cloud.