Jing Wang, Xuchen Lin, Ze-Zhong Liang, W. J. G. De Blok, Hong Guo, Zhijie Qu, Céline Péroux, Kentaro Nagamine, Luis C. Ho, Dong Yang, Simon Weng, Claudia Del P. Lagos, Xinkai Chen, George Heald, J. Healy, Qifeng Huang, Peter Kamphuis, D. Kleiner, Di Li, Siqi Liu, F. M. Maccagni, Lister Staveley-Smith, Zherong Su, Freeke Van De Voort, Fabian Walter, Fangxiong Zhong, Siwei Zou

We present the first $z=0$ HI column density distribution function, $f(N_\mathrm{HI})$, extending down to $\log (N_\mathrm{HI}/\mathrm{cm}^{-2})=17.8$. This was derived from high-sensitivity 21-cm emission-line imaging at $\sim$1 kpc resolution. At high-column-densities (19.8$< \log (N_\mathrm{HI}/\mathrm{cm}^{-2}) <$21.3), our results align with earlier $z=0$ studies but benefit from 100 times greater sensitivity. Comparisons with $z\sim3$ quasar absorption-line studies reveal that $f(N_\mathrm{HI})$ at $z=0$ is systematically lower by 0.1-0.4 dex for $19.2< \log (N_\mathrm{HI}/\mathrm{cm}^{-2}) <21$. However, the distributions become comparable at $17.8< \log (N_\mathrm{HI}/\mathrm{cm}^{-2}) <19.2$, suggesting weak evolution in this regime. Extrapolating the length incidence ($\mathrm{d}N/\mathrm{d}X$) for $\log (N_\mathrm{HI}/\mathrm{cm}^{-2}) >17.5$ implies a covering fraction ($f_\mathrm{cov}$) of $\sim0.7$ within 1-kpc-scale HI-detected pixels at $z=0$. Notably, for $17.8< \log (N_\mathrm{HI}/\mathrm{cm}^{-2}) <20$, impact parameters at a given $N_\mathrm{HI}$ are significantly lower than previous $z\sim0$ absorption-line results and TNG50 simulation predictions. This discrepancy indicates challenges in identifying galaxy counterparts for absorbers and in recovering low-column-density HI within cosmological simulations. Finally, we derive a covering fraction of 0.006 for $\log (N_\mathrm{HI}/\mathrm{cm}^{-2}) >17.8$ gas within the virial radius around Milky-Way-like galaxies. These findings provide new constraints on the baryonic flows and gaseous dynamics governing galaxy evolution.