Not yet reviewed by Pith; the record is open.

Void size function (VSF) contains information of the cosmic large-scale structure (LSS), and can be used to derive the properties of dark energy and dark matter. We predict the VSFs measured from the spectroscopic galaxy survey operated by the China Space Station Telescope (CSST), and study the strength of cosmological constraint. We employ a high-resolution Jiutian simulation to get CSST galaxy mock samples based on an improved semi-analytical model. We identify voids from this galaxy catalog using the watershed algorithm without assuming a spherical shape, and estimate the VSFs at different redshift bins from $z=0.5$ to 1.1. We propose a void selection method based on the ellipticity, and assume the void linear underdensity threshold $\delta_{\rm v}$ in the theoretical model is redshift-dependent and set it as a free parameter in each redshift bin. The Markov Chain Monte Carlo (MCMC) method is adopted to implement the constraints on the cosmological and void parameters. We find that the CSST VSF measurement can constrain the cosmological parameters to a few percent level. The best-fit values of $\delta_{\rm v}$ are ranging from $\sim-0.4$ to $-0.1$ as the redshift increases from 0.5 to 1.1, which has a distinct difference from the theoretical calculation with $\delta_{\rm v}\simeq-2.7$ assuming the spherical evolution and using particles as tracer. Our method can provide a good reference for void identification and selection in the VSF analysis of the spectroscopic galaxy surveys.