We propose to observe the COSMOS UltraDeep (UD) field with HSC in order to investigate the unexplored time domain of the variable Universe - the long and faint. To explore the long-timescale frontier of the variable Universe, we have been accumulating the time domain legacy data with HSC at the COSMOS UD field for 5 seasons in the i and z bands with the median limiting magnitudes of 26.0 mag and 25.5 mag, respectively. We propose to add the new season data as deep as the previous seasons. The proposed long-term survey can discover high-redshift pair-instability and superluminous SNe and intrinsically long-lasting SNe. Long-term AGN activities can also be investigated. Unknown long-timescale transients may be discovered. Obtaining the time domain data in this year is essential to identify long-lasting transient candidates to follow with JWST. We have been discovering long-lasting faint transients in the previous seasons. The live long-lasting SNe to be observed with JWST will show up in 2023 and it is required to obtain the long-term time domain data in S23A to make full use of JWST.
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