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, the time domain legacy data with HSC at the COSMOS UD field for 6 seasons in the i and z bands with the median limiting magnitudes of 26.0 mag and 25.5 mag, respectively, have been accumulated. 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. Long-lasting faint transients in the previous seasons have been discovered. The live long-lasting SNe to be observed with JWST will show up in 2024 and it is required to obtain the long-term time domain data in S24A to make full use of JWST.
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