Is the construction work and test your magical abilities in explore city supposed be one time event?
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They're both one time event that's only available on chapter 2 for now. But, I'm planning for the construction work to be a repeatable event for the next update.
Edit:Wait, the learn magic event that you mentioned, are you perhaps meaning to ask about the star statue event or the Rigor's traning event? They're still both a one time event though...