Yes, just a calculation, independant of the UD production. Every free money could define this unit easily. Better than that : only some of the people who share a free money can adopt this unit, while the other ones can adopt it, or not, the money stay the same.
That’s it. Whatever the unit you decide to define as a % of M/N, hourly, daily, monthly, every 17 days if you want, the amount of this unit increase the whole money mass at the same rate. The proportion of the money as a unit is independant of the money increase rate.