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Hi Maha,
The formula says that the stock(t,y) (stock of the technology t, in the year y) is calculated by summing the stock(t,y,v) (stock of the technology t, in the year y, for the vintage v) over all different vintages in the model.
The "P" in the distance-based emission calculation is an index, used to designate each different pollutant being emitted by the technology. It is not a variable with any associated units.
Best,
Taylor