The true invariant of an arbitrage free portfolio

It is shown that the arbitrage free portfolio paradigm being applied to a portfolio with an arbitrary number of shares N allows for the extended solution in which the option price F depends on N. However the resulting stock hedging expense Q=MF (where M is the number of options in the portfolio) does not depend on whether N is treated as an independent variable or as a parameter. Therefore the stock hedging expense is the true invariant of the arbitrage free portfolio paradigm.