You can't prove it scientifically or mathematically with reference to other coins because it's apples and oranges.   Almost every coin including bitcoin and litecoin have halving schedules that were coded in from the genesis block.    Potcoin's block reward schedule was flawed at its creation.  Show me a coin that is all mined out that isn't proof of stake.   Halving the coin is about giving us more time for adoption so there are uses for the coin by the time its all mined out.  The only other alternative I can think of is to increase the total coin supply and implement proof of stake so people holding up until now can retain their positions.  Either way, the mining phase must be extended or it's toast.