Boy talk about fast!  I sent a PM and bang there's the GRE, a sharp contrast to trying to get fiat onto the exchange to buy some bitcoin; thanks ncsupanda!

As for PoS - it is hard to come up with any mathematical proof but there are some pretty good swags I can put out there for considering.  From my experience the coins that retain their value or grow mint coins at a rate that is somehow sustainable by the value the community that adopts that coin can sustain.  There's too many factors to consider mathematically without some analysis of variance design experiment laced with economic theory type jargon. 

One thing you should consider is that every time you create a block of coins using PoW you are making new coins - the value of which is going primarily to the miner for running what is turning into collectively a very large power hungry system with more computing power than is required for the security of the block chain.  That miner may not really value the coins that much if they are made as a side effect of going after coins that they are typically mining and pools may dump the coin just to pay out in a coin the miner wants.  Somethings got to eventually pay for that value or the coin will gradually go down in price.

People talk about PoS as having an “interest rate” and most people think that the compounding effect will cause issues.  My view is that it is more like vesting interest in the coin and if you don't trade out  your newly minted PoS coins, your percent of the total market cap of the coin will grow as the coin grows.  This is more like a worker owned cooperative where people who retain the coin have an interest is seeing it grow.  The danger is that if the coin is not dispersed widely enough during the PoW phase the coin can degenerate into a bunch of large bag holders trading back and forth between each other.

I guess my basic thoughts on this is that if your coin value is dripping down faster than you like you are likely putting coins out faster than the community that uses or produces that coin is growing or have some technical issue that is reducing investment.  If that is the case it might be a good option to lower the PoW block reward, add PoS or do something more to build community and coin adoption.  PoS coin blocks can be minted on basically any computer with minimal CPU power and if your goal is to produce a working secure block chain with minimal carbon footprint it makes sense to me to add PoS and restrict PoW. (Just my opinion)

I've been thinking about writing a more detailed article on how PoS works and I might do that... soon.  I can add some more specific technical suggestions but perhaps people will fall fast asleep.