In order to maintain a constant value of your coin you must be able to both add and remove coins from the economy. Now, you might be able to come up with an automatic system that can do that in theory, but it will be close to impossible in practice.
That's easy: destructive transaction fees. I.e. transaction fee must be included, but it doesn't go to miner. Thus we assume that there is a loss proportional to coin's "GDP".
Consider that this is exactly what the Federal Reserve is supposed to do -- make the value the dollar constant. Not only have they never come up with an automatic system that works, but they have consistently done a poor job trying to maintain it manually.
For some values of 'poor'. Fluctuations of USD exchange rate are usually small, something like 5% per year.
On the other hand, Bitcoin exchange rate went from 0.01 to 10 USD within one year (IIRC), so we have 100000% change.
That's quite a difference, right?
Three orders of magnitude vs zero.
Of course, coin backed by energy would have much higher exchange rate fluctuations than USD, something like price fluctuations of base commodities, i.e. 100% change within a year is quite possible.
But still we don't have same situation as with Bitcoin where it can shoot up 1000x.
For more information on the mathematics of it all, look up dynamical systems and numerical integration.
Thank you, I just have M.Sc. in applied math, what do I know about mathematics?
My description was hand-wavy because I consider all details kinda obvious, not because I don't know math, lol
I suspect you're focusing too much on mining and ignore economic aspects of this: when participants KNOW that coin is pegged, and they KNOW that pegging mechanism works in long term under broad assumptions, price will be stabilized through arbitrage, not through mining.
I think I mentioned this, do you know what arbitrage means?