Consider the proof of burn algorithm as an effective cryptocoin algorithm. Then turn this on it’s head. If a pseudo random burn density is exhibited, previous mined coins, can be used as the burn sink. If this process is considered an also method of a mine success, then the burn creates an associated make in the protocol. As this can be a fixed multiplier, it maintains a mint standard. An “I could have burnt block, proof of could have” as it were. And get coins for doing it.
Something like Slimcoin with a kick in, kick out coins balancer keeping the fixed-sh multiplier net around a centroid. And having “modulable” kicks within limits. An “alternative slicer” can split this transact delta into a “modulable” stream for storing data. So if a method of “moving root block” can maintain a maximal blockchain size, data compression and a fixed bound cryptocoin with some injected coin total supply “chaos” results.
Of course the minimalist right to sign and signing would work in effect, but would encourage opening many intermediate wallets. Burning these intermediate wallets also provides the final coins for the real wallet. This in essence is proof of work. The next step of proof of stake would be to put any chosen coin into the mix for the hash, to gain right to sign, as this would have the effect of maintaining a faster hashing with more coins to try, and block number and chain check hash would prevent rehashing doubles. Or as some have it, selection of the coin for the right of hash, a la premium bonds. Publishing private key hashes of intermediate wallets such that the coin can be “seen” as mined and owned looks promising. And maybe a right to sign transfer dole for the under coined, although this would negate its use as a bit exchange.
That all explains why some of the best are hybrid in the mechanistic building of the blockchain. The proof of burn allows for coin supply modulation, and on fixed supply coins a possible under representation over time. The idea that calculating something useful would be good is good at heart, but misses the easy re-seeding duplication necessity, as the useful result is an open plain text. In many ways Ethereum will excel at derivatives …
The whole crypto-currency market is full of clones with different marketing and some have a slight tech advantage. The main differences which are coming up are memory intensive hashes, and even some block chain as random data hashes. Proof of stake looks good in principal, but does have a non mining aspect, and so is locked out for new users to mine without initial stake, and in some sense why would they mine? In such a situation it’s not mining but interest payments for service. Which devalues the market without effort, which is sort of not getting paid without equitable burn.
Proof of work maybe environmentally inefficient, but better that the box does it.