Proof of activity - Coin based on coin days destroyed

[joey.rich]

I've been working on a concept which could have the following benefits over pure proof of work.
 - Reduce the amount of energy spent on proof of work, while still using proof of work to secure the blockchain.
 - Resolve the risk that fees will not be enough to maintain a secure level of mining as block rewards decrease.

The idea is that miners still get proof of work rewards for mining blocks, but additionally, coins are minted based on the number of coin days destroyed or "coin blocks destroyed" in a block.  This would effectively reduce the energy expenditure on proof of work since proof of work rewards are reduced in comparison to the market cap of the coin.  For example, imagine a coin with the same inflation schedule as Bitcoin, but with an additional 3x of coins being given out for "proof of activity" based on the transactions in each block.  So in this example, the currency would initially be inflating at a rate of 50 coins for POW + 150 coins by proof of activity for a total of 200 coins per block.

Nodes would need to track all UTXOs and the block where each UTXO was created (confirmed).  Then the proof of activity reward in each block (150 coins per block in this example) would be divided up and paid out to addresses in proportion to the amount of coin blocks destroyed in each transaction.

Variations of this could implement linear or exponential inflation.  But exponential inflation is not so bad if the coins in your wallet are also increasing exponentially just by occasionally making a transaction.