My 7th suggestion. Payments by shares.
There is in Ethereum such a thing as uncle blocks (uncle is the brother of the paternal block), these are orphans that are monetized and added to the blockchain and increase its difficulty and safety, due to the computations embedded in them. Uncle included in the unit, receive a 7/8 static block award.
I propose to extend this mechanism not only to orphans (ideal alternative block solutions) but also to shares (non-ideal alternative block solutions) and to pay them a reward proportionally to the degree of ideality of the shares (like in proportional pool system), from 7/8 for ideal orphan and down to the ultimate lower ideality of accepting the share, ULIOATS is fixed and corresponds to the daily work of the statistical middle-user cpu-processor for example core-i5 2400.
This system will provide a guaranteed periodic award for any even for the weakest processors. Due to this, weakest processors will not escape from solo-mining even in case of strong increasing difficulty of the network and increasing of time between their blocks to unacceptable values, measured in years.
The problem of a heavy blockchain, I propose to solve by cutting off the tail of blockchain. Let's assume so: every 50 thousand blocks (with block time of 1 minute - this is about a month) creates a checkpoint block containing a complete list of all non-zero wallets and their balances. And every 300 thousand blocks, the most ancient tail under the most ancient 50 thousand checkpoint block is cutting off.
Good suggestion, there are some incentives with "uncle blocks" for the slow processors and we'd love to find a way to secure it for sure. We've run into the possibility that some people might focus on mining empty uncle blocks, in which case the whole system can be abused/circumvented. I didn't follow this on ETH but I think their solution was to mine empty blocks at the same speed as blocks with tx. Not sure if they implemented this. As with many good ideas, having to protect against abuse sometimes prevents adding new features or requires more dev time to make sure it's implemented and used as designed. That being said, we're certainly interested in a reward mechanism for slower processors. We are continuing the research into such mechanism. Thanks for the suggestion and keep posting ideas.