What you are describing requires strict identity verification, and thus also requires a central authority (to do said verifications) and lots of trust.
just record balances in a database.
just record balances in a database.
Yes, this is strict identity verification. There are numerous authorities which do so and which are not central. Every identity verification system of a modern state is distributed and depends on trust relations between the various offices and employees. as mentioned, this is not Bitcoin-related work and it is much more vague than the thoughts on PoW.
Absent some centralized mechanism, which is contrary to everything Bitcoin stands for, you have to realize that there is absolutely no way to distinguish any sort of difference between one person running one hundred computers or one hundred people running one computer each. If you cannot tell who is running what there is no way any sort of "non-parallelizable proof of work" could possibly work.
I agree - although challenging every absolutely I find is part of my daily work as researcher and the way I feed myself
A non-parallelizable PoW will not help me to distinguish 1 person running 100 computers from 100 persons running 1 computer each and this also is not what I intend to do with non-parallelizable PoWs.
So what do I want to do?
Right now, Bitcoin uses PoW to (1) randomly select a winner (2) ensure a waiting time between two blocks. Both, selection of winner and waiting time, may be described by a probability distribution. The currently employed PoW in Bitcoin produces two very particular probability distributions. Probability of selection is proportional to (pooled) performance and waiting time is Poisson / exponential with a mean which can be nearly arbitrarily lowered by an attacker.
1) I want to prevent an attacker from arbitrarily lowering the mean of the waiting time (this is a direct consequence of parallelizability)
2) I want to understand if the distributions we get from the current implementation really are the distributions we want (non-parallelizable PoWs give rise to completely different distributions)