PoW and PoS are algorithms to order transactions, but how many transactions and how often to order them are just tunable parameters.
the real scalability "tech" that is being sneaked in while everybody is busy talking about PoS is sharding, which essentially means abandoning the idea of serializability of the underlying database, leading to vastly more complex failure modes, reliance on very tight clock synchronization and zero real world testing of such approach.
so yeah, good luck...
You're wrong, PoW is a poisson process which means time to generate blocks must be a very small fraction of average block time. Block times in PoS have a normal distribution with tight std, which means block generation can take even 1/3 of block time, giving some leeway for propagation.
1) The length of comments posted in Internet discussion forums
2) Users' dwell time on online articles
3) income of 97%–99% of the population
4) Milk production by cows
5) Amounts of rainfall
6) Size distributions of rainfall droplets
7) The size of cash payments and size of transactions in Bitcoin
Many other examples could be found here: https://en.wikipedia.org/wiki/Log-normal_distribution
There's some confusion in this question. A log normal distribution is proof enough that multiplication exists.
3 and 7 are trivial because there are clear compounding effects - they are most obvious in finance. 5 is easy too, more rainfall means more water evaporates, it's a simple multiplicative cycle. 1 because larger response is more likely to generate more larger responses.
There's no causal relation between multiple factors in block propagation. It snows and latency to starlink rises. There's congestion somewhere because a new tv series is being massively downloaded. A node has random clock skew of 1 s. These are all additive.
Ha-ha. Maybe it's a good reason to forge the evidence. However, it doesn't mean you can't forge an additive law here!
In 3 you can add value of house to the value of car instead of "multiplying" them. In 7 you can add values "cent by cent". "Multiplicative cycle" in 5 is a real conspiracy theory. Is there the same thing for "cow's milk"? Could you increase milk yield with the same "multiplicative cycle"?
According to this logic bank interests for credits with "simple interest" should have a normal distribution and those with "compound interest" should have a log-normal one!
I can give you more simple criteria for all cases above:
1) "The length of comments" can't be negative
2) "Users' dwell time" can't be negative
3) income can't be negative
4) cow's don't suck milk from farmers
5) Law of Gravity works for rainfalls
6) Size rainfall droplets can't be negative
7) Payer is the one who pays
8) "Latency" and "delay" for nodes can't be negative too. It's very likely that it has a log-normal distribution as many other sort of delay.
Eth2 is also not hard fork. The old chain will be attached to the new chain