- 96% reduction in block space over the naive approach, per the paper. (EDIT: the signature aggregation being referred to is Schnorr signatures, and it's become reality since the paper was published)
- 7 transactions per second, 86400 seconds per day, 365 days per year
8000000000*(1-0.96)/7/86400/365 = 1.45 years
Current transaction fees are $3. Assuming that stays constant, every group of 20 users would need to come up with $3 between them.
Are you assuming the chain does nothing else at the time? And that fees wouldn't explode the second people actually tried to use it, and block space would dry up? Seems like using only the free portion of block space would allow you to arrive at a more realistic conclusion. Blocks seem to be going out pretty full thanks to ordinals.
I expect lightning adoption (to the extent it happens) to take place over decades, not just 1.45 years, so there's plenty of buffer already.
In the past, fees have at times been both lower than today and higher than today. That will be true in the future too. Satoshi Dice didn't ruin bitcoin in 2013, and neither will ordinals in 2023.
The paper from 2017: https://www.researchgate.net/publication/320247611_Scalable_...
The general idea is called channel factories.