I also wanted to point out I fully agree with you that there are still many optimizations we could do to reduce costs, and think many of these things are certainly worth doing. However, there’s only so much we can do in this regard. Sooner or later we still run up against theoretical limitations. These optimizations can reduce costs by some factor…but they are highly unlikely to overcome the Ω(n) validation complexity barring some major algorithmic breakthrough (and perhaps allowing for nondeterminism, perhaps accepting a negligible but finite error probability).