This isn’t what is proved. What is proved is that there is some constant K, dependent on choice programming language, such that Komolgorov complexity is dominated by at most K explanations. The proof provides an upper bound on K, as the exponential of the length of program needed to do various bits of fiddling around with encoding schemes. In other words, K may well be >10^100 for sensible choices of programming language.
This isn’t what is proved. What is proved is that there is some constant K, dependent on choice programming language, such that Komolgorov complexity is dominated by at most K explanations. The proof provides an upper bound on K, as the exponential of the length of program needed to do various bits of fiddling around with encoding schemes. In other words, K may well be >10^100 for sensible choices of programming language.
Fair. I was summarizing “dominates within a constant factor” as just “dominates”, which admittedly is not totally accurate ;)