[tromp]

> However it's always in principle possible for someone to prove that the KC of some particular string is X.

Only for a bounded number of strings. I.e. there is a finite set of string X such that for strings outside of X, you can not prove their KC, even in principle.

This result by Chaitin [1] can be paraphrased as: you cannot prove a 2 kilo theorem with a 1 kilo theory.

[1] https://www.jucs.org/jucs_2_5/the_limits_of_mathematics/Chai...