[Proof Complexity] Paper for comments: "An Isomorphism Between Hard and Impossible Tasks"

[proofcomplexity at huntermonroe.com]

I would appreciate your comments on this paper: https://speedupblogger.wordpress.com/2022/12/21/an-isomorphism-between-hard-and-impossible-tasks/

If a finite version of Chaitin's Incompleteness Theorem holds, then to create a family of tautologies hard with high probability for a proof system P, randomly choose a string x longer than the description of a Turing machine enumerating the theorems of a theory T extending Peano arithmetic (PA) and proving “P is sound”, and construct a family of tautologies encoding "PA lacks length t proofs of 'x is Kolmogorov random'". The assumption implies that this and other results in computability theory implied by Chaitin's Theorem and their proofs translate directly into complexity theory.

Hunter Monroe