Yes, for a busy beaver properly defined in information theoretic terms, like BBλ2 [1], one can prove that its champions must be incompressible up to some consta

Yes, for a busy beaver properly defined in information theoretic terms, like BBλ2 [1], one can prove that its champions must be incompressible up to some constant. Mikhail Andreev's article "Busy Beavers and Kolmogorov complexity" [2] explores these connections. [1] https://oeis.org/A361211 https://oeis.org/A361211 [2] https://arxiv.org/pdf/1703.05170 https://arxiv.org/pdf/1703.05170