User blog comment:Hyp cos/tree function and TREE(3)/@comment-5150073-20140624084600/@comment-5150073-20140624165427

But we can use $$\omega_1^\text{CK}[n]$$ for fixed n. That would be a recursive ordinal and $$f_{\omega_1^\text{CK}[n]}(m)$$ is a computable function (say, $$f_{\omega_1^\text{CK}[65536]}(m)$$. I defined it, but the definition didn't require so much time and memory.