User blog comment:Kyodaisuu/Classifying numbers with ordinals/@comment-11227630-20180420013035

If ordinals in the form $$\gamma[n_1][n_2]\cdots[n_k]$$ do not contain all ordinals $$\le\gamma$$ (example), then we may get a higher C(n) than expected.

So there should be some restrictions to the FS system we use, such as "every ordinal $$\alpha\le\gamma$$ can be expressed as $$\alpha=\gamma[n_1][n_2]\cdots[n_k]$$".