This category contains numbers that can be defined or estimated using fast-growing hierarchy in the form fα(n) with α made from polynomial of ω and reasonably small values of n, which is roughly equivalent to Jonathan Bowers' linear array.
The lower bound of this category is \(f_{\omega^3}(f_3(10))\), and the upper bound is \(f_{\omega^\omega}(f_3(10))\).
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