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This category contains numbers that can be defined or estimated using fast-growing hierarchy in the form fα(n) with α made from quadratic function of ω and reasonably small values of n, which is roughly equivalent to Jonathan Bowers' 5-entrical array.

The lower bound of this category is \(f_{\omega^2}(f_3(10))\), and the upper bound is \(f_{\omega^3}(f_3(10))\).

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