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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 linear function of ω and reasonably small values of n, which is roughly equivalent to chained arrow notation and Jonathan Bowers' 4-entrical array.

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

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