string theory - In Cardy-Verlinde generalized uncertainty principle (GUP), how we know that the alpha is a constant of order one?

The GUP equation [1] is, $$\Delta x_i\geq\frac{\hbar}{\Delta p_i}+\alpha^2l_p^2\frac{\Delta p_i}{\hbar},$$ where $l_p$ is the Planck length. How do we know that $\alpha$ has a order of unity [1]? What's the proof?

Reference:

1. Setare, M. R. "Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle." Physical Review D 70 no. 8 (2004): 087501, arXiv:hep-th/0410044.