Perfect giygas

Perfect giygas is one of the biggest googolisms ever defined by Sbiis Saibian, being equal to 616^666{#&#&#}666. Unfortunately, the number isn't defined fully at this level.
== Approximations==
Since it is not defined by now, the following approximations are just expected values:
Notation 	Approximation
Bird's array notation 	\(\{666, 666 [1 [1 [1 \sim 1, 2 /_3 2] 2] 2] 2\}\)
Fast-growing hierarchy (using this system
of fundamental sequences)	\(f_{\psi_0(\Omega_2^{\Omega_2^\omega})}(666)\)
Hardy hierarchy 	\(H_{\psi_0(\Omega_2^{\Omega_2^\omega})}(666)\)
Slow-growing hierarchy	\(g_{\psi_0(\Omega_3^{\Omega_3^\omega})}(666)\)
== Sources ==
Category:Numbers
Category:Numbers by Sbiis Saibian
Category:ExE numbers using higher BEAF structures
Category:Powers of 616
Category:Unformalised
Category:Class disputed