Extended Universe Size Index

The Extended Universe Size Index (EUSI) is a number, which indicates the deepest nestation of other verses within a specific verse.It can be used to tell the size of a universe, without needing to say its size, due to most verses having beyond infinite sizes, or ordinals/cardinals that aren't named yet.

Definition
We define a function

$$ \psi(\alpha) = \alpha + 1$$$$ \psi(\alpha,\beta,\gamma \cdots \delta) = \psi(\alpha-1,\psi(\alpha,\beta,\gamma \cdots \delta),\gamma \cdots \delta)$$$$ \psi(0,\beta,\gamma \cdots \delta) = \psi(\beta,\gamma \cdots \delta)$$

$$ \psi(0,0,\gamma \cdots \delta) = \psi(1,\gamma \cdots \delta)$$

After this, we can create another extention, by borrowing some things from other functions, such as the veblen function, by asserting:

$$\psi(\Omega^{\alpha}) = \psi(\overbrace{1,0,0 \cdots 0,0}^{\alpha})$$

$$\psi(\Omega^{\Omega}) = \psi(\Omega^{\psi(\Omega^{\psi(\Omega^{\cdots})})})$$

$$\psi(\Omega^{\Omega^{\Omega}}) = \psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^{\cdots}})}})$$

EUSI equations
$$ \psi(\alpha+\beta)=\psi^{\beta+1}(\alpha)$$

$$ \psi(\alpha)+\psi(\beta)=\psi(\alpha+\beta+1)=\psi(\alpha+\beta)+1$$but in general:

$$\psi^\gamma(\alpha)+\psi^\delta(\beta)=\psi^{\gamma+\delta}(\alpha+\beta)$$, where $$\gamma\ \text{and}\ \delta$$signify iteration.

EUSI in number form
EUSIs can obviously be broken down into ordinals / cardinals after they've been fully decomposed. The article of these is here.