The existence of a Unit is considered to Mathamancers as a debt, that would be repaid, eventually, by the croaking of that unit.
Several forms of magic seem to create 'debts' similar to that caused by the existence of units; debts which must be paid back to achieve balance. Luckamancy creates a debt of Numbers: the good numbers borrowed by Luckamancy must be paid back through opposing numbers. Either the side will have an equal amount of bad luck or an opposing side will have an equal amount of good luck. Carnymancy creates a debt of Fate: by rigging the rules in the favor of one unit, the rules will be rigged against another.
It is possible that Zero is the metaphysical incarnation of the Numbers Axis. By this view, G-Strings would be the incarnations of the Fate Axis, while Erfworld itself is the incarnation of the Erf Axis.
Zero might be a reference to the term "Zero Sum Game" - in game theory, it's a game where one's gains are balanced exactly by another's losses, and vice versa.
Zero may also be a reference to a quantum vacuum state, also called a zero point field. This is the state of lowest possible energy, and usually contains no physical particles. However, it does give rise to virtual particles, temporarily borrowing energy from the field to create a particle pair, paying back the "debt" when the particles are annihilated again, much like the debt that is owed and repaid when a unit pops and croaks.
The concept of zero as a plane may be a reference to nullspace. Which is an idea that describes the domain of values that become zero when plugged into a system of linear functions or equations.