Zero as Ontological Boundary: The Trinity of Properties and the Hypothesis of Universal Duality

Zero is conventionally defined as the additive identity: the number that, when added to any value, leaves it unchanged. This is a functional description. It tells us what zero does within a mathematical system. It does not tell us what zero is. This paper proposes a different starting point. We argue that zero is best understood as an ontological boundary — not a value located between −1 and +1, but the condition that makes the existence of −1 and +1 possible in the first place. From this reframing, we derive three irreducible and interdependent properties of zero: persistence (zero cannot itself become zero under any operation), absorption (any encounter with zero returns to zero), and generativity (zero's continued existence maintains the structural conditions for both sides to exist). We demonstrate through systematic elimination that these three properties form an inseparable unity: removing any one causes the remaining two to degrade or collapse. We also address the prior question of anchor selection — the recognition that every system of reasoning begins with a starting point not derived from within the system, and that making this starting point explicit is a precondition for honest reasoning. We propose this as an independent epistemological layer, the zeroth layer, that has been largely implicit in the history of thought. Finally, we extend the boundary model into a speculative hypothesis: if zero is a genuine two-sided boundary, the universe we inhabit may be one side of a larger symmetric structure — what we call the Greater Universe. We mark this explicitly as a hypothesis, not a conclusion.