We propose a new cosmological principle for the foundations of arithmetic: the Dark Foam Universe. In this framework, the number 2 acts as the stabilising symmetry of a quantum foam of vacua. Even perfect numbers are the allowed,coherent structures that respect this symmetry, while an odd perfect number is a forbidden architecture that would break the conclusionary horizon—a logical boundary analogous to the de Sitter horizon in spacetime. We demonstrate thatevery known attack on the odd perfect number problem fails in a way precisely analogous to the impossibility of observing beyond a cosmological horizon. Using the mathematical apparatus of de Sitter space, nonstandard models of arithmetic, and the limits of provability, we argue that an odd perfect number can only inhabit a de Sitterlike 'unreal' place where knowledge is fundamentally inaccessible, andthat its nonexistence in the standard model of arithmetic is a necessary stability condition for the mathematical universe. The paper formalises this vision and shows how the number 2 guards the boundary between the real and the unreal.