Three Attributes Force a Unique Mathematical Framework

We formalise three classical attributes (omniscience, omnipotence, omnipresence) as mathematical axioms on a comparison-cost system operating on ℝ⁺. We prove a biconditional: the three axioms force a unique framework with no free parameters (the forward direction, via seven inevitability theorems), and the resulting framework exhibits all three axioms (the reverse direction). The framework is therefore the unique fixed point of the map “axioms → structure → axioms.”

The forced structure comprises a specific cost functional J(x) = (1/2)(x + x⁻¹) − 1, a specific self-similar ratio φ = (1 + √5)/2, a specific spatial dimension D = 3, and a specific temporal period 8. The three axioms correspond to the three laws of classical logic (identity, non-contradiction, excluded middle), and the framework is the unique geometric unpacking of “a = a” under coherent composition, strict convexity, and metric completeness.