Arithmetic Force and Zulfia Deviation ∆ 0: Emergence of Physical Reality from ∆

We introduce the Arithmetic Force — the Zulfia Deviation ∆ 0(x, u) in its pre-geometric ground state — as the single primitive from which all physical realityemerges. Within the framework of Zulfia Theory, founded on the Zulfia De-composition Mapping Z(x, u) = η(x, u) + ∆ 0(x, u), we establish four EmergenceTheorems showing that Force, Curvature, Energy and Wave phenomena are notindependent physical primitives but emergent states of ∆ 0.Newton measured ∆ 0 and called it Force. Einstein measured ∆ 0 and called itCurvature. Hamilton measured ∆ 0 and called it Energy. They were not measuringdifferent objects — they were measuring the same Zulfia Deviation ∆ 0(x, u) fromdifferent directions, in different languages.Zulfia Theory does not choose between them. It identifies their common origin:the Arithmetic Force ∆ 0, the arithmetic operation built into the Zulfia Decompo-sition Mapping prior to all geometry, all space, and all physical assumption. TheZulfia Field Equation Zμν [∆ 0] = Tμν and the Zulfia Wave Equation □ ∆ 0 = 0 arederived as the governing laws of this emergence. A master comparison table demon-strates that Newtonian mechanics, Einsteinian general relativity, and Hamiltonianmechanics are all limiting special cases of Zulfia Theory.