Three Laws of Regimetime: The Arithmetic Framework for a Theory of Everything Everywhere

AbstractContemporary physics is fragmented: Quantum Mechanics governs the small, GeneralRelativity governs the large, and no arithmetic bridge exists between them.This paper presents the Three Laws of Regimetime: a foundational arithmeticframework built on the Regimetime Field EquationˆR(x, u) = η(x, u) + ∆(x, u) + D(x, u) + S(x, u) (1)where η is Tendency, ∆ is Deviation, D is Dimensional layer, and S is Structural Coher-ence. From this equation emerges the Regime Parameterκ = ||∆||||η|| (2)which governs all physical phenomena across Spacetime [3] and Regimetime [1].We prove that three major theories are recovered as limiting cases of κ:1. General Relativity and E = mc2 are recovered in the limit κ → 0.2. Quantum Mechanics and probabilistic behavior emerge in the limit κ >> 1.3. Newton’s F = ma and classical dynamics arise in the Critical Regime κ ∼ 1.Thus, Newton [4], Einstein [3], and Bohr [5] are unified under a single arithmetic law.Regimetime provides the first arithmetic Theory of Everything Everywhere,unifying dynamics and existence from atoms to galaxies across all scales of κ.