"The τ₀ Theorem: Unifying Newtonian Mechanics, Relativity, and Information Theory via Response Grammar"

This paper proposes and validates the τ₀ theorem—a universal response function (Ŝ = {τ̂}{τ̂_0 + τ̂}) constrained by thermodynamic limits, informational delays, and control-theoretic stability. By demonstrating the irreducible minimal response time τ₀, the theorem unifies Newtonian mechanics (instantaneous action at τ_0 → 0), Einsteinian relativity (speed-of-light limit with τ_0 = d/c), and Shannon information theory (bandwidth delay τ_0 = 1/B) as special cases of a single framework. Empirical evidence shows that systems ranging from enzyme kinetics (Michaelis-Menten equation), neural adaptation (divisive normalization), to behavioral discounting all obey τ₀ constraints. This discovery not only reformulates cross-disciplinary response models mathematically but also proves that energy, information, and control jointly dictate the universe’s response grammar.