The Tautology of Mass: Why Inertial and Gravitational Mass Are Informationally Identical

Title: The Tautology of Mass: Why Inertial and Gravitational Mass Are Informationally Identical Description: The equivalence of inertial and gravitational mass, verified to one part in 10¹⁵ by the MICROSCOPE satellite, remains unexplained: general relativity assumes it as an axiom. This paper shows that within holographic-entropic frameworks the identity mᵢ ≡ mᵧ is not contingent but logically necessary—a tautology. The central argument is the Boundary Counting Principle: if physical information resides on a holographic boundary rather than in bulk spacetime, then any quantity measuring "how much stuff" a system contains must count the same thing—the number of boundary degrees of freedom the system engages. Inertial mass counts this. Gravitational mass counts this. They are the same count. From this principle we derive: (i) the speed of light as the maximum update rate of the boundary; (ii) mass as informational weight; (iii) E = mc² as an accounting identity. An explicit derivation via AdS/CFT demonstrates that both masses couple to the same boundary object: the modular Hamiltonian. The framework predicts testable deviations: systems with identical mass-energy but different entanglement structure should exhibit δ(mᵢ/mᵧ) ~ ε · (ℓ_eff/L_eff)² · ΔS_ent, accessible to next-generation equivalence-principle experiments. Core thesis: Within holographic frameworks, the equivalence principle is not a law of nature discovered by experiment. It is a theorem of information theory applied to holographic boundaries. This paper is part of an interconnected corpus exploring emergent gravity, entropic hysteresis, and the informational foundations of physics. Keywords: equivalence principle, holographic principle, inertial mass, gravitational mass, entropic gravity, AdS/CFT, modular Hamiltonian, information theory, emergent gravity