Cosmic Broth Equivalence Principle from Substrate Fixed-Point Dynamics

This work begins with a radical question: what if the equality between inertial mass and gravitational mass is not fundamental, but the outcome of a deeper dynamical balance? In classical physics, the equivalence between free fall and inertia is an experimentally verified fact. Yet we rarely ask why it must hold. In this paper, the idea is that inertia emerges from the interaction between matter and an underlying substrate — a kind of “cosmic broth” permeating space. If this is true, the equivalence between inertial and gravitational mass would not be a postulate, but the result of a natural dynamical equilibrium — a fixed point — reached at low energies. In other words: nature does not impose equivalence, it builds it. The paper shows that, under minimal assumptions and without violating General Relativity in regimes already tested, this dynamical structure naturally leads to universal inertial response. What we observe as “mass” becomes an emergent property stabilized by interaction with the substrate. The equivalence principle is therefore not a mystery to accept, but a consequence of deeper dynamics.