This paper demonstrates that the equivalence principle—the local indistinguishability of acceleration and gravity—is not an independent postulate of general relativity but a rigorous theorem within the Planck Core Framework. I prove that both inertial mass and gravitational mass arise from the same underlying property of the entanglement network: the energetic response to changes in local entanglement deficit. Inertial mass corresponds to the energy required to displace a topological vortex defect through the network, breaking and reconnecting entanglement threads. Gravitational mass corresponds to the entropic force driving a system towards regions of higher entanglement deficit. The local entanglement deficit gradient experienced by an accelerating observer is proved to be mathematically identical to that experienced by an observer at rest in a gravitational field: ∇δacc=∇δgrav. The Unruh temperature emerges as the network's thermal response to the changing entanglement configuration under acceleration. The equivalence principle, long regarded as a mysterious starting point for general relativity, is thus derived from the information-theoretic foundations of the Planck Core Framework. The result is fully consistent with all experimental tests and makes the falsifiable prediction that no violation of the equivalence principle will ever be observed, for any composition of test bodies, at any accessible energy scale.
Wengang Yu (Sun,) studied this question.