Axiomatic Emergence F; The Physical Origin of Spacetime Geometry and Gravitational Dynamics

This paper systematically explores the emergence mechanism of spacetime geometry and its gravitational dynamics based on two fundamental principles—InformationConservation (conservation of von Neumann entropy in closed systems) and Computability of physical laws (any physical process can be simulated by a finite program in finite time). By introducing the scalar field of ”information potential difference” (Δ𝜇), which describes the complexity difference of local information statesrelative to a global reference state, and deriving its dynamical equations under theconstraints of covariance, conservation laws, and gauge invariance, the theory naturally incorporates the geometric structure of the Einstein field equations. Thisdemonstrates that gravity and spacetime curvature can emerge as macroscopic responses to information complexity. The key coupling constant 𝜅 in the theory is nota free parameter; its numerical value can be independently determined through themodulation effect of information fluctuations during early-universe inflation on theprimordial gravitational wave power spectrum, predicting a characteristic oscillatory signal with an amplitude of approximately 0.03 and a characteristic frequencyaround 10−3 Hz. This prediction provides a direct observational target for futurespace-based gravitational-wave detectors (such as LISA), thereby placing the proposition that ”geometry originates from information” within an observable physicalframework.