Reinterpreting Gravitational Potential Energy as an Internal Line-Integral Quantity in the 0-Sphere Model

[37 Application] This work presents a systematic reinterpretation of gravitational potential energy within the 0-Sphere model framework, addressing the conceptual circularity inherent in classical position-assigned potentials (pp. 1-2). While classical mechanics and general relativity successfully treat potential energy as an abstract scalar field Φ(𝑥) assigned to spatial coordinates, the 0-Sphere model shifts this ontological primacy to the internal degrees of freedom of matter (pp. 2, 4). Potential energy is described as an accumulated quantity (a line integral) along a particle's worldline, rather than a property of space itself (pp. 1, 4). Key Developments: Resolution of Tautology: The model replaces the circular definition of "higher position" with a measurable state of faster internal Zitterbewegung (ZB) oscillationand reduced synchronization with surroundings (pp. 2-3). Mechanism of Free Fall: Free fall is reinterpreted as an entropic synchronization process—a "thermal geodesic" where internal oscillatory energy is released as translational kinetic energy (pp. 5-6). Numerical Consistency: The framework predicts a gravitational redshift of internal oscillation frequencies (e.g., Δ𝜈≈2.64×10^9 Hz at GPS altitudes) that is numerically identical to standard general-relativistic results (pp. 4, 7). Parameter-Free Prediction: A characteristic internal oscillation velocity, 𝑣𝑍𝐵≈0.04047𝑐 is uniquely determined from the electron's anomalous magnetic moment through special-relativistic Lorentz contraction, without adjustable parameters (pp. 2, 7) This work provides a concrete microscopic foundation for the classical expression 𝐸=𝑚𝑔ℎ, suggesting that gravity is an emergent phenomenon arising from the collective phase dynamics of matter's internal structure (pp. 5, 7).