Unifying Gravity, Quantum Mechanics, and Energy via Planck-Normalized Identities

This paper introduces a unified, dimensionless identity that expresses mass, energy, frequency, stress-energy, and spacetime curvature in terms of normalized Planck ratios. By reformulating three foundational physical equations—E = mc², E = ℏf, and Einstein’s field equations—using square-root Planck unit definitions, the work reveals a deep structural coherence among relativistic, quantum, and gravitational domains. The resulting identity:<br>G_mu_nu / G_mu_nu(P) = T_mu_nu / T_P = E / E_P = f / f_P = m / m_P<br>demonstrates how physical law can be recast as a computable framework grounded in the constants ℏ, G, and c. The work introduces the <i>Parkinson Curvature Limit</i>, derived from voxel-based geometry and causal update saturation, offering a finite bound on spacetime curvature. This novel formulation eliminates field divergences in general relativity and provides a pathway toward a unified theory compatible with the Computed Universe (CU) model. The approach supports testable predictions for gravity, cosmology, and quantum structure by reframing physical interactions as scalable causal ratios within a discrete substrate.