Processual General Relativity: Mathematical Foundation, Computational Validation, and Applications to Quasar Jet Physics with Comprehensive Falsifiability Framework

This preprint presents Processual General Relativity (PGR), a comprehensive theoretical framework extending Einstein's general relativity through processual density fields that govern spacetime dynamics and resolve mathematical singularities via finite-density Planck Objects. The work derives complete mathematical formalism including field equations, conservation laws, and dimensional consistency verification with classical limit recovery.Applied to quasar jet formation, PGR yields a nuclear acceleration mechanism predicting sub-relativistic velocities around 0.35c based on thermonuclear energy conversion efficiency. Monte Carlo analysis of 347 MOJAVE survey sources demonstrates superior statistical fit quality compared to standard ultra-relativistic models, with chi-squared per degree of freedom of 1.08 versus 3.45 for conventional approaches.The framework establishes explicit falsifiability criteria across multiple observational domains including atomic clock frequency variations, low-temperature nuclear decay measurements, cosmic microwave background modulation patterns, and gamma-ray emission signatures. This approach treats time as emergent from underlying process rates rather than absolute background parameter, providing solutions to fundamental problems in gravitational physics while maintaining scientific rigor and testability.