Pattana-Relational Dynamics (PRD) v1.4 : Full 24-Operator SU(5) Framework and Emergent Einstein Tensor with Simulation-Ready Appendix

This work presents the full 24-operator SU(5) formulation of Pattana-Relational Dynamics (PRD) and demonstrates how classical spacetime geometry can emerge from correlations of quantum relational operators.Within this framework, the 24 generators of the SU(5) Lie algebra represent the complete set of causal relational conditions (Paccaya). These operators act on a relational Hilbert space, and their quantum correlations dynamically generate an effective spacetime structure.A relational metric operator is defined using covariant derivatives of the SU(5) generators. Taking expectation values with respect to physical quantum states yields an emergent classical metric tensor. From this metric the full geometric structure of spacetime—Christoffel symbols, Riemann curvature tensor, Ricci tensor, and Ricci scalar—is derived using differential geometric methods.The relational curvature naturally leads to an Einstein-like tensor satisfying the contracted Bianchi identity. A variational principle based on an action functional yields relational field equations that reproduce the standard Einstein field equations in the macroscopic low-energy limit. A scale-dependent weighting function connects Planck-scale relational fluctuations with classical gravitational behavior.A major feature of this version is the inclusion of a simulation-ready appendix, providing explicit SU(5) generator matrices and complete Python implementations for symbolic and numerical computations. The provided code enables immediate computational exploration of relational metric generation, field evolution, and emergent spacetime dynamics.This framework offers a background-independent pathway toward quantum gravity, combining algebraic structure, geometric emergence, and computational simulation. The theory also provides potential testable implications for cosmology, black hole thermodynamics, and quantum gravitational dynamics.