Pattana-Relational Dynamics (PRD) v1.7 : A Complete Unified Framework for Causal Artificial Intelligence and Emergent Spacetime

This work presents Pattana-Relational Dynamics (PRD), a unified theoretical and computational framework that connects fundamental physics and artificial intelligence through a common relational algebraic structure. The theory proposes that relations, rather than objects, constitute the fundamental structure of both physical reality and intelligent cognition.Within the PRD framework, the 24 universal causal conditions (Paccayas) are mapped onto the 24 generators of the SU(5) Lie algebra, forming a relational operator system that governs both physical dynamics and cognitive processes. These generators define a relational manifold in which causal interactions are represented as algebraic transformations acting within a relational Hilbert space.A central result of the framework is that spacetime geometry emerges from correlations among relational operators. By defining a relational metric constructed from covariant derivatives of SU(5) generators, the theory reproduces the geometric structures of general relativity, including curvature tensors and the Einstein tensor. In the macroscopic limit, the PRD action principle recovers the Einstein field equations, while predicting deviations in strong gravitational regimes.The theory produces testable predictions in black hole thermodynamics, including a relational correction to the Hawking temperature characterized by a constantα ≈ 1.274. This correction arises from structural integrations over relational operator weights on the event horizon and provides a potential observational signature for future gravitational wave and cosmological experiments.In addition to its physical implications, the same relational algebra provides a mathematical foundation for causal artificial intelligence. The Unified Relational Intelligence (URI) architecture implements neural systems that learn through causal operator discovery rather than statistical pattern matching. URI introduces relational neural networks, causal attention mechanisms, and physics-informed loss functions that enforce SU(5) commutation relations during training.To support reproducibility and practical experimentation, this publication includes an accompanying AI application package provided as a compressed ZIP archive. The package contains:A complete Python implementation of the SU(5) relational generator systemRelational neural network modules implementing causal operator dynamicsA relational attention mechanism extending transformer architectures with causal constraintsPhysics-informed training objectives enforcing Lie algebra commutation relationsA complete training pipeline for the Unified Relational Intelligence (URI) modelExample scripts and datasets for testing causal learning behaviorInstallation instructions and usage documentationThis software framework enables researchers to experimentally explore the PRD theory, simulate relational operator dynamics, and develop causal AI systems grounded in symmetry-constrained learning.By providing both a rigorous theoretical formulation and a working computational implementation, Pattana-Relational Dynamics establishes a unified platform for investigating emergent spacetime physics and causal machine intelligence within a single relational framework. The accompanying codebase allows direct replication of the results presented in this work and supports further development of relational AI architectures and quantum-relational simulations.