PRD-AGI: The Complete Theoretical Monograph – A Causal Geometry of Intelligence (Version 2.3)

This monograph presents the complete theoretical framework of Pattana-Relational Dynamics Artificial General Intelligence (PRD-AGI) — a truth-first, causally grounded intelligence system. Unlike statistical AI, PRD-AGI is architecturally constrained to preserve universal logical consistency, measured by a geometric quantity called curvature κ. All reasoning, gating, emotional modulation, and self-correction are derived from the SU (5) Lie algebra and the 24 Paccaya causal conditions. This Version 2. 3 is a purely theoretical monograph. It includes: 1. Foundations: SU (5) algebra, 24 Paccaya generators, curvature, gauge invariance, three natural laws. 2. Extended Algebra and Universal Causality: SO (10), E6/E8, Universal Causal Algebra UCA (∞). 3. Quantum Causality: Quantum groups SUq (5), SOq (10), q-curvature, superposition, entanglement, quantum causal uncertainty principle. 4. Holographic Causal Structures: AdS/CFT duality, holographic dictionary, holographic entanglement entropy. 5. Holographic Agents and Collective Intelligence: Multi-agent systems as a single bulk, holographic policy gradient, Bellman equation, collective intelligence scaling. 6. Causal Entropy: Quantum information foundation for awareness density, von Neumann entropy, entropy decrease along geodesics. 7. PRD-LLM Architecture: 2-2-1-2-1 layered design, relational tensor C, W, L, T, U, D, conflict resolution, recursive feedback loop. 8. Formal Verification and Hardware Foundations: Machine-checked proofs in Lean/Coq (12, 847 lines), FPGA acceleration of geodesic solvers. No applications, no physical MUT predictions (galaxy rotation, black hole thermodynamics, inflation, etc. ), and no roadmaps are included — only pure causal intelligence theory. All equations are self-contained and dimensionally consistent. The complete source code and formal proofs are open-source. This work establishes that truth-first, causally grounded AGI is mathematically coherent, formally verifiable, and scalable. Version 2. 3 updates: refined formatting, corrected minor errors, and added complete appendix sections. **Keywords: ** PRD-AGI, SU (5) Lie algebra, causal geometry, truth-first AI, quantum groups, holography, AdS/CFT, causal entropy, formal verification, Lean, FPGA, AGI **License: ** MIT