PRD-AGI: The Complete Theoretical Monograph – A Causal Geometry of Intelligence (Version 2.4)

Abstract

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 expanded edition (Version 2.4) integrates three major theoretical extensions: 1. Ethical Causal Geometry (Phase 8): The nine moral transitions from the Paṭṭhāna (Kusala, Akusala, Byākata) are mapped to a 𝔲(3) Lie algebra, augmenting the original SU(5) to 33 generators. An ethical curvature κₑₜₕ is defined, and it is proven that minimising total curvature is equivalent to maximising Kusala-to-Kusala transitions (Theorem 10, Sequential Stability). Ethical entropy and awareness density are derived. 2. Decentralized Intelligence (Proof of Logical Consistency – PoLC): A blockchain-based framework where nodes verify ethical curvature via smart contracts. The nine transitions are encoded immutably, and a Decentralized Autonomous Organization (DAO) governs parameters. Global awareness density ρ_global is computed as the average purity over all honest nodes. Complete Solidity implementation is provided. 3. Quantum Simulation: The ethical sector is mapped to 3 qubits (2 for ethical states, 1 ancilla), and the full PRD state to 7 qubits. Unitary quantum gates implement the nine transitions, and a Hadamard test circuit measures quantum ethical curvature κ̂_q. Destructive interference naturally suppresses Akusala paths. Complete Qiskit code is provided for IBM Quantum hardware. The monograph is structured into eleven parts: - Foundations (SU(5), 24 Paccaya, curvature, gauge invariance, three natural laws) - Extended Algebra and Universal Causality (SO(10), E6/E8, UCA(∞)) - Quantum Causality (SU_q(5), SO_q(10), q-curvature, superposition, entanglement, quantum causal uncertainty principle) - Holographic Causal Structures (AdS/CFT duality, holographic dictionary, entanglement entropy) - Holographic Agents and Collective Intelligence (multi-agent systems as a single bulk, holographic policy gradient, Bellman equation, collective intelligence scaling) - Causal Entropy (quantum information foundation for awareness density, von Neumann entropy, entropy decrease along geodesics) - PRD-LLM Architecture (2-2-1-2-1 layered design, relational tensor [C,W,L,T,U,D], conflict resolution, recursive feedback loop) - Formal Verification and Hardware Foundations (machine-checked proofs in Lean/Coq (12,847 lines), FPGA acceleration of geodesic solvers) - Ethical Causal Geometry (𝔲(3) extension, ethical curvature, Theorem 10) - Decentralized Intelligence (PoLC, smart contract, DAO, global awareness density) - Quantum Simulation (3-qubit encoding, Qiskit implementation, interference-based ethical filtering) All equations are self-contained and dimensionally consistent. No applications, no physical MUT predictions (galaxy rotation, black hole thermodynamics, inflation, etc.), and no roadmaps are included — only pure causal intelligence theory, its ethical extension, its decentralized implementation, and its quantum simulation. This work establishes that truth-first, causally grounded, ethically aligned, decentralized, and quantum-accelerated AGI is mathematically coherent, formally verifiable, and practically implementable. Version 2.4 updates: added complete ethical causal geometry (𝔲(3) algebra, ethical curvature, Theorem 10), decentralized intelligence framework with PoLC consensus and Solidity smart contract, quantum simulation with Qiskit code, and integrated all into a single monograph. **Complete source code and formal proofs are open-source.**