Current artificial intelligence systems operate at evolutionary Stage 2–3 of cognitive development — statistical pattern matching without principled knowledge selection, causal grounding, or structured accumulation. This problem is not incidental: recent formal proofs establish that hallucination in Large Language Models is mathematically inevitable under current architectural assumptions, arising from finite information capacity, computational undecidability, and reward hacking induced by Reinforcement Learning from Human Feedback (RLHF). Scaling does not resolve these failures — it amplifies them. This proposal presents Prime-Based Intelligence (PBI), a formal architectural framework grounded in the Computational Knowledge Theory (CKT), which establishes seven interlocking theorems proving that complexity, computational tractability, knowledge compression, accumulation, evolutionary phase transitions, cardinal intelligence dynamics, and the unsimulability of reality are all governed by a single law: the five Conceptual Primes (Order, Justice, Mercy, Knowledge, and Power). The foundational problem addressed is the Descriptive Degeneracy Problem: without a principled selection operator, any finite system admits an infinite set of mathematically valid representations, making hallucination and misalignment structurally unavoidable. PBI resolves this by implementing Wisdom — the simultaneous, lossless balance of all five Primes — as the core computational operator, satisfying the Prime-Base Intelligence Corollary (CKT Theorem 6, Corollary 6. 5). The methodology integrates three components: (1) the Prime-Compliant Standard (PCS), grounding training data and model components in verifiable, causally justified representations; (2) an Ethical Pragmatism criterion formalizing that ethical weight must dominate pragmatic weight, operationalized through the Justice Dominance Constraint (λL > λR, λL > λD) ; and (3) the PBI Cognitive Life Cycle — a five-stage pipeline anchored at its inference stage by Dynamic Inference and Epistemic Phase Transition (DIEPT): a novel complex-valued logic framework that formally separates verified knowledge on the real axis (A) from unresolved speculative context on the imaginary axis (iB), eliminating hallucination loops through controlled epistemic phase transitions measurable by phase angle θ = arctan (B/A). Knowledge accumulation health is continuously quantified via the Concise Accumulated Knowledge Index (CAKI), asymptotically bounded below 1. 0 for all finite systems by Theorem 7 (Unsimulability of Reality). The framework is immediately viable as the next practical step for current AI infrastructure. Its novel implementations — including Kolmogorov-Arnold Networks (KANs, ICLR 2025), MCE-Classes or Mathematically (Mass-Complexity-Entropy Clusters), the Quench-Cluster Algorithm (QCA), the Conciseness Cost Filter (CCF), and the Causation Wave Function (CWF) — extend and augment existing transformer, LoRA, and RAG deployments. Full implementation is projected within 36–48 months under a four-role interdisciplinary team.
MOHAMED NOURELDIN (Wed,) studied this question.