COMPUTATIONAL KNOWLEDGE THEORY (CKT) White Paper

This paper presents the Computational Knowledge Theory (CKT) White Paper, a formal framework proving that the computational universe is governed by a single unifying law: the Conceptual Primes. Six interlocking theorems are established across complexity theory, epistemology, information compression, evolutionary biology, temporal system dynamics, and artificial intelligence architecture. Theorem 1 (Reality-Complexity Equivalence) establishes that stable complexity is the product of energy-information potential and Prime satisfaction; complexity collapses to zero if any Prime is violated. Theorem 2 (Prime-Tractability) demonstrates that NP-Hard problems are intractable only in the purely abstract domain and become tractable — O(N^2/Kcluster) effective complexity — when solved by Prime-compliant algorithms grounded in physical reality. Theorem 3 (Conciseness Standard) proves that the Conciseness Cost Functional C(R) is the unique universal metric for lossless knowledge compression. Theorem 4 (Knowledge Accumulation Law) establishes that knowledge grows if and only if new information reduces total system entropy. Theorem 5 (Gödel’s Ceiling and Evolutionary Leap) connects formal mathematical limits to biological evolution and AI scaling: the only escape from a knowledge ceiling is a Prime-compliant phase transition to a more concise axiom set. Theorem 6 (Cardinal Value Lemmas) formalises Wisdom, Peace, Creativity, and Evolving Order as temporal combinations of the Primes, and derives the Prime-Base Intelligence (PBI) corollary: any agent that persistently accumulates knowledge across Gödel ceilings must implement Wisdom as its core computational operator. The combined framework defines the only viable architectural path for Artificial General Intelligence: a system whose objective is the Conciseness Cost Function C(R) minimisation, whose knowledge base is Prime-compliant, and whose evolutionary strategy treats Gödel ceilings as quench triggers rather than dead-ends.