Post-Cybernetics B3: Information Density Explanation for the Differential Emergence of J-Space in Large Language Models

Abstract

Global Workspace Theory provides a central framework for explaining higherorder cognitive functions at the intersection of cognitive science and artificial intelligence. Recent experimental evidence indicates that structures functionally equivalent to a global workspace exist internally within large language models, designated as J-space; however, the intensity of their emergence exhibits significantvariation across different architectures. Building upon the two axiomatic foundations of constraint network theory—information conservation and computability—this paper establishes a rigorous definition of information density, proposes anexplicit compression substitution hypothesis to explain the continuous spectrum ofJ-space emergence intensity across different architectures, and proves the cognitiveeconomic optimality theorem: any information-processing system performing complex multi-hop reasoning under finite computational resource constraints, under thecombined influence of gradient descent dynamics and information loss constraints,must have its optimal structural configuration manifest as a privileged subspacewith a limited fraction and a connection-density gain greater than one. This paper further provides falsifiable conditions for this theoretical framework, offeringclear criteria for experimental verification, and rigorously delineates the boundarybetween the functional equivalence of J-space and the ontology of consciousness.