Cognitive OS: Mathematical Model of Time and Semantic Reproducibility

Cognitive OS is the structural externalization of human cognition, formalized as an operating system rather than a theory. It defines information as Dynamic Sets, models meaning generation as Irreversible Mappings, and introduces Cognitive Time as the monotonic decrease of semantic entropy. This framework describes how meaning is born, compressed, dies, and is resurrected within a standalone cognitive architecture. The document establishes the mathematical and structural foundations of: the four cognitive layers (Base, Assumption, Concept, Expression) semantic entropy and the arrow of cognitive time the reproductive mapping that restores dead information the ontology of Otherness through Deep Sync the critical communication state termed Lossless Minimalism Although Cognitive OS can be applied to AI—revealing a fundamental divergence from generative models—it is not an AI theory. It is the origin specification of a self-externalized cognitive architecture, independent of existing academic categories or machine learning paradigms. This text stands as the original and standalone specification of Cognitive OS. Related works (Vol.1 and Vol.2) explore AI applications, but this document defines the core OS itself.