A Topological and Information-Theoretic Framework for the Single-Interpreter Cognitive Architecture

Abstract A Topological and Information-Theoretic Framework for the Single-Interpreter Cognitive Architecture presents a deterministic mathematical model that rigorously bridges algebraic topology, non-linear dynamics, and neural thermodynamics to elucidate the emergence of a unified cognitive narrative. This framework postulates that peripheral sensory networks execute continuous manifold dimensionality reduction, effectively projecting high-entropy environmental data streams as discrete 0-simplices into a singular Global Neuronal Workspace. At the theoretical core of this architecture lies the "Single Interpreter," mathematically redefined herein as a dynamic absolute attractor embedded within the high-dimensional neural phase space. Driven by the fundamental physical imperative of Variational Free Energy minimization, this mechanism strategically leverages stochastic resonance to overcome thermodynamic energetic barriers. Consequently, it forces the mathematical collapse of 1-dimensional topological voids (quantified by the Betti number $\beta_1$). This critical phase transition physically instantiates a coherent, strictly causal narrative characterized by irreducible arity, thereby maximizing the integrated information metric ($\varphi_s$). Furthermore, the proposed framework explicitly derives the mechanical linkage between topological resolution and macroscopic neural ignition. By utilizing the Kramers escape rate to rigorously govern the effective coupling strength ($K_{eff}$), the system is demonstrably capable of breaching the Kuramoto critical threshold. This non-linear transition directly triggers a systemic, top-down cortical broadcast of the low-dimensional narrative payload. Finally, the model extends its theoretical apparatus to clinical neuroscience by providing a formal mathematical definition of psychopathology as topological limit cycles driven by system overfitting. It proposes the Perturbational Complexity Index (PCI) as a highly robust clinical proxy for empirically verifying the geometric irreducibility of the global workspace. Ultimately, this synthetic approach offers a strictly physical, empirically falsifiable blueprint for consciousness, highly applicable to both biological substrates and synthetic cognitive systems. Keywords Algebraic Topology & Manifold Reduction Variational Free Energy Minimization Global Neuronal Workspace Dynamics Integrated Information ($\varphi_s$) Kuramoto Synchronization Threshold