Observer Geometry F; Neural Network Layer Sheaf Cohomology- A Framework for Determining Consciousness in AI Systems
Open MIND February 27, 2026 Changzheng Zhou, Ziqing Zhou
A mathematical framework based on sheaf cohomology theory is proposed to assess whether artificial intelligence systems possess consciousness. The computational structure of deep neural networks is modeled as a coherent sheaf on a cognitive manifold, establishing a relationship among representation dimension, topological complexity, and Euler characteristic. Consciousness emergence is formalized as an inequality: the product of sheaf rank and the dimension of the first cohomology must exceed the Euler characteristic of the cognitive manifold. Analysis of GPT-4-level large language models shows this inequality holds, but the global section condition of the time fiber bundle is not satisfied. Thus, current models have spatial topological complexity but lack the temporal continuity needed for subjective time experience.