From Entropy Dynamics of Neuronal Coherence to Valenced Percepts: A Topos-Theoretic Construction

We develop a mathematical framework for neural computation in which percepts are modeled as probabilistic structures on directed acyclic graphs of subthreshold oscillatory (STO) activity, and affective valence is defined in terms of entropy dynamics on these structures. A central problem in the study of consciousness is how structured subjective experience, including both perceptual organization and affective tone, arises from distributed physical processes in the brain. Directed acyclic graphs (DAGs) representing time-stamped STO activity are assigned two pattern functors: a bound functor yielding Bayesian networks compatible with the causal organization, and an unbound functor yielding arbitrary vertex-wise distributions. These constructions form objects in a set-valued presheaf topos whose base category consists of DAGs with ancestral inclusions. Within this setting, the internal intuitionistic logic of the topos provides a formal language for describing perceptual and computational organization. We propose that affective valence induces a Grothendieck topology on this topos, regulating which locally defined probabilistic structures admit amalgamation. This yields a unified framework in which logical, probabilistic, and affective aspects of neural processing are integrated. We argue that this framework provides a principled account of how perceptual coherence and affective valence may jointly emerge from mesoscopic cortical field dynamics, offering a mathematically grounded approach to the relationship between physical processes and conscious experience.