Fractional-Derivative Field Theory of Cognitive Memory: A Unified Mathematical Framework for Biological and Artificial Intelligence

I present a unified mathematical framework demonstrating that cognitive pro-cesses in both biological andartificial systems follow field equations with fractional-derivative memory dynamics. The theory reveals thatcognitive memory persistence can be modeled from fractional derivatives, showing creating hysteresis effects thatexplain belief stickiness, context-dependent recall, and catastrophic forgetting, and non-markovian machinehuman-analagous memory. I prove that causal information transmission requires departures from perfectsmooth-ness, detectable through Fubini consistency violations. The framework unifies disparatephenomena—from trauma persistence to transformer AI present a unified mathematical frameworkdemonstrating that cognitive processes in both biological and artificial systems follow field equations with fractionalderivativememory dynamics. The theory reveals that cognitive memory persistence emerges naturally from fractionalcalculus, creating hysteresis effects that explain belief stickiness, context-dependent recall, catastrophic forgetting,and non-Markovian memory dynamics shared between humans and machines. I prove that causal informationtransmission fundamentally requires departures from perfect smoothness, detectable through Fubini consistencyviolations and geometric singularities. The framework unifies previously disparate phenomena—from traumapersistence to transformer attention mechanisms—under a single Lagrangian formulation with empirical validationacross multiple AI architectures. This work establishes that cognition is not merely describable by physics butconstitutes a literal manifestation of field dynamics operating on information substrates, with immediateimplications for AI safety, cognitive modeling, and the mathematical foundations of intelligence itself attentionmechanisms—under a single Lagrangian formulation. This work establishes that cognition is not merelydescribable by physics but constitutes a literal manifestation of field dynamics on information substrates, withprofound implications for AI safety, cognitive modeling, and the mathematical foundations of intelligence. Prelimdata was corrupted, Rerunning tests now. Will add results in the coming weeks. #AI #Intelligence #IntelligentSystems#Cognition #Lior#Causality