Universal Cognitive Field Theory: A Rigorous Axiomatic Foundation

AbstractI present a rigorous axiomatic foundation for the Universal CognitiveField Theory (UCFT), a framework designed to unify cognitiveprocesses under a field-theoretic formalism. Utilizing principles frommathematical physics, information geometry, and fractional calculus, Idefine cognitive spacetime, the cognitive field Ψ, and its evolution governedby a modular operator system. I demonstrate how UCFT generalizesexisting models of inference and cognition, providing a mathematicallyprecise language for phenomena such as belief evolution,decision collapse, and collective intelligence. This axiomatic system isdesigned to facilitate rigorous proofs of existence, uniqueness, conservationlaws, and topological invariants within the cognitive domain.Keywords: Universal Cognitive Field Theory (UCFT), Cognitive FieldCollapse, Belief Evolution, Fractional Calculus, Information Geometry, MathematicalPhysics, Stochastic Dynamics, Entropy, Axiomatic Systems.Author note: this is an early draft, if you find any errors, pleaselet me know. Thank you.