A first step towards automated conjecture-making in higher arithmetic geometry

We present a framework for encoding information about objects from higher arithmetic geometry. This framework is built around a new kind of data type called a Tannakian symbol. The arithmetic objects we have in mind include modular forms (and more general automorphic representations), elliptic curves (and more general schemes, motives and algebraic stacks), finite graphs, group representations, and multiplicative functions (like the Euler totient function). The language of Tannakian symbols not only allows for representations of individual objects, but also representations of classes of objects, relations between objects, and various important unary and binary operations on objects. The development of this framework is the first small step in a long-term project aiming to apply machine-learning algorithms to some problems of current interest in modern arithmetic geometry.