Ben-Gen: A Symbolic Pattern Language for Structured Integer Representation

This preprint presents Ben-Gen, a symbolic pattern language for representing astronomically large integers with regular structural properties. The manuscript introduces the formal syntax, operators, axioms, and semantics of the system, along with illustrative examples, limitations, and potential applications.Ben-Gen is not intended as a general arithmetic system or data compression method, but as a structured symbolic framework motivated by educational, visualization, and procedural generation needs. This work is shared as an exploratory, non-peer-reviewed mathematical preprint.