Bentu Numeration System (BNS)

Bentu Numeration System (BNS) is a novel positional numeration framework in which every base N employs digits 0 through N — one more digit than standard positional notation. This single extension produces a coherent system with elegant arithmetic properties: a shifted carry threshold, natural divisibility rules readable by inspection, compact representation of powers, and full compatibility with standard base 10 arithmetic. Five foundational rules define the system, and five theorems — each with proof and computational verification — establish its key properties.