Digit Strings

This paper develops a structural theory of digit strings in positional notation, introducing repunits, corepunits, replimits, and coreplimits as palindromic constructs whose dualities and product identities reveal profound symmetries in arithmetic. These digit structures show that powers of a base can be constructed directly from string patterns, offering new perspectives on computation and divisibility. Extending the study of digit strings, recurring decimals are reinterpreted as infinite series within the paradox class, a collection framework that accommodates simultaneous consistency and inconsistency, reframing foundational questions of rationality. The d‑index table further tabulates digital indices of digit products, exhibiting striking symmetries and invariants. Together, these contributions establish a unified perspective on digit strings, uncovering hidden structural laws in number theory.