Classification of composite numbers

This paper introduces a novel taxonomic framework that classifies composite numbers entirely by their total number of positive divisors, denoted by τ(n), organizing them into distinct structural factor classes rather than traditional magnitude-based categories. To systematically name high-order highly composite numbers, the author proposes the Digit Syllable System—a phonetic compression cipher that maps the digits 0 through 9 to unique, short syllables. By utilizing structured positional concatenation, index multiplier rules for repeating digits, and segmented mixing, any multi-digit divisor count is instantly converted into a brief, scannable, and standardized class name, effectively bridging pure arithmetic properties with an intuitive natural language nomenclature.