Mathematical Optimization in the Genetic Code Architecture

Companion paper to the "Mathematical Coordinate System for Analyzing Genetic Code Organization Patterns" (Pfennigschmidt 2025). That paper proves only one organizational framework survives systematic constraint elimination. This paper asks: what architectural features does that uniqueness force? Starting from four axioms derived from molecular geometry and base-4 arithmetic, we show that the genetic code's entire organizational structure, coordinate system, binary family partitioning, diagonal architecture, and domain boundaries, follows from mathematics alone, without biological input. The addresses are fixed by quaternary constraints. Evolution assigned the meanings.