This paper presents a novel Gödelian completeness framework for deterministiccipher decoding. Applying recursive modular symmetry, prime-based symbolic encoding, and harmonic substitution, we show that the Zodiac Z13 cipher is derivable from a single axiom: the name Karl Werner. By assigning primes to letters based on their frequency rank, exponentiating by occurrence count, and mapping the result to a modular ring with parity rotation, we construct a complete, self-validating symbolic systemthat resolves the cipher with polynomial—not factorial—complexity