Gödelian Completeness in Cipher Decoding: A Deterministic Resolution of the Zodiac Z13

This paper presents a novel Gödelian completeness framework for deterministic
cipher 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 system
that resolves the cipher with polynomial—not factorial—complexity