The Zodiac Z32 Cipher as a Formally Underdetermined Instruction System

This paper analyzes the Zodiac Killer’s Z32 cipher using a formal constraint and degrees-of-freedom framework. Rather than attempting a literal decoding, it defines solvability operationally and evaluates whether Z32 contains sufficient constraints to uniquely determine a physical location, geometric construction, or finite terminating procedure. Using a locked transcription and explicit symbol assumptions, the analysis demonstrates that the number of independent geometric and symbolic freedoms exceeds the constraints supplied by the cipher. The result is a rigorous negative finding: Z32 is underdetermined by construction and cannot uniquely encode a physical referent under reasonable assumptions. The paper reframes Z32 as a structurally non-closing technical artifact rather than a failed or unsolved cipher.