Alphabet Formation and the Epistemic Limits of Cryptographic Analysis

This work examines an epistemic boundary of cryptographic and statistical analysis that is usually taken for granted but rarely articulated explicitly: the presupposition of alphabet formation and stabilized symbolic identity.

Classical cryptography, information theory, and statistical signal analysis implicitly assume that an observer can identify repeated symbolic units in a ciphertext and treat them as instances of the same symbol. Frequency analysis, entropy estimation, n-gram models, and even Shannon-style definitions of secrecy rely on this assumption. In this paper, we analyze a boundary case in which this assumption fails.

The paper introduces and analyzes non-canonical encoding schemes in which each source symbol is mapped not to a single codeword but to a large set of equally admissible representations, selected independently at each occurrence. In such settings, symbolic identity at the ciphertext level does not stabilize, and a ciphertext alphabet does not emerge for an external observer. As a result, standard cryptographic and statistical tools do not merely become ineffective; they cease to be well-defined.

The central claim is epistemic rather than technical: the limitation arises not from insufficient complexity, randomness, or computational power, but from the absence of symbolic units required for interpretation. The observed signal remains indistinguishable from non-signifying physical variation, despite originating from a meaningful source sequence.

The paper does not propose a new cryptographic algorithm. Instead, it delineates a fundamental limit on what cryptographic analysis can presuppose, clarifying the distinction between secrecy within an established symbolic framework and a stronger boundary case described here as non-recognizability.

A companion proof-of-concept (POC), released separately ( https://doi.org/10.5281/zenodo.18140158 ), provides a simulation-based demonstration of the core claims by empirically illustrating the failure of alphabet stabilization under non-canonical encoding. The POC is intended as a practical illustration rather than a formal proof and complements the conceptual analysis presented here.