Unifying Shannon Information Theory and Turing Computation Through Deterministic Representation

Shannon's information theory and Turing's theory of computation constitute the two foundational pillars of modern information and computation science. Shannon's framework characterizes information in probabilistic terms-uncertainty, entropy, and compression-while Turing's framework models computation as deterministic symbolic state evolution governed by fixed transition rules. Although deeply complementary, these theories are traditionally treated as conceptually separate, leaving implicit the mechanism by which probabilistic information can be reliably incorporated into deterministic computation. This paper introduces a high-level, non-operational framework that structurally unifies Shannon information theory and Turing computation through the concept of deterministic state representation. We formalize an axiomatic representational mapping that deterministically and reproducibly maps inputs into stable computational states, inducing equivalence classes and quotient-space semantics within which informational invariants and computational invariants can be jointly analyzed. Reproducibility and environmental invariance are treated as foundational axioms rather than implementation-dependent properties. The framework does not modify, subsume, or replace either Shannon's or Turing's theories, nor does it propose algorithms or system architectures. Instead, it clarifies a missing conceptual layer: the representational structure required for probabilistic information to support deterministic computation. By making this structure explicit, the paper provides a mathematically coherent lens through which information-theoretic and computation-theoretic descriptions can be understood within a single abstract model.