Information Conservation Under Deterministic Computation A Canonical Invariance Theorem for Representation-Independent Information

This work provides a deterministic, representation-independent notion of information that remains invariant under all semantics-preserving computation. By introducing a canonicalization-based information measure, the framework eliminates dependence on representation choices, probabilistic assumptions, or stochastic modeling.

The approach assumes a total, idempotent operator that maps all semantically equivalent representations to a unique canonical form, without requiring that the operator be computable. Information content is defined as the length of this canonical representation and depends only on semantic content rather than syntactic form.

We prove an Information Conservation Theorem showing that any deterministic computation preserving semantic equivalence cannot change canonical information content. This result generalizes the intuition behind entropy conservation in classical information theory, while operating on equivalence classes of representations instead of probability distributions.

The framework further yields model-relative results for minimal description length, compression lower bounds, structural mutual information, and deterministic equivalence testing. All results follow from explicitly stated axioms and are mathematically valid without assuming computability of the canonicalization process.