Conservation of Rationality: How Finite Systems Represent an Irreducible World

Finite observers—biological, computational, or instrumental—must compress continuous, high‑dimensional reality into finite representational models. This compression inevitably produces a structural mismatch between model and world. I call this mismatch dimensional residue: the conserved remainder of unmodeled complexity that appears as noise, aliasing, prediction error, or anomalous patterns across scientific domains. The Conservation of Rationality is an epistemological principle describing how this residue behaves. Observation is treated not as passive recording but as an active representational transformation in which implicit complexity is forced into explicit structure. Drawing on work in algorithmic information theory, active inference, decoherence, renormalization, and holographic information preservation, the framework explains why representational mismatch is unavoidable and why its structure is conserved rather than eliminated. The paper outlines how dimensional residue manifests in quantum measurement, cosmology, cognition, and artificial intelligence, and proposes concrete tests for measuring residue in finite systems. A brief note on terminology reflects ongoing refinement as the framework develops. This work does not propose new physical laws; it clarifies the informational constraints that shape how finite observers model an irreducible world.