Value, Information, and the Cartesian Degeneracy

Value and information are categorically distinct mathematical domains. This paper establishes the precise categorical distinction between them, proves that no structure-preserving embedding can map value into information, and demonstrates that information processing is a strict special case of value management.We introduce the Cartesian Degeneracy: the condition under which the general structure of value collapses into the special case of information processing, parametrically occurring when the participant dimension reduces to the trivial unit object.Three consequences follow: (i) Cartesian systems are symmetric monoidal systems with strict additional structure imposed; (ii) symmetric monoidal systems subsume classical computation; and (iii) the coordination and consistency overhead endemic to value systems built on Cartesian foundations cannot be eliminated — it is mandated by the categorical mismatch.Companion paper to: Contextual Compute: The General Theory of Computation (Sarva Labs, March 2026).