The Evoluist Theorem: Formal Core

This paper develops the formal core of the Evoluist claim that no theory can become both unrestricted in scope and semantically determinate. It does not claim to prove the strongest universality thesis. Instead, it establishes a narrower result concerning terminal evaluative closure. The formal architecture considered in the paper contains a coding apparatus, a total valuation, a single transparent evaluator applying to the full language, and uniform formula constructions for exact semantic-status testing and conditional status construction. Under the corresponding conditions of diagonal self-application, these resources cannot all coexist within one status-evaluative architecture. The General Status-Diagonal Theorem formulates this obstruction for arbitrary spaces of semantic statuses, rather than only for classical truth and falsity. The Status Discrimination Lemma shows how a fixed-point-free status transformation can be generated from uniform exact-status discrimination and uniform conditional construction. Together, these results yield the Evoluist Terminal Status-Completeness Theorem. The paper then examines the limits of the theorem through four-valued semantics, semantic hierarchies, external truth oracles, higher-order metalanguages, fixed-point-safe semantics, and non-uniform evaluation. The result does not exclude external valuations, local or pointwise adequacy, relative evaluation, semantic hierarchy, or non-uniform correspondence. It excludes only their combination within one total, transparent, uniformly self-applicable, and terminal evaluator for the full language. The stronger Evoluist claim concerning unrestricted, pointwise adequate, semantically determinate, and terminally self-contained theoretical architectures remains an open conjecture.