We derive the four structural properties of sub-limit dynamics — finite vocabulary, early saturation, interaction bottleneck, and efficiency paradox — from semantic first principles, without presupposing the axiomatic framework in which they were originally established. Starting from the observation that meaning requires real difference as its minimal necessary condition, we show that when active differences traverse a finite channel toward a non-identical receiver, the deposited forms are necessarily discrete, classifiable, and irreversibly consumed. From these conditions alone, we derive that the system necessarily exhibits finite vocabulary, early saturation, structural polysemy, and an efficiency paradox in which local precision accelerates global exhaustion. The derivation is independent of the three prior derivations — from positional arithmetic, constrained geometric trajectories, and AI agent behavior under irreversible constraint. The convergence of four independent paths on the same four specific properties constitutes evidence that sub-limit dynamics is not a theory applied to systems, but the necessary structure of any process in which meaning manifests under finite constraint. We propose Word Duel — a semantic game satisfying the three axioms of Constrained Generative Systems by construction — as an empirical laboratory for testing the framework's predictions in the semantic domain. We test the five predictions on a 90-run dataset across two LLM architectures (Sonnet 4.5, GPT-5.2); all five are confirmed with strong effect sizes, validating the structural isomorphism in the semantic domain. We specify formal falsification conditions under which the framework collapses.
davide lugli (Mon,) studied this question.