The Intervention-Coverage Barrier: Why Finite Functional Tests Cannot Certify Neural Replacement Fidelity

Abstract

Functional tests are indispensable for evaluating neural replacements, brain emulations, and other dynamical substitutes. A failed test can falsify fidelity at a declared interface, but success on a finite battery cannot by itself certify uniform fidelity over a continuous intervention domain.This paper formalizes an intervention-coverage barrier and separates three claims that are often compressed into the word "validation": finite-battery falsification, distributional validation under an explicit intervention law, and worst-case certification over a declared domain. It provides a constructive recurrent counterexample, a tight fill-distance audit under a sound global Lipschitz assumption, a dimensional lower bound, and the additional candidate-inclusive reachable-domain condition needed for recurrent transport.A frozen synthetic confirmation tested five parameterized recurrent packets. Across 368 trajectories and 3,632 tested state-input pairs, every candidate matched its source exactly on its finite battery but diverged by 0.12 to 0.20 at a reachable unseen intervention. Every sound one-step coverage audit rejected a 0.01 uniform certificate.This is a methods and theory preprint. It does not show that any specific neural replacement fails, that whole-brain emulation is impossible, or that consciousness, personal identity, survival, biological replaceability, or substrate independence is preserved or lost.