The Two Limits of Human Verification

Abstract

Human verification of large-volume content can fail in two distinct ways. A single judgment can become less informative, as the thing being checked grows harder to distinguish from what it imitates; and, independently, fewer judgments can be attempted at all, as volume outpaces a fixed capacity to pay attention, making verification less scalable. This note develops both failure modes as exact, provable consequences of a shared setup, and proves that they are formally independent: neither is a special case, a cause, or a remedy of the other. The informativeness result is derived first in terms of the total variation distance between two source distributions (Proposition 1), then restated in terms of Kullback–Leibler divergence, the quantity actually minimized whenever one distribution is trained to resemble another (Proposition 2); as that divergence shrinks, no test, however constructed, can do better than chance (Corollary 1). The scalability result shows, separately, that a fixed budget for confident judgment caps coverage at a fixed count regardless of how large the stream grows, so the fraction of items ever checked converges to zero (Proposition 3); a fourth result proves the two constraints are genuinely independent, each realizable at any value regardless of the other (Proposition 4). The motivating case throughout is distinguishing human from machine-generated text, where the theory's two failure modes have an exact reading: an accuracy ceiling that falls as language models improve, and a coverage limit that falls as content volume grows, together explaining why verification can erode on both fronts at once, and why fixing one front does nothing for the other.