Unprovable Competence: When Output Stops Proving Understanding

AI-augmented knowledge workers produce high-quality output without the domain mastery such output once signaled, and are distrusted even when correct — often concealing their tool use rather than disclosing it. This paper argues that a dispersed literature — human-factors research, the responsibility-gap debate, the social epistemology of opaque AI, the philosophy of transparency, and the empirical study of AI at work — describes a single structure, and isolates the feature that makes the worker's legitimacy gap resist the remedy each side reaches for: the inference from output to competence has been severed by a process that is reliable but opaque, non-stationary, and characteristically prone to coherent failure — fluent, plausible error that survives the inspection delegation can afford — while the only warrant that could replace it, demonstrated error-detection, cannot be made legible without being expended. The result is what I call unprovable competence — competence that is real but cannot be shown to whoever must decide to rely on it — and the gap it opens is therefore structural rather than transitional. The analysis recasts the much-discussed "responsibility gap" as nearer its opposite (accountability intact but undischargeable), makes the "secret cyborg" a partly rational response to a real warrant deficit rather than merely a policy failure, and takes a definite side in the dispute over whether opaque AI poses "novel problems" for social epistemology — arguing that the structure is not new (proprietary trading and intelligence tradecraft have exhibited it for decades) but that its escape from those rarefied, institutionally-accommodated domains into ordinary knowledge work is.