Classical sensing rests on one foundational assumption: the quantity of interest must be colocated with the measurement device. This is not an engineering convenience. It is the organizing principle of every instrumentation standard developed over the past century, and it fails completely at aviation altitude, where no physical sensor can survive long enough to monitor the cosmic radiation field that irradiates millions of aircrew annually. We establish that this barrier is resolved by a new sensing principle: when the sensor manifold and the target field manifold are physically disjoint, a learned operator bridging them \emph{is} the instrument. We term this \textbf{operator-theoretic virtual sensing} and instantiate it in \textbf{STONe}, which maps \textbf{twelve} ground-based neutron monitors (sparse, indirect, surface-bound) to the complete global dose field at 10{,}000\,m across \textbf{180-day} horizons, achieving sub-millisecond inference where Monte Carlo transport requires hours. Deployed without modification on an NVIDIA Jetson Orin Nano embedded AI platform at 7.3\,W average system power and 143.3\,MB GPU memory footprint; within the envelope of photovoltaic-powered field hardware co-locatable with existing neutron monitor stations, STONe constitutes a physically realizable sensing device of a new category: an instrument whose measurement principle is operator-theoretic and whose deployment constraint is the power budget of remote environmental monitoring infrastructure, not the accessibility of the target domain.