Frustration Certificates for Independently Calibrated Sensor Systems

Multi-sensor systems are calibrated pairwise, in sessions, at different times — and a calibration that drifts between sessions produces a fault that no pairwise monitor can see, because every sensor pair remains internally self-consistent. We prove a dichotomy that organizes when such faults are even detectable: if all pairwise relations are estimated from one joint sample, frustration of the signed relation graph is geometrically capped (a frustrated cycle of length L forces some edge confidence below cos(π/L), for any joint distribution), whereas independently calibrated relations admit unbounded frustration — so observed frustration above the cap is a distribution-free certificate that no single consistent calibration exists, and a leave-one-out filtration names the suspect sensor. On real fusion-diagnostic data from two machines of different confinement physics and data provenance — MAST magnetics and LHD bolometry — the certificate detects planted polarity drift at AUC 0.976–1.000 and localizes it at 0.93–1.00, under a single untuned pipeline, while the fault remains statistically invisible to pairwise inconsistency (0.218 faulted vs 0.223 null). A third, deliberately adversarial study characterizes the operating envelope and yields the method's preconditions: a shared latent and relation stationarity across sessions. We close with an honest composition-budgeting rule: a pre-registered test falsifies the product-form capacity rule we ourselves expected, and the operational law is two-regime, max(1.405σ√k, 0.6B/√n).