Physics-Guided Detection of Multiplicative Under-Registration in Smart Meter Time Series Under Smart-City Confounders

Smart-city advanced metering infrastructure enables utility-scale remote analytics, but some forms of under-registration closely resemble lawful changes in demand and are hard to model as anomalies. We study a narrow, physically motivated event family at the single-meter level, namely multiplicative under-registration with unknown onset (a shunt-like attack), in which recorded active energy is approximately scaled by a factor $\alpha <1$ after a change-point while the daily-profile structure and spectral shape remain invariant. We formalize the problem and develop a physics-guided detector family based on weighted daily-profile regression (GLS) and its robust variant (RGLS), with quality-control filters, spectral-consistency checks, and an optional reactive-channel gate, designed to stay selective under confounders such as rooftop photovoltaics, electric-vehicle charging, and heat-pump onsets. On a device-disjoint Low Carbon London benchmark (487 households) the preferred GLS detector attains precision $0.915$, recall $0.978$, and $F_1=0.945$ at $\alpha =0.10$ while keeping the non-theft suspected rate near $1\%$; a cross-dataset check on Open Power System Data with real EV/PV/heat-pump overlays yields zero false alarms on all 72 cases, and Mendeley and WPuQ benchmarks add a second large family and a reactive-channel test. We compare against external baselines (classical change-point detection, Isolation Forest, autoencoder, LSTM, gradient boosting, and a supervised statistical pipeline) on the same protocol: generic anomaly detectors fail on this shape-preserving attack, and supervised models match the detector only in-distribution while, unlike it, failing to transfer to real lawful confounders. All metrics carry bootstrap confidence intervals, and a full reproducibility bundle accompanies the submission.