NV-Diamond Thermometry Geometric Invariance Sensor Calibration
A geometric method’s invariance properties determine which sensor noise sources it can detect and which it is blind to. We establish this principle on simulated NV-diamond intracellular thermometry.
Geometric Invariance Predicts Sensor Blind Spots
Geometric invariance predicts sensor blind spots: a pre-registered comparison of 23 methods on simulated NV-diamond thermometry
Zenodo 10.5281/zenodo.21299293
Any method invariant to translations in feature space (Grassmannian geodesic, CKA, Berry phase, and others) will fail to detect device calibration variation, the dominant noise source in multi-sensor deployments, because per-device offsets are additive. A pre-registered experiment on simulated NV-diamond intracellular thermometry comparing 23 geometric methods and 7 scalar baselines across five decoherence axes (150,000 evaluations, 100 seeds, bootstrap CIs) confirms this without exception — every translation-invariant method achieves |ρ| < 0.15 on device variation, while every non-invariant method exceeds |ρ| > 0.5. The principle also explains a pre-registered refutation: Grassmannian geodesic distance, predicted to outperform bracket norms, instead underperforms (Δρ = −0.39 and −0.62, both |d| > 1.4). The resulting method–axis sensitivity map shows that 25 of 30 methods track the composite coherence axis at |ρ| > 0.8, but no single method covers all five axes.