MATHEMATICALLY PROVED (Exact Symmetries)
Noether's Theorem & $SO(1,3)$ Group Action: Continuous space-time translation and Lorentz rotations strictly preserve the 4-momentum tensor $P^\mu = (E, \vec{p})$ such that invariant mass $m^2 = P_\mu P^\mu$ is strictly constant under coordinate boosts.
Equivariance Guarantee: In a Lorentz-equivariant neural network, shifting frame or rotating transverse coordinates guarantees $\phi(g \cdot x) = g \cdot \phi(x)$. No false resonant mass peak can be generated by uncalibrated coordinate transformations.
EMPIRICALLY CONJECTURED (AI Surrogates)
Unconstrained Generalization Bounds: Black-box deep networks claim to discover subtle non-linear correlations in jet substructure, but lack bounded generalization when calorimeter calibrations shift outside training distributions ($OOD$).
Hallucinated Resonances: An unconstrained network trained on background dijets exposed to a $+5\%$ drift regularly creates spurious "bumps" in invariant mass spectra, mimicking false new particle discoveries (5σ false alarms).