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The strong interaction, i.e., quantum chromodynamics at the low energynuclear regime, is notoriously known to be challenging for predictive modeling.Here, we use the simplest possible nuclear effective field theory (EFT), andshow that in the case of the magnetic structure of nuclear systems with $A=2$and $A=3$ nucleons, it is highly precise as well as predictive. The theoreticalframework is the pionless EFT (\pilesseft), of point nucleons with contactinteractions, expanded consistently up to next-to-leading order (NLO) inperturbation theory, i.e., including only eleven low-energy parameters, andaugmented by a novel Bayesian analysis of theoretical uncertainties. The theoryaccurately predicts the shell structure reflected in the values of the magneticmoments and reactions of these nuclei within $\approx 1\%$ calculatedtheoretical uncertainty.  We show that this perfect prediction originates in implicit a-posterioriproperties of the calculation, particularly an unexpectedly small expansionparameter, as well as a vanishing contribution from the two-body isoscalarcurrent.

First-principles modelling of the magnetic structure of the lightest nuclear systems using effective field theory without pions