Dynamic scaling behavior in the presence of a periodic magnetic driving across Ising continuous transitions

What the math gives to ML

The paper identifies a nontrivial dynamic-scaling mechanism for a system driven periodically through a continuous transition: time enters through the phase \(\tau=t/P\), while forcing amplitude and period combine into the scaling variable \(\sigma=AP^{\kappa}\), with \(\kappa=y_h/z\). This predicts that responses at different amplitudes and periods should collapse when \(AP^{\kappa}\) is held fixed, rather than depending independently on amplitude and period. A transferable neural-network use is a dimensionless periodic optimizer schedule whose amplitude is scaled with its period, followed by direct trajectory-collapse and instability-boundary tests. The paper does not by itself guarantee better optimization, so this is a moderate-value, falsifiable scheduler mechanism rather than a drop-in theorem.