“Unlike black-box methods, MCEMOL delivers dual value: interpretable transformation rules researchers can understand and trust, alongside high-quality molecular libraries for practical applications.”

“The analysis identifies an onset crossover mass $\tilde{m}^* \simeq 3.865$ for the emergence of secondary clusters and yields quantitative criteria for predicting both the crossover mass and the termination coupling strength at which they vanish.”

“The NPRG approach allows one, in principle, to take into account all nonlinearities present in the elastic theory, in contrast to the SCSA treatment which requires, already at the formal level, significant simplifications.”

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“Ce$^{3+}$ substitution at Sm$^{3+}$ sites transform the weak ferromagnetic (FM) $Γ_4$ state into robust AFM $Γ_1$ configuration through a gradual crossover.”

“The emergence of a well-defined inertial response depends sensitively on cone geometry. Blunt cones exhibit quadratic scaling with impact speed over the full range of velocities studied, whereas sharper cones display a delayed transition to inertial behavior at higher speeds.”