This book reinterprets the Fermi–Pasta–Ulam–Tsingou paradox through the "Trojan framework," arguing that FPUT recurrence is not evidence against nonlinearity but evidence for organized nonlinearity. The central claim is that nonlinear coupling and nonlinear transport are distinct: in recurrent FPUT regimes, energy moves between modes but remains structurally confined near a coherent modal backbone, delaying thermalization. The book supports this with experimental optical recurrence data showing integrable-skeleton control, and with discrete q-breather analysis showing localized periodic orbits, resonant exits via relations like mΩ1=ΩkmΩ1=Ωk, and composite periodic orbits as stages of structural thickening. It concludes that FPUT recurrence is protected nonlinear coherence, while FPUT thermalization is resonant thickening of that coherence.