Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems

The paper defines the uncoupled 3-DoF Hamiltonian with oscillator terms (ωj/2)(qj^2 + pj^2), identifies the isoenergetic NHIM NE as a 3-sphere at q1 = p1 = 0, and shows that the transverse section Σ0.5 intersects Ws,u in a 3-sphere with p1 = √(7/32) (Eq. (2)); it computes the unidirectional flux via Stokes’ theorem as the 4D Liouville volume, obtaining 2π^2 E^2/(ω2 ω3) . The model reproduces the same geometric construction and Stokes argument (including a clear transversality check), but initially writes the oscillators with (ωj^2/2); it explicitly notes the paper’s convention and gives the same flux value under that convention. Hence, apart from a harmless normalization difference that the model itself flags, both are aligned .