Isostables for stochastic oscillators

The paper explicitly states d/dt E[Σ] = λ_Floq E[Σ] for the isostable eigenfunction Σ of the backward generator L† (its eq. (6)) and defines the effective field F by ∇Q*±·F = λ±Q*± and ∇Σ·F = λ_Floq Σ, noting uniqueness when the gradients are linearly independent (its eq. (7)); these match items A and B of the model’s solution. Item C follows immediately from ∇Σ·F = λ_Floq Σ along integral curves. For D, the paper asserts that Re[F] has a limit-cycle solution coinciding with Σ0 and demonstrates it in examples, while the model supplies standard regularity conditions (e.g., ∇Σ≠0 on Σ0, nonvanishing Re[F] on Σ0) to make the closed-orbit claim rigorous. Thus, both arguments agree in substance; the model adds routine technical conditions and a standard level-set/flow argument to formalize what the Letter states and illustrates numerically and analytically (see the general framework and eqs. (4)–(7), and the OU example) .