Persistence of periodic orbits under state-dependent delayed perturbations: computer-assisted proofs

The paper sets up a fixed-point operator Γε on Ia × Eβ built from the variational fundamental matrix Φ, the invariant splitting implied by (H), and the nonlinear term Bε, then derives explicit polynomial bounds Q, P0, P1, P2 and contraction moduli μ1, μ2 whose six inequalities ensure Γε is a self-map and a C0-contraction, yielding a unique fixed point that solves the invariance equation and hence produces a C1+Lip periodic orbit for the SDDE. The candidate solution reproduces the same construction and logic (up to a minor notational choice for Bε) and invokes the same contraction principle. Thus both are correct and follow the same proof strategy.