Small changes at single nodes can shift global network dynamics

The paper’s main empirical claims are consistent and well-supported by simulations: (i) very large sample-to-sample (STS) fluctuations in R near both coupling- and topology-induced transitions, including Δ ≈ 0.99 for Watts–Strogatz networks with N=501 and up to Δ ≈ 0.7 for distance-dependent networks, (ii) non-Gaussian sample distributions of R near onset (even all-to-all), (iii) a clear single-node sensitivity threshold with non-monotone δR(δω), and (iv) a peak of malleability at intermediate short/long-range balance κ . The candidate model’s “refutation” of Δ ≥ 0.99 relies on treating the Rayleigh mean for i.i.d. phases as a universal lower bound on time-averaged R; this is not a valid bound for deterministic unlocked trajectories, so it cannot preclude Δ values arbitrarily close to 1 under the paper’s definition of R as a time average over long simulations . Aside from this error, the model’s qualitative mechanisms (cut-set necessity, small-angle sufficiency, mixture-driven non-Gaussianity, κ-peak heuristic) align with the paper’s phenomenology.